The equation of the plane is -x(tan(r/4)) + z(sin(r/4)) = 1.
Let the equation of the plane be Ax + By + Cz = D. Since the plane contains the y-axis, we know that x = 0 when y = 0. Therefore, the equation becomes:
0A + 0B + Cz = D
=> Cz = D
This means that the plane is perpendicular to the y-axis and intersects the z-axis at z = D/C.
Now, we need to find the values of A, B, and C. Since the plane makes an angle of r/4 with the positive x-axis, we can use the direction cosines to find these values. The direction cosines of a vector are the cosines of the angles it makes with the x, y, and z axes.
Let the direction cosines of the vector perpendicular to the plane be (l, m, n). Then, we have:
cos(r/4) = l/√(l^2 + m^2 + n^2)
=> l = cos(r/4) / √2
cos(π/2) = m/√(l^2 + m^2 + n^2)
=> m = 0
cos(π/2) = n/√(l^2 + m^2 + n^2)
=> n = sin(r/4) / √2
Therefore, the vector perpendicular to the plane is:
(l, m, n) = (cos(r/4) / √2, 0, sin(r/4) / √2)
Since the plane contains the y-axis, we know that it is perpendicular to the vector (0, 1, 0). Therefore, the dot product of the two vectors is zero:
0A + B + 0C = 0
=> B = 0
Finally, we can use the fact that the vector (A, B, C) is perpendicular to the vector (cos(r/4) / √2, 0, sin(r/4) / √2) to find A and C:
A(cos(r/4) / √2) + 0 + C(sin(r/4) / √2) = 0
=> A = -C(tan(r/4) / √2)
Therefore, the equation of the plane is:
-C(tan(r/4) / √2)x + 0y + C(sin(r/4) / √2)z = D
Multiplying through by √2/C and setting D = √2, we get:
-x(tan(r/4)) + z(sin(r/4)) = 1
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The opposite of z is greater than 5 what are two possible options for z
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
Given that the opposite of z is greater than 5, we can write this as an inequality:
-z > 5
To find the possible options for z, we can follow these steps:
Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:
z < -5
Step 2: Choose two values for z that satisfy the inequality z < -5.
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
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A trader made profit of 24percent by selling an article for GHC 3720.00.How much should he have sold it to make a profit of 48percent?
Therefore, the trader should sell the article for GHC 4440.00 to make a profit of 48%.
What is percent?Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.
Here,
Let's call the original cost of the article "C".
We know that the trader made a profit of 24%, which means that he sold the article for 100% + 24% = 124% of its cost:
124% of C = GHC 3720.00
To find C, we can divide both sides by 1.24:
C = GHC 3720.00 / 1.24
C = GHC 3000.00
So the trader originally purchased the article for GHC 3000.00.
Now we want to know how much the trader should sell the article for to make a profit of 48%. This means that he wants to sell the article for 100% + 48% = 148% of its cost:
148% of C = ?
Substituting C = GHC 3000.00, we get:
148% of GHC 3000.00 = (148/100) x GHC 3000.00
= GHC 4440.00
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During the holiday season Andrew has to help his mother wrap the candy that she makes. The number of pieces that she can wrap (y) can be described as
y = 73. Andrew takes a lot more breaks to eat pieces of the candy, so he wraps at a rate of y = 3x + 8.
At how many minutes (s) have Andrew and his mother wrapped the same number of candy pieces?
2 minutes
O 3 minutes
0 4 minutes
t
8 minutes
Andrew and his mother will have wrapped the same number of candy pieces in 21.6 minutes.
We need to find out how many minutes (s) Andrew and his mother wrapped the same number of candy pieces.
Given data:
The number of pieces that Andrew’s mother can wrap is y = 73.
Andrew wraps at a rate of y = 3x + 8.
To find the number of minutes (s) at which Andrew and his mother have wrapped the same number of candy pieces, we need to equate both equations and then find the value of x the equation is given as,
73 = 3x + 8
65 = 3x
x = 21.6
Therefore, Andrew and his mother will have wrapped the same number of candy pieces after 21.6 minutes.
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A teacher tells her students she is just over 1 and 1/2 billion seconds old.
a. Write her age in seconds using scientific notation (using for multiplication and for your exponent).
b. What is a more reasonable unit of measurement for this situation?
c. How old is she when you use a more reasonable unit of measurement?
a. The teacher's age in seconds can be written in scientific notation as 1.5 × [tex]10^{9}[/tex] seconds.
b. A more reasonable unit of measurement for this situation could be years, as it is a common unit used to express human age.
c. To convert the teacher's age from seconds to years, we can divide the number of seconds by the number of seconds in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and approximately 365 days in a year. So,
1.5 × [tex]10^{9}[/tex] seconds ÷ (60 seconds/minute × 60 minutes/hour × 24 hours/day × 365 days/year) = approximately 47.5 years
Therefore, the teacher is approximately 47.5 years old when using the more reasonable unit of measurement.
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An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function =Cx+−0.5x2180x25,609. How many engines must be made to minimize the unit cost?
Do not round your answer.
The number of engines that must be made to minimize the unit cost are 180
How many engines must be made to minimize the unit cost?From the question, we have the following parameters that can be used in our computation:
C(x) = −0.5x² + 180x + 25,609.
Differentiate the above equation
So, we have the following representation
C'(x) = -x + 180
Set the equation to 0
So, we have the following representation
-x + 180 = 0
This gives
x = 180
Substitute x = 180 in the above equation, so, we have the following representation
C(180) = −0.5(180)² + 180(180) + 25,609
Evaluate
C(180) = 41809
Hence, the engines that must be made to minimize the unit cost are 180
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4. You decide to purchase a home for $225,000. The bank requires a 10% down payment.
You take out a 30-year, fixed rate mortgage at 4. 5%.
a. How much is the down payment?
b. How much is the mortgage (In other words, how much money are you
borrowing?)
c. What is your monthly mortgage payment?
a. The down payment is $22,500.
b. The mortgage is $202,500.
c. The monthly mortgage payment is $1,027.
a. The down payment is 10% of the home price, which is $225,000 x 0.1 = $22,500.
b. The mortgage is the remaining amount that you need to pay, which is $225,000 - $22,500 = $202,500.
c. The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:
Monthly Payment = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where P is the principal amount (the mortgage), i is the monthly interest rate (4.5% / 12 = 0.375%), and n is the total number of monthly payments (30 years x 12 months/year = 360).
Plugging in the values, we get:
Monthly Payment = $202,500 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1] = $1,027.
Therefore, your monthly mortgage payment will be $1,027.
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A croissant, a cup of coffee, and a fruit bowl from Kelley's Coffee Cart cost a total of $5. 25. Kelley posts a notice announcing that, effective next week, the price of a croissant will go up 15% and the price of coffee will go up 40%. After the increase, the total price of the purchase will be and a fruit bowl will cost 3 times as much as a croissant. Find the cost of each item before the increase
The cost of a croissant before the increase was $0.75, the cost of a cup of coffee was $0.75, and the cost of a fruit bowl was $2.25.
Let's start by assigning variables to the cost of each item before the price increase. Let x be the cost of a croissant, y be the cost of a cup of coffee, and z be the cost of a fruit bowl.
From the problem statement, we know that:
x + y + z = 5.25 (total cost before price increase)
z = 3x (fruit bowl costs 3 times as much as a croissant)
Substituting z = 3x into the first equation, we get:
x + y + 3x = 5.25
4x + y = 5.25
Now we need to solve for x and y. We don't have an equation directly relating the price increase to the new prices, but we can use the percentage increase to write:
New croissant price = x + 0.15x = 1.15x
New coffee price = y + 0.4y = 1.4y
The new total cost will be:
1.15x + 1.4y + z
Substituting z = 3x, we get:
1.15x + 1.4y + 3x
Simplifying this expression and using the equation 4x + y = 5.25 to eliminate y, we get:
1.15x + 1.4y + 3x = 4.15x + 1.4(5.25 - 4x)
4.15x + 1.4(4x - 5.25) = 4.55x - 5.85
Therefore, the new total cost will be $4.55x - $5.85. To find the cost of each item before the increase, we can solve the system of equations:
4x + y = 5.25
z = 3x
Substituting z = 3x into the first equation, we get:
4x + y + 3x = 5.25
7x + y = 5.25
Solving for y in terms of x, we get:
y = 5.25 - 7x
Substituting this expression into the equation for the new total cost, we get:
4.55x - 5.85 = 1.15x + 1.4(5.25 - 4x) + 3x
Simplifying and solving for x, we get:
x = 0.75
Substituting this value of x into the equation for y, we get:
y = 5.25 - 7(0.75) = 0.75
Substituting x and z = 3x into the equation for the total cost before the increase, we get:
0.75 + 0.75 + 3(0.75) = 3.75
Therefore, the cost of a croissant before the increase was $0.75, the cost of a cup of coffee was $0.75, and the cost of a fruit bowl was $2.25.
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Convert 7 gallons an hour to cups per minute.
When 7 gallons an hour is converted to cups per minute it would be = 1.9 cups /min.
How to convert gallons per hour to cups per minute?To convert gallons per hour to cups per minute the following is carried out.
The constitution of a gallon when measured in cups = 16 cups.
Therefore if 1 gallon = 16 cups
7 gallons = X cups
Make X the subject of formula;
X = 16×7
= 112 cups
This means that , 112 cups = 1 hour(60 mins)
y cups = 1 min
make y the subject of formula;
y = 112/60
= 1.9 cups /min
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|x-6|=-10
thanks in advance
Answer:
I guess you need the value of (x) if that's so then
x= -4
Step-by-step explanation:
Fei Yen dog eats 8 ounces of dog food each day. Fei Yen bought a 28 pound of dog food. How many 8 ounces servings are in a 28 pound bag of dog food?
There are 56 servings in a 28 pound bag of dog food.
We have the information from the question is:
Fei Yen dog eats 8 ounces of dog food each day.
Fei Yen bought a 28 pound of dog food.
To find the how many 8 ounces servings are in a 28 pound bag of dog food?
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
Now, Firstly convert the pounds into ounces.
We know that:
1 pound = 16 ounces
Then, 28 pounds = 28 × 16 = 448 ounces
The number of 8 ounces servings are in a 28 pound bag of dog food:
=> [tex]\frac{448}{8} =56[/tex]
Hence, there are 56 servings in a 28 pound bag of dog food.
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What is -3x - 2x -5 = -7
Step-by-step explanation:
-3x - 2x - 5 = -7
-5x - 5 = -7
-5x = -7 + 5
-5x = -2
x = 2/5
#CMIIW3 1 point Usually the professors give you a function and they ask you to compute the linear approximation at a given point (a, f(a)). In this particular case, I will give you already the linear approximation at 2 = 3. 5 L(x) = 121 (1 - 3) + 172. What is the value of f(3) Type your answer Previous 1 point Usually the professors give you a function and they ask you to compute the linear approximation at a given point (a, f(a)). In this particular case, I will give you already the linear approximation at I = 5, L42) = (2-6) + 23 5 4 Relate appropriately 2- 1 (9) aproximately 25.5 28 f(5)- 1.25 23 (5) 5 17) - 7 ) is approximately
The value of f(3) is 172.
The problem provides us with the linear approximation of a function at a given point. In this case, we are given the linear approximation at x=3.5 as L(x) = 121(x-3) + 172. We are asked to find the value of the original function f(3). Since 3 is to the left of the given point 3.5, we need to use the left-hand side of the linear approximation.
To find the value of f(3), we substitute x=3 in the linear approximation:
L(3) = 121(3-3.5) + 172
= 121(-0.5) + 172
= -60.5 + 172
= 111.5
Therefore, the value of f(3) is 172.
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Calculate the value of X, C is the center of the circle.
Answer:
38
Step-by-step explanation:
Formula
Inscribed angle = Central angle/2
Here
Inscribed angle = x
Central angle = 76
x = 76/2
x = 38
If pp and qq vary inversely and pp is 19 when qq is 30, determine qq when pp is equal to 95
When the value of pp=95 the value of qq will be equal to 6.
It is given that pp varies inversely with qq, so we can write that
pp=k/qq
where k is the proportionality constant.
here we can find the value of k by substituting the value of pp and qq with 19 and 30 in the relation that is given above, we get:
30=k/19
k=30*19
k=570
we the value of k to be 570 after putting the values in the relation.
Now if pp is changed to 95, and k is equal to 570 we can get the value of qq by putting the known values in the same relation.
pp=k/qq
qq=570/95
qq=6.
Therefore, when the value of pp is 95 the value for qq will be equal to 6.
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A bucket held 24 gallons of water. Water leaked out of a hole in the bucket at a rate of 3 gallons every 4 days. At this rate, how many days did it take for all 24 gallons to leak out?
It will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
If water is leaking out of a bucket at a rate of 3 gallons every 4 days, then the rate of leakage is 3/4 gallons per day.
Let x be the number of days it takes for all 24 gallons to leak out. To explain this situation, we can construct an equation.
24=3/4*x
To solve for x, we can cross-multiply.
24*4=3x
3x=96
x=96/3
x = 32
Therefore, it will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
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Find the volume of a pyramid with a square base, where the side length of the base is 16. 6 m and the height of the pyramid is 9. 1 m. Round your answer to the nearest tenth of a cubic meter
The volume of the pyramid with a square base of side length 16.6 meters and a height of 9.1 meters is approximately 836.6 cubic meters.
To find the volume of a pyramid with a square base, you'll need to know the side length of the base and the height of the pyramid. In this case, the side length of the square base is 16.6 meters, and the height of the pyramid is 9.1 meters. Here's a step-by-step explanation to calculate the volume:
1. Find the area of the square base: Since the base is a square, you'll need to multiply the side length by itself.
Area = side_length × side_length
Area = 16.6 m × 16.6 m
Area ≈ 275.56 m²
2. Calculate the volume of the pyramid: To find the volume, you'll multiply the area of the base by the height of the pyramid and divide the result by 3.
Volume = (Area × Height) / 3
Volume ≈ (275.56 m² × 9.1 m) / 3
Volume ≈ 836.626 m³
3. Round the answer to the nearest tenth of a cubic meter:
Volume ≈ 836.6 m³
So, the volume of the pyramid with a square base of side length 16.6 meters and a height of 9.1 meters is approximately 836.6 cubic meters.
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Find the value of x. round to the nearest degree.
14
5
x =
degrees
anybody knows the answer to this ?
x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
General process of solving for an unknown angle.
1. Determine the type of angle: Determine whether the angle is a right angle (90 degrees), acute (less than 90 degrees), or obtuse (greater than 90 degrees).
2. Use geometric properties: If there are geometric properties or relationships given in the problem, such as angles formed by parallel lines or within a triangle, apply those properties to find the value of x.
3. Apply trigonometric functions: If the problem involves trigonometry, use sine, cosine, or tangent functions along with the given information to solve for x.
4. Apply algebraic equations: If there is an algebraic equation involving x, set up the equation and solve for x by isolating it on one side of the equation.
To find the value of x in the given triangle, we can use the inverse tangent function, which is tan^-1.
tan(x) = opposite/adjacent
tan(x) = 5/14
To isolate x, we take the inverse tangent of both sides:
x = tan^-1(5/14)
Using a calculator, we can find that x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
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There are 46 giraffes in the San Antonio Zoo. The population increases at a rate of 8%
each year. The function y = 46(1. 08)* can be used to determine y, the number of giraffes
at the zoo after x years. What is the domain and range that represents this situation?
A Domain: All real numbers less than or equal to 46
Range: All real numbers
B Domain: All real numbers greater than or equal to 0
Range: All real numbers greater than or equal to 46
C Domain: All real numbers greater than or equal to 1. 08
Range: All real numbers greater than 0
D Domain: All real numbers
Range: All real numbers greater than or equal to 0
The domain and range that represents this situation is: B Domain All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.
In the given situation, the number of giraffes in the San Antonio Zoo is represented by the function y = 46(1.08)ˣ To determine the domain and range that represent this situation, we must consider the context and the variables involved.
The domain represents the possible values of x, which corresponds to the number of years. Since time cannot be negative in this context, the domain includes all real numbers greater than or equal to 0.
The range represents the possible values of y, which corresponds to the number of giraffes. The initial number of giraffes is 46, and the population is increasing each year. Therefore, the range includes all real numbers greater than or equal to 46.
Based on this information, the correct answer is B: Domain: All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.
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Complete question:
There are 46 giraffes in the San Antonio Zoo. The population increases at a rate of 8% each year. The function y = 46(1.08)* can be used to determine y, the number of giraffes
at the zoo after x years. What is the domain and range that represents this situation?
A Domain: All real numbers less than or equal to 46
Range: All real numbers
B Domain: All real numbers greater than or equal to 0
Range: All real numbers greater than or equal to 46
C Domain: All real numbers greater than or equal to 1.08
Range: All real numbers greater than 0
D Domain: All real numbers
Range: All real numbers greater than or equal to 0
Consider functions f and g. What is the approximate solution to the equation after three iterations of successive approximations? Use the graph as a starting point. 3x^2 - 6x - 4 = 2/x+3 +1
The required values on the graph, the solution is approximate x = -0.33.
How to solve the equationWe can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
The area of a rectangle is 72.8cm? if one side of the length is 6.52cm. find the length of the other two to two decimal places
Answer:
11.17, my answer needs to be 20+ characters soooooooo
Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. f(x) = ** + 5x 10x-60 (Use decimal notation)
The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.
To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:
f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²
Simplifying, we get:
f'(x) = 50 / (10x - 60)²
The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:
50 / (10x - 60)² = 0
This occurs when x = 6 and x = -6/5.
Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:
For x < -6/5, we choose x = -2:
f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0
Therefore, the function is decreasing on (-∞, -6/5).
For -6/5 < x < 6, we choose x = 0:
f'(0) = 50 / (10(0) - 60)² = 5/9 > 0
Therefore, the function is increasing on (-6/5, 6).
For x > 6, we choose x = 10:
f'(10) = 50 / (10(10) - 60)² = 5/81 > 0
Therefore, the function is increasing on (6, ∞).
Finally, we can use the First Derivative Test to determine the nature of the critical points.
For x = -6/5:
f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.
Therefore, x = -6/5 is a local maximum.
For x = 6:
f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.
Therefore, x = 6 is a local minimum.
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Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. sin lim 5 X400 :) X lim 5 X00 64--m-0 - sin)=(Type an exact answer)
Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:
The evaluated limit using l'Hôpital's Rule is 5.
Given limit,
lim (x -> 0) (sin(5x) / x)
Since both the numerator and denominator approach 0 as x approaches 0,
we can apply l'Hôpital's Rule.
Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1
Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)
Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.
Therefore, the limit is: 5*1 = 5
So, the evaluated limit using l'Hôpital's Rule is 5
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Use the Lagrange Error Bound to give a bound on the error, E₄, when eˣ is ap- proximated by its fourth-degree (n = 4) Taylor polynomial about 0 for 0 ≤ x ≤ 0.9.
The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.
How to find the Lagrange error bound for the fourth-degree Taylor polynomial?To find the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0, we need to find the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].
Since the nth derivative of [tex]e^x[/tex] is [tex]e^x[/tex] for all n, the fifth derivative is also [tex]e^x[/tex]. To find the maximum value of[tex]e^x[/tex]on the interval [0, 0.9].
We evaluate [tex]e^x[/tex] at the endpoints and at the critical point x = 0.45, which is the midpoint of the interval:
[tex]e^0[/tex] = 1
[tex]e^0.9[/tex]≈ 2.4596
[tex]e^0.45[/tex] ≈ 1.5684
The maximum value of [tex]e^x[/tex] on the interval [0, 0.9] is approximately 2.4596.
The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 is given by:
E₄(x) ≤ (M/5!)[tex]|x-0|^5[/tex]
where M is the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].
So, we have:
E₄(x) ≤ (2.4596/5!) [tex]|x|^5[/tex] for 0 ≤ x ≤ 0.9
Substituting x = 0.9 into this inequality, we get:
E₄(0.9) ≤ (2.4596/5!)[tex](0.9)^5[/tex] ≈ 0.000129
Therefore, the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.
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If Nori made 2% in interest on $5,000 and her brother Sean made 1% in interest
on $10,000, who made more money in interest?
Both Nori and her brother Sean made the same amount in interest, $100, assuming that their investments lasted 1 year.
What is interest?The interest refers to the income or payment received or made for giving or taking credit from a lender.
The interest is usually depicted using a rate, which is expressed over 100.
Nori's Investment = $5,000
Interest rate = 2%
Interest amount = $100 ($5,000 x 2%)
Sean's investment = $10,000
Interest rate = 1%
Interest amount = $100 ($10,000 x 1%)
Thus, Nori and Sean equally made $100 in interest from their investments.
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Aaliyah goes on a 5 mile run each Saturday. Her run typically takes her 45 minutes. She wants to increase the distance to 7 miles. Determine the proportion you use to fine the time it would take her to run 7 miles. Solve the proportion. What proportion can be used to determine the time it takes for her to run a marathon, which is approximately 26 miles? What is her time?
what the answear to y=4x-9
The ordered pairs of the linear expression y = 4x - 9 is (0, -9)
What are the ordered pairs of the linear expressionFrom the question, we have the following parameters that can be used in our computation:
The linear expression y = 4x - 9
To determine the ordered pairs of the linear expression, we set x to any value say x = 0 and then calculate the value of y
Using the above as a guide, we have the following:
y = 4(0) - 9
Evauate
y = -9
Divide both sides by 1
y = -9
This means that the value of y is equal to -9
So, we have (0, -9)
Hence, the ordered pairs of the linear expression is (0, -9)
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6. ifmxkl=(8x - 6)° and the measure of major arc jml = (25x - 13), solve for the actual
measure of major arc jml. assume that lines which appear tangent are tangent.
k
ј,
l
m
a. 196°
b. 287°
c. 262°
d. 154°
The actual measure of major arc JML is approximately 289.33°, which is closest to 287°.
We know that minor arc KL is supplementary to major arc JML. So,
m∠KL = 180° - m∠JML
Substituting the given values, we get:
8x - 6 = 180 - (25x - 13)
Solving for x, we get:
33x = 193
x = 193/33
Substituting this value of x in the expression for m∠JML, we get:
m∠JML = 25(193/33) - 13
m∠JML = 1468/3
m∠JML ≈ 489.33°
However, since lines KL and JM appear tangent, we know that minor arc KL and major arc JML share the same endpoint and thus are part of the same circle. So, the actual measure of major arc JML is:
m(arc JML) = 360° - m(arc KL)
We can find m(arc KL) by subtracting m∠KLM from 180°:
m(arc KL) = 180° - m∠KLM
m(arc KL) = 180° - (8(193/33) - 6)
m(arc KL) ≈ 70.67°
Substituting in the formula for m(arc JML), we get:
m(arc JML) = 360° - 70.67°
m(arc JML) ≈ 289.33°
Therefore, the actual measure of major arc JML is approximately 289.33°, which is closest to option (b) 287°.
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What is the quotient of 1. 892×10^8 and 4. 3×10^3
expressed in scientific notation? Please tell me the answer!
The quotient of 1.892×10^8 and 4.3×10^3 expressed in scientific notation is 4.4×10^4.
The quotient is determined by dividing any two numbers. In this case, the two numbers are 1.892×10^8 and 4.3×10^3. In order to calculate the quotient here, we will divide 1.892×10^8 by 4.3×10^3. Hence,
1. Divide the coefficients: 1.892 ÷ 4.3 = 0.44
2. Subtract the exponents: (10^8) ÷ (10^3) = 10^(8-3) = 10^5
3. Combine the results: 0.44 × 10^5
To express this answer in scientific notation, we need to move the decimal point one place to the left and adjust the exponent accordingly:
0.44 × 10^5 = 4.4×10^4
Therefore, the quotient expressed in scientific notation is 4.4×10^4.
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Shayla purchases 10 Virtual Gold lottery tickets for $2.00 eachDetermine the probability of Shayla winning the $200.00 prize if the odds are 1-in-3,598
The probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.
Describe Probability?In a probability context, an event refers to an outcome or set of outcomes of an experiment or process. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The probability of winning the lottery can be calculated using the formula:
Probability of winning = 1 / odds
Here, the odds of winning are given as 1-in-3,598. So, the probability of winning is:
Probability of winning = 1 / 3,598
= 0.000278
= 0.0278%
Shayla has bought 10 lottery tickets. So, the probability of winning the $200 prize with at least one ticket can be calculated as the complement of the probability of not winning with any of the tickets. That is:
Probability of winning with at least one ticket = 1 - Probability of not winning with any ticket
The probability of not winning with a single ticket is 1 - 0.000278 = 0.999722. So, the probability of not winning with all 10 tickets is:
Probability of not winning with all 10 tickets = (0.999722)¹⁰
= 0.997247
Therefore, the probability of winning with at least one ticket is:
Probability of winning with at least one ticket = 1 - Probability of not winning with all tickets
= 1 - 0.997247
= 0.002753
= 0.2753% (approx)
So, the probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.
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Shayla's probability of winning the $200 prize with 10 lottery tickets are at 0.2753%.
Describe Probability?An event in the context of probability is a result, or series of results, of an experiment or procedure. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.
The following formula can be used to determine the likelihood of winning the lottery:
Probability of winning = 1 / odds
The odds of winning in this case are 1 in 3,598. Therefore, the likelihood of winning is:
Probability of winning = 1 / 3,598
= 0.000278
= 0.0278%
Shayla purchased ten lottery tickets. As a result, the likelihood that at least one ticket will win the $200 reward can be computed as the complement of the likelihood that none of the tickets will win. Which is:
winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket
The likelihood that a single ticket won't be the winner is 1 - 0.000278 = 0.999722. Consequently, the likelihood of not winning with all ten
tickets is:
with all ten tickets, what is the likelihood of not winning = (0.999722)¹⁰
= 0.997247
Consequently, the following is the likelihood of winning with at least one ticket:
winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket
= 1 - 0.997247
= 0.002753
= 0.2753% (approx)
Shayla's chances of winning the $200 prize with 10 lottery tickets are at 0.2753%.
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A direct variation includes the points (2,
–
10) and (n,5). Find n.
Write and solve a direct variation equation to find the answer.
Solving a direct variation equation to find n gives n = -1
Writing and solving a direct variation equation to find nFrom the question, we have the following parameters that can be used in our computation:
A direct variation includes the points (2, –10) and (n,5).
This means that
(2, –10) = (n,5)
Express as an equation
So, we have
-2/10 = n/5
Multiply both sides of the equation by 5
So, we have the following representation
n = -2/10 * 5
Evaluate the product
n = -1
Hence, the value of n in the equation is -1
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