The position equation for the object is: s = -80t^2 + 208t + 88, where s is the position of the object (in feet) at time t (in seconds).
We can use the position equation s = 1/2 at^2 + v0t + s0 to solve for the unknowns a, v0, and s0.
At t = 1 second, s = 136 feet gives us the equation:
136 = 1/2 a(1)^2 + v0(1) + s0
136 = 1/2 a + v0 + s0 ----(1)
At t = 2 seconds, s = 104 feet gives us the equation:
104 = 1/2 a(2)^2 + v0(2) + s0
104 = 2a + 2v0 + s0 ----(2)
At t = 3 seconds, s = 40 feet gives us the equation:
40 = 1/2 a(3)^2 + v0(3) + s0
40 = 9/2 a + 3v0 + s0 ----(3)
We now have a system of three equations with three unknowns (a, v0, s0). We can solve this system by eliminating one of the variables. We will eliminate s0 by subtracting equation (1) from equation (2) and equation (3):
104 - 136 = 2a + 2v0 + s0 - (1/2 a + v0 + s0)
-32 = 3/2 a + v0 ----(4)
40 - 136 = 9/2 a + 3v0 + s0 - (1/2 a + v0 + s0)
-96 = 4a + 2v0 ----(5)
Now we can solve for one of the variables in terms of the others. Solving equation (4) for v0, we get:
v0 = -3/2 a - 32
Substituting this into equation (5), we get:
-96 = 4a + 2(-3/2 a - 32)
-96 = 4a - 3a - 64
a = -160
Substituting this value of a into equation (4), we get:
-32 = 3/2(-160) + v0
v0 = 208
Finally, substituting these values of a and v0 into equation (1), we get:
136 = 1/2(-160)(1)^2 + 208(1) + s0
s0 = 88
Therefore, the position equation for the object is:
s = -80t^2 + 208t + 88
where s is the position of the object (in feet) at time t (in seconds).
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Find a formula for the sum of n terms. Use the formula to find the limit as n = [infinity].
lim ∑ ( 6 + i/n) (2/n)
To find a formula for the sum of n terms, we need to first write out the first few terms of the series and look for a pattern:
n=1: (6+1/1) (2/1) = 14
n=2: (6+1/2) (2/2) + (6+2/2) (2/2) = 16
n=3: (6+1/3) (2/3) + (6+2/3) (2/3) + (6+3/3) (2/3) = 17 1/3
n=4: (6+1/4) (2/4) + (6+2/4) (2/4) + (6+3/4) (2/4) + (6+4/4) (2/4) = 18
From this, we can see that the nth term is given by (6+i/n) (2/n). To find the sum of n terms, we simply add up all of the terms from i=1 to i=n:
∑ (6+i/n) (2/n) = (2/n) ∑ (6+i/n)
Using the formula for the sum of an arithmetic series, we get:
∑ (6+i/n) = n/2 (6 + (6+n)/n)
Substituting this back into our expression for the sum of n terms, we get:
∑ (6+i/n) (2/n) = (2/n) * (n/2) * (6 + (6+n)/n) = 6 + (6+n)/n
Taking the limit as n approaches infinity, we get:
lim (6 + (6+n)/n) = 6 + lim ((6+n)/n) = 6 + 1 = 7
Therefore, the limit of the given series as n approaches infinity is 7.
To find the formula for the sum of n terms, we will use the concept of Riemann sums. Given the expression you provided, it appears that you are trying to compute the limit of the Riemann sum as n approaches infinity, which will give you the integral of the function.
Expression: lim (n→∞) ∑ (6 + i/n) (2/n)
First, let's rewrite the Riemann sum in integral form:
∫(6 + x)dx
Now we need to find the integral of the function and evaluate it over a specific interval. However, you haven't provided the interval, so I'll assume it is [a, b].
∫(6 + x)dx evaluated from a to b will give us the formula for the sum of n terms:
F(x) = 6x + (1/2)x^2
Now, evaluate F(x) over the interval [a, b]:
F(b) - F(a) = [6b + (1/2)b^2] - [6a + (1/2)a^2]
This is the formula for the sum of n terms. To find the limit as n approaches infinity, you will need to provide the specific interval [a, b]. Otherwise, the limit cannot be determined without further information.
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Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes.
Drag a number and symbols to represent the amount of time Carl worked on problems.
X
M
25
The amount of time Carl represent is 25-m on the problems.
The statement "Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes" means that Carl spent some amount of time working on math problems, but that amount is m minutes less than what Davis spent.
To represent the amount of time Carl worked on math problems, we can use the variable X. We know that X is equal to the amount of time Carl worked on math problems, and that X is equal to 25 minus m.
This is because Davis spent 25 minutes on math problems, and Carl worked on them for m fewer minutes. So if we subtract m from 25, we get the amount of time Carl worked on math problems.
Therefore, the equation X = 25 - m represents the amount of time Carl worked on math problems, where X is the amount of time in minutes and m is the number of minutes Carl worked less than Davis.
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which fraction is equivalent to 0.48 in simplest form?
[A] 12/25
[B] 12/50
[c] 24/50
[D] 48/100
Answer:
0.48 = 48/100
48/100 ÷ 4/4 = 12/25
0.48 = 12/25 =A
At Olivia's Hats, 90% of the 80 hats are baseball caps. How many baseball caps are there?
Please help me with this math problem!!! Will give brainliest!!
The average price of milk in 2018 was 6.45 dollars per gallon.
The average price of milk in 2021 was 189.95 dollars per gallon.
How to calculate the priceThe given function is: Price = 3.55 + 2.90(1 + x)³
In order to find the average price of milk in 2018, we need to set x = 0:
Price in 2018 = 3.55 + 2.90(1 + 0)³ = 3.55 + 2.90(1) = 6.45 dollars per gallon
Price in 2021 = 3.55 + 2.90(1 + 3)³ = 3.55 + 2.90(64) = 189.95 dollars per gallon
Hence, the average price of milk in 2021 was 189.95 dollars per gallon.
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Help with the problem in photo
The measure of the unknown arc is 76°
What is arc angle relationship?An arc is a smooth curve joining two endpoints. It can also be defined as a portion of a circle.
Arc angle relationship states that If two chords intersect inside a circle, then the measure of each angle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Therefore angle 30° = 1/2 ( x-61)
30 = 1/2( x -61)
15 = x -61
x = 15 + 61
x = 76°
therefore the measure of the unknown arc is 76°
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Find f'(-2) for f(x) = ln((x^4 + 5)^2). Answer as an exact fraction or round to at least 2 decimal places.
Using the chain rule, we have: f'(x) = 2ln(x^4 + 5) * 2(x^4 + 5)^1 * 4x^3
f'(x) = 16x^3 * ln(x^4 + 5) * (x^4 + 5)
To find f'(-2), we plug in -2 for x:
f'(-2) = 16(-2)^3 * ln((-2)^4 + 5) * ((-2)^4 + 5)
f'(-2) = -128 * ln(21) * 21
f'(-2) ≈ -599.92 (rounded to 2 decimal places)
Therefore, f'(-2) is approximately -599.92.
To find f'(-2) for the function f(x) = ln((x^4 + 5)^2), we will first find the derivative of the function, and then evaluate it at x = -2.
1. Differentiate the function using the chain rule:
f'(x) = (d/dx) ln((x^4 + 5)^2) = (1/((x^4 + 5)^2)) * (d/dx) ((x^4 + 5)^2)
2. Differentiate the inner function:
(d/dx) ((x^4 + 5)^2) = 2(x^4 + 5) * (d/dx) (x^4 + 5) = 2(x^4 + 5) * (4x^3)
3. Combine the derivatives:
f'(x) = (1/((x^4 + 5)^2)) * (2(x^4 + 5) * (4x^3)) = (8x^3(x^4 + 5))/((x^4 + 5)^2)
4. Evaluate the derivative at x = -2:
f'(-2) = (8(-2)^3((-2)^4 + 5))/((-2)^4 + 5)^2 = (-128(21))/(21^2) = -128/21
So, f'(-2) is -128/21 as an exact fraction.
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The area of a rooftop can be
expressed as (x + 9)2. The rooftop
is a rectangle with side lengths
that are factors of the expression
describing its area. Which expression
describes the length of one side of
the rooftop?
The expression that describes the length of one side of the rooftop is therefore: x - 9.
What is expression?In mathematics, an expression is a combination of one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An expression can be as simple as a single variable or constant, or it can be a more complex combination of variables and operations.
Here,
The expression for the area of the rooftop is (x + 9)², where x is a variable representing the length of one side of the rectangle. To find the factors of this expression, we can expand it using the identity (a+b)² = a² + 2ab + b².
Expanding (x + 9)², we get:
(x + 9)² = x² + 18x + 81
Now, we need to find the factors of this expression that are also factors of the length of the sides of the rectangle. Since the sides of the rectangle must have a common factor of x, we can factor out x from the expression:
x² + 18x + 81 = x(x + 18) + 81
The factors of (x + 9)² are x(x + 18) + 81, (x + 9)(x + 9), (x - 9)(x - 9), and -(x + 9)(x + 9).
Since we are looking for factors that represent the length of one side of the rooftop, we can eliminate the negative factor and the factor (x + 9)(x + 9), since the sides of a rectangle must be positive.
That leaves us with x(x + 18) + 81 and (x - 9)(x - 9).
The expression describes the length of one side of the rooftop: x - 9
This is because the sides of a rectangle must be positive, and (x - 9) is a factor of (x + 9)² that represents a positive length.
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Find dx/dt at x = -5 if y = -5x^2 + 2 and dy/dt = - 4.
dx/dt = ?
x = -5, dx/dt is equal to -2/25.
To find dx/dt, we need to use the chain rule of differentiation.
We know that dy/dt = -4 and we have the equation y = -5x^2 + 2.
Taking the derivative of both sides with respect to t, we get:
dy/dt = d/dt (-5x^2 + 2)
Using the chain rule, we can write this as:
dy/dt = (-10x) (dx/dt)
Now, we can plug in x = -5 and dy/dt = -4:
-4 = (-10(-5)) (dx/dt)
Simplifying, we get:
-4 = 50 (dx/dt)
Dividing both sides by 50, we get:
dx/dt = -4/50
Simplifying further, we get:
dx/dt = -2/25
Therefore, at x = -5, dx/dt is equal to -2/25.
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The arrow on this spinner is equally likely to land on each section. the arrow is spun 72 times. how many times do you expect the arrow to land on 4?
we know that the spinner has an equal chance of landing on each section. Since there are a total of six sections on the spinner, we can assume that the probability of the arrow landing on any one section is 1/6 or approximately 0.1667.
Now, if the arrow is spun 72 times, we can use this probability to calculate the expected number of times the arrow will land on 4. To do this, we simply multiply the probability by the number of spins, as follows:
Expected number of times arrow lands on 4 = Probability of arrow landing on 4 x Number of spins
Expected number of times arrow lands on 4 = 0.1667 x 72
Expected number of times arrow lands on 4 = 12
So, we can expect the arrow to land on 4 approximately 12 times out of 72 spins. Of course, this is just an expected value, and the actual number of times the arrow lands on 4 may vary from this value due to random chance.
In summary, if we assume that the arrow on the spinner is equally likely to land on each section, and it is spun 72 times, we can expect the arrow to land on 4 approximately 12 times based on probability calculations.
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Try Again ml A patient is being treated for a chronic illness. The concentration C(x) (in of a certain medication in her bloodstream x weeks from now is approximated by the following equation 28² 2x+7 CG) - x²–2x+2 Complete the following (a) Use the ALEKS.chine calculator to find the value of x that maximizes the concentration Then give the maximum concentration, Round your answers to the nearest hundredth Value of that maximizes concentration 119 weeks Maximum concentration: 7:19 ml (b) Complete the following sentence For very large, the concentration appears to increase without bound.
The value of x that maximizes the concentration is 119 weeks, and the maximum concentration is approximately 7.19 ml.
How to find maximum concentration?Based on the provided equation, the concentration C(x) is a quadratic function of x with a negative coefficient for the quadratic term, which means that it has a maximum point.
(a) To find the value of x that maximizes the concentration, we can take the derivative of the concentration function with respect to x, set it equal to zero, and solve for x. The derivative of C(x) is:
C'(x) = 56x + 7
Setting C'(x) equal to zero, we get:
56x + 7 = 0
Solving for x, we get:
x = -7/56 = -0.125
However, x represents the number of weeks from now, which cannot be negative. Therefore, the maximum concentration occurs at the endpoint of the interval we are considering, which is x = 119 weeks.
To find the maximum concentration, we can substitute x = 119 into the concentration function:
C(119) = 28²(2119)+7 - 119²-2119+2 ≈ 7.19 ml
So, the value of x that maximizes the concentration is 119 weeks, and the maximum concentration is approximately 7.19 ml.
(b) For very large values of x, the quadratic term (-x²) dominates the concentration function, and the concentration appears to decrease without bound.
This is because the negative quadratic term becomes much larger than the linear term (2x) and the constant term (2), causing the concentration to become more and more negative as x increases.
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Can someone please answer the question below (Level: Year 8 (7th Grade) ) about algebra equations?
Thanks ^^
Which equation represents a line passing through the points (0, 1) and (2, -3)?
The equation of the line passing through the points (0, 1) and (2, -3) is y = -2x + 1.
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (0, 1) and (2, -3).
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (-3 - 1) / (2 - 0)
m = -4 / 2
m = -2
Using the point-slope form, plug in one of the given points and slope m = -2 to find the equation of the line.
Let's use the point (0, 1):
y - y₁ = m(x - x₁)
y - 1 = -2(x - 0)
y - 1 = -2x
y = -2x + 1
Therefore, the equation of the line is y = -2x + 1.
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Would anyone be willing to help me out with a few math questions? I'm up late and could really use the help!
How many zeros are in the product 50 x 6,000
The number of zeros are in the product of the number 50 and 6000 is 50 x 6000 = 300,000 are five.
Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.
A product is the outcome of multiplication in mathematics, or an expression that specifies the elements (numbers or variables) to be multiplied.
The commutative law of multiplication states that the result is independent of the order in which real or complex numbers are multiplied. The result of a multiplication of matrices or the elements of other associative algebras typically depends on the order of the components. For instance, matrix multiplication and multiplication in general in other algebras are non-commutative operations.
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A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0 the function of its parent function over the x-axis Which function could be the function described?
The function that could be described is f(x) = 10cos(2πx/3), where the amplitude is 10, the period is 3, and the maximum value is 20.
In a cosine function, the amplitude represents the vertical distance from the midline to the maximum or minimum value. Here, the maximum value is 20, which means the amplitude is half of that, i.e., 10. The period of the function is the distance it takes for one complete cycle, and in this case, it is 3 units.
By using the formula f(x) = A*cos(2πx/P), where A is the amplitude and P is the period, we can determine that the given function matches the described characteristics.
The function f(x) = 10cos(2πx/3) has a maximum value of 20 and a minimum value of 0, and it completes one cycle over the interval of the period, which is 3 units.
In conclusion, the function f(x) = 10cos(2πx/3) satisfies all the given conditions and represents the described function.
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Clarissa is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 10 inches × 14 1/2
inches. She needs to cut another rectangle that is 10 1/4
inches by 10 1/2 inches. How many total square inches of construction paper does Clarissa need for her project?
Clarissa needs a total of 251.25 square inches of construction paper for her project.
To find the total area of construction paper needed, we need to find the area of each rectangle and add them together.
The first rectangle has an area of 10 inches × 14.5 inches = 145 square inches.
The second rectangle has an area of 10.25 inches × 10.5 inches = 107.625 square inches.
Adding these two areas together, we get a total of 145 + 107.625 = 252.625 square inches.
Therefore, Clarissa needs a total of 251.25 square inches (rounded to two decimal places) of construction paper for her project.
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Khloe is a teacher and takes home 90 papers to grade over the weekend. She can
grade at â rate of 10 papers per hour. Write a recursive sequence to represent how
many papers Khloe has remaining to grade after working for n hours.
The recursive sequence representing how many papers Khloe has remaining to grade after working for n hours is given by a_n = a_{n-1} - 10, where a_0 = 90.
Let a_n denote the number of papers Khloe has remaining to grade after n hours of work. After the first hour of work, she will have 90 - 10 = 80 papers remaining. Therefore, we have a_1 = 90 - 10 = 80.
After the second hour of work, she will have a_2 = a_1 - 10 = 80 - 10 = 70 papers remaining. Similarly, after the third hour of work, she will have a_3 = a_2 - 10 = 70 - 10 = 60 papers remaining.
In general, after n hours of work, Khloe will have a_n = a_{n-1} - 10 papers remaining to grade. This is a recursive sequence, where the value of a_n depends on the value of a_{n-1}. The initial value of a_0 is given as 90, since she starts with 90 papers to grade. Therefore, the recursive sequence is given by a_n = a_{n-1} - 10, where a_0 = 90.
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Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator. In(8x2 – 72x + 112) Enter the
The fully expanded expression using logarithm properties is:
[tex]In(8x^2 - 72x + 112) = 2.079 + In(x - 2) + In(x –-7)[/tex]
How to expand an expression?To expand the given expression[tex]In(8x^2 - 72x + 112)[/tex], we can use the following logarithmic properties:
Product Rule: [tex]logb (xy) = logb x + logb y[/tex]
Quotient Rule: [tex]logb (x/y) = logb x - logb y[/tex]
Power Rule:[tex]logb (x^a) = a logb x[/tex]
We can first factor out a common factor of 8 from the expression inside the logarithm:
[tex]In(8x^2 - 72x + 112) = In[8(x^2 - 9x + 14)][/tex]
Using the distributive property, we can expand the expression inside the logarithm:
[tex]In[8(x^2 - 9x + 14)] = In(8) + In(x^2 - 9x + 14)[/tex]
Now, we need to expand the second logarithm. We notice that the expression inside the logarithm can be factored as follows:
[tex]x^2 - 9x + 14 = (x - 2)(x - 7)[/tex]
Using the product rule, we can write:
[tex]In(x^2 - 9x + 14) = In[(x - 2)(x - 7)][/tex]
[tex]= In(x - 2) + In(x - 7)[/tex]
Putting all the pieces together, we get:
[tex]In(8x^2 - 72x + 112) = In(8) + In(x^2 - 9x + 14)[/tex]
[tex]= In(8) + In(x -2) + In(x - 7)[/tex]
Finally, we can simplify the numerical expression In(8) by using the fact that ln(e) = 1:
[tex]In(8) = ln(8)/ln(e) = 2.079/1 = 2.079[/tex]
So the fully expanded expression using logarithm properties is:
[tex]In(8x^2 - 72x + 112) = 2.079 + In(x - 2) + In(x -7)[/tex]
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Mathematics/g12
nsc
march 2021
question1
a group of workers is erecting a fence around a nature reserve. they store their tools in a shed at
the entrance to the reserve. each day they collect their tools and erect 0,8km of new fence. they
then lock up their tools in the shed and return the next day.
1.1 if the fence takes 40 days to erect, how far would the workers have travelled in total?
(4)
The workers would have traveled a total of 32 km while erecting the fence over 40 days.
To determine the total distance the workers traveled while erecting the fence, we can use the following terms: daily distance, number of days, and total distance.
Step 1: Determine the daily distance traveled.
The workers erect 0.8 km of new fence each day.
Step 2: Determine the number of days it takes to erect the fence.
It takes 40 days to erect the fence.
Step 3: Calculate the total distance traveled.
To find the total distance, multiply the daily distance (0.8 km) by the number of days (40).
Total distance = Daily distance × Number of days
Total distance = 0.8 km × 40
Total distance = 32 km
So, the workers would have traveled a total of 32 km while erecting the fence over 40 days.
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A museum groundskeeper is creating a simicircular stauary garden with a diameter of 38 feet there will be a fence around the garden the fencing cost $9.25 per linear foot . About how much will the fencing cost although? Round to the nearest hundredth use 3.14 for n the fencing will cost about $
The amount for the fencing cost is $903. 36
How to determine the valueFrom the information given, we have that the shape of the garden is semi -circle.
Now, the formula that is used for calculating the circumference of a semicircle is expressed as;
C = πr + 2r
Given that the parameters of the equation are;
C is the circumference of the semicircler is the radius of the semicircleFrom the information given,
Substitute the values, we have;
Circumference = 3.14(19) + 2(19)
expand the bracket
Circumference = 59. 66 + 38
Add the values
Circumference = 97. 66 feet
Then,
if 1 feet = $9.25
Then, 97. 66 feet = x
x = $903. 36
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Find the smallest number of terms of the series ∑ n = 1 (-1)^n+1/2^n you need to be certain that the partial sum Sn is within 1/100 of the sum.n=2 n=4 n=6 n=8 n=7
We need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
We want to find the smallest value of n such that the absolute value of the difference between the sum of the first n terms and the sum of the entire series is less than 1/100.
The sum of the first n terms of the series is given by:
Sn = ∑_(k=1[tex])^n[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
We can write the sum of the entire series as:
S = ∑_(k=[tex]1)^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
The absolute value of the difference between the sum of the first n terms and the sum of the entire series is:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] [tex](-1)^(k+1)/2^k|[/tex]
We want to find the smallest value of n such that |S - Sn| < 1/100.
Let's start by evaluating the sum of the series:
S = ∑_(k=1) (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex] = 1/2 - 1/4 + 1/8 - 1/16 + ...
This is a geometric series with first term a = 1/2 and common ratio r = -1/2. The sum of the series is:
S = a/(1-r) = (1/2)/(1+1/2) = 1/3
Now we can write:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k|[/tex] <= 1/[tex]2^(n+1)[/tex]
The last inequality is true because the terms of the series are decreasing in absolute value, and we are summing an infinite number of terms.
Therefore, we need to find the smallest value of n such that 1/2^(n+1) < 1/100. This gives:
n+1 > log2(100)
n > log2(100) - 1
n > 6.64
The smallest integer value of n that satisfies this inequality is n = 7.
Therefore, we need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
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£4500 is shared between 4 charities.
the donation to charity b is 5/6 of the donation to charity d
charity d's donation is twice the donation to charity c.
the ratio of donations for charity c to charity a is 3:4.
work out the donation to charity b.
If the donation to charity b is 5/6 of the donation to charity d, charity d's donation is twice the donation to charity c and the ratio of donations for charity c to charity a is 3:4 then the donation to charity b is £1250.
Let's denote the donation to charity a as x. Then the donation to charity c is (3/4)x, and the donation to charity d is 2(3/4)x = (3/2)x.
We know that the donation to charity b is 5/6 of the donation to charity d, so:
donation to charity b = (5/6)(3/2)x = (5/4)x
We also know that the total donation is £4500, so we can set up an equation:
x + (3/4)x + (3/2)x + (5/4)x = £4500
Multiplying through by 4 to get rid of the fractions, we have:
4x + 3x + 6x + 5x = £18,000
18x = £18,000
x = £1000
So the donation to charity b is: (5/4)x = (5/4)(£1000) = £1250
Therefore, the donation to charity b is £1250.
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WHY CANT YOU JUST GIVE AN ANSWER WITHOUT MAKING THE PERSON PAY I JUST WANT A EXPLANAITION FOR A QUESTION STILL YOUR MAKING ME PAY ME JUST FOR A ANSWER AND A SIMPLE EXPLANAITION YOUR ADDS ALWAYS FREEZE SO NOW K HAVE TO PAY? OH MY GOD EVERY OTHER WEBSITE DOES THE SAME THING WHY DO YOU DO THAT WITH THE REST IM JUST A GUEST oop sorry caps lock.
steal it
Step-by-step explanation:
2
A rhombus has a perimeter of 136 inches and one diagonal of 60 in.
What is the length of the other diagonal?
Find the area of the rhombus. .
Diagonal =
in
Area =
in2
The area of the rhombus is 1140 square inches.
Let the side length of the rhombus be "a" and let the length of the other diagonal be "d".
Since a rhombus has all sides congruent, the perimeter is given by:
4a = 136
Simplifying, we get:
a = 34
We can use the formula for the area of a rhombus:
Area = (diagonal 1 x diagonal 2)/2
Substituting the given values:
Area = (60 x d)/2
Area = 30d
Now we can substitute the value of "a" in terms of "d" into the formula for the length of the diagonal:
d = √(a² + b²)
d = √(34² + b²)
d = √(1156 + b²)
We also know that the perimeter of the rhombus is given by:
4a = 136
Substituting the value of "a" we found earlier:
4(34) = 136
So the length of the other diagonal can be found by subtracting the length of the given diagonal from the perimeter, and dividing by 2:
d = (136 - 60)/2 = 38
Therefore, the length of the other diagonal is 38 inches.
To find the area, we can substitute the value we found for "d" into the formula we derived earlier:
Area = 30d = 30(38) = 1140
So the area of the rhombus is 1140 square inches.
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Let g(x) be continuous with g(0) = 3. g(1)
8, g(2) = 4. Use the Intermediate Value Theorem to ex-
plain why s(x) is not invertible.
The Intermediate Value Theorem states that if a function f(x) is continuous on a closed interval [a,b], and if M is any number between f(a) and f(b), then there exists at least one number c in the interval [a,b] such that f(c) = M.
In this case, we are given a continuous function g(x) with g(0) = 3, g(1) = 8, and g(2) = 4. Let s(x) be the inverse of g(x), which means that s(g(x)) = x for all x in the domain of g(x).
Suppose s(x) is invertible. Then for any y in the range of g(x), there exists a unique x such that g(x) = y, and therefore s(y) = x. In particular, let y = 5, which is between g(1) = 8 and g(2) = 4. By the Intermediate Value Theorem, there exists a number c in the interval [1,2] such that g(c) = 5.
However, this means that s(5) is not well-defined, since there are two values of x (namely c and s(5)) that satisfy g(x) = 5. Therefore, s(x) is not invertible.
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and k is any number between f(a) and f(b), then there exists a number c in the interval [a, b] such that f(c) = k.
Let g(x) be continuous with g(0) = 3, g(1) = 8, and g(2) = 4. Since g(x) is continuous, the Intermediate Value Theorem applies. However, to show that s(x) is not invertible, we need to show that g(x) is not one-to-one.
Notice that g(0) = 3 and g(2) = 4, with g(1) = 8 in between. This means that there must exist a point c1 in the interval (0, 1) such that g(c1) = 4, and another point c2 in the interval (1, 2) such that g(c2) = 3, due to the Intermediate Value Theorem.
Since g(c1) = g(c2) = 4 and c1 ≠ c2, g(x) is not one-to-one. Therefore, its inverse function s(x) does not exist, and s(x) is not invertible.
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What is the area of EFG
Answer:
A = 28 units²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = FG = 8 and h = FE = 7 , then
A = [tex]\frac{1}{2}[/tex] × 8 × 7 = 4 × 7 = 28 units²
Question 1 of 10
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Points N and L on the circle K and points Q and P on the circle O. NP and QL intersect at point M. NP is tangent to Circle K at point N and tangent to circle O at point P. LQ is tangent to Circle
and tangent to circle O at point Q.
if NM=72-18, LM-31, QM=62-4, and PM=5y-12, which of the following statements are true? Select all that apply.
the length of PM is 98.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
OM/MN = OP2/P2M
[tex]OM/(r_1 - r_2) = (r_2 + y - 12)/yOM = (r_1 - r_2)*(r_2 + y - 12)/y[/tex]
Similarly, since LQ is tangent to both circles at L and Q respectively, we have OL1 and OQ2 perpendicular to LQ. Therefore, triangle LOM and triangle QOM are similar triangles. Using this similarity, we can find the length of OM in terms of r1 and r2:
OM/ML = OQ2/Q2M
[tex]OM/(r_1 + r_2 - 31) = (r_2 + 62 - 4)/yOM = (r_1 + r_2 - 31)*(r_2 + 62 - 4)/y[/tex]
Since both expressions above represent the same length of OM, we can equate them:
[tex](r_1 - r_2)(r_2 + y - 12)/y = (r_1 + r_2 - 31)(r_2 + 62 - 4)/y[/tex]
Simplifying and solving for y, we get:
y = 22
Therefore, PM = 5y - 12 = 98.
Hence, the length of PM is 98.
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What adds to +10 and multiplys to 290
help please
Use substitution to find the indefinite integral. x² - 2x 3 X - S dx x4 - 4x + 4 - X x - 2x 4 - 4x + 4 dx=
To solve this problem, we can use substitution. Let's set u = x-2. Then, du/dx = 1 and dx = du. Using this substitution, we can rewrite the integral as:
∫ (u+2)² - 2(u+2) 3 (u+2) - Su du
Expanding the terms inside the integral, we get:
∫ (u² + 4u + 4) - 2(u+2)³ (u+2) - Su du
Simplifying, we get:
∫ u⁴ - 4u³ + 4u² - u³ + 6u² - 12u - u² + 6u - 9 du
Combining like terms, we get:
∫ u⁴ - 5u³ + 9u² - 6u - 9 du
Now, we can integrate each term separately using the power rule of integration:
∫ u⁴ - 5u³ + 9u² - 6u - 9 du = (1/5)u⁵ - (5/4)u⁴ + (9/3)u³ - 3u² - 9u + C
Substituting back u = x-2, we get:
(1/5)(x-2)⁵ - (5/4)(x-2)⁴ + (3)x³ - 3(x-2)² - 9(x-2) + C
Therefore, the indefinite integral of x² - 2x 3 X - S dx x⁴ - 4x + 4 - X x - 2x⁴ - 4x + 4 dx is (1/5)(x-2)⁵ - (5/4)(x-2)⁴ + (3)x³ - 3(x-2)² - 9(x-2) + C.
Hi! I'd be happy to help you with your integration problem. To find the indefinite integral using substitution, let's first rewrite the given integral:
∫(x² - 2x) / (x⁴ - 4x² + 4) dx
Now, let's perform substitution:
Let u = x² - 2x
Then, du/dx = 2x - 2
And also let v = x⁴ - 4x² + 4
Then, dv/dx = 4x³ - 8x
We need to find du in terms of dx, so:
du = (2x - 2) dx
Now, we can rewrite the integral in terms of u and v:
∫(u) / (v) (du / (2x - 2))
Now we can integrate:
(1/2) ∫(u) / (v) du
Unfortunately, this integral does not have a straightforward elementary antiderivative. However, you can use numerical integration methods or special functions to approximate the indefinite integral if necessary.
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