The answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.
The correct inequality that represents the situation is g ≤ 6. The problem states that the maximum number of goldfish that can live in a small tank is 6, meaning that the number of goldfish must be less than or equal to 6.
The symbol ≤ represents "less than or equal to", while the symbol > represents "greater than".
Therefore, the answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.
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Find the derivative of the vector function r(t) = ln(7-t^2)i + sqrt(13+tj – 4e^{9t} r’(t) =
The derivative of the vector function is: r'(t) = (-2t/(7-t^2)) i + (1/(2sqrt(13+t))) j - 36e^(9t) k
We are given a vector function r(t) = ln(7-t^2)i + sqrt(13+t)j – 4e^(9t)k, and we need to find its derivative r'(t).
The derivative of a vector function is obtained by differentiating each component of the vector function separately.
So, let's differentiate each component:
r(t) = ln(7-t^2)i + sqrt(13+t)j – 4e^(9t)k
r'(t) = (d/dt) ln(7-t^2) i + (d/dt) sqrt(13+t) j - (d/dt) 4e^(9t) k
Using the chain rule of differentiation, we have:
r'(t) = -2t/(7-t^2) i + 1/(2sqrt(13+t)) j - 36e^(9t) k
Therefore, the derivative of the vector function is:
r'(t) = (-2t/(7-t^2)) i + (1/(2sqrt(13+t))) j - 36e^(9t) k
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a police car is parked 40 feet due north of a stop sign on straight road. a red car is travelling towards the stop sign from a point 160 feet due east on the road. the police radar reads that the distance between the police car and the red car is decreasing at a rate of 100 feet per second. how fast is the red car actually traveling along the road?
The red car is actually traveling along the road at a speed of approximately 26.67 feet per second.
We can start by drawing a diagram of the situation:
P (police car)
|
|
|
40 | S (stop sign)
-------|--------------------
| 160
| R (red car)
Let's use the Pythagorean theorem to find the distance between the police car and the red car at any time t:
d(t)² = 40² + (160 - v*t)²
Where v is the speed of the red car in feet per second, and d(t) is the distance between the police car and the red car at time t.
We want to find how fast the red car is actually traveling along the road, so we need to find v when the distance between the police car and the red car is decreasing at a rate of 100 feet per second:
d'(t) = -100
We can take the derivative of the equation for d(t) with respect to time:
2d(t)d'(t) = 0 + 2(160 - v*t)(-v)
Simplifying and plugging in d'(t) = -100, we get:
-4000 + 2v²t = -100(160 - vt)
Solving for v, we get:
v = 80/3 ≈ 26.67 feet per second
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3) Find the maximum and minimum values of f(x,y) = xyon the region inside the triangle whose vertices are (6,2), (0,3), and (6.0).
Therefore, the maximum value of f(x,y) inside the triangle is 80/9, which occurs along the line y = (-1/2)x + 4 at the point (8/3, 10/3), and the minimum value is -32, which occurs at the critical point (-8,4).
To find the maximum and minimum values of f(x,y) = xy on the region inside the triangle whose vertices are (6,2), (0,3), and (6,0), we use the method of Lagrange multipliers.
First, we need to find the critical points of f(x,y) subject to the constraint that (x,y) lies inside the triangle. We can express this constraint using the equations of the lines that form the sides of the triangle:
y = (-1/2)x + 4
y = (3/2)x
y = 0
Next, we set up the Lagrange multiplier equation:
∇f = λ∇g
where g(x,y) is the equation of the constraint, i.e., the triangle.
We have:
f(x,y) = xy
∇f = <y, x>
g(x,y) = y - (-1/2)x - 4 = 0
∇g = <-1/2, 1>
Setting ∇f = λ∇g, we get:
y = (-1/2)λ
x = λ
Substituting these into the constraint equation, we get:
(-1/2)λ - 4 = 0
Solving for λ, we get:
λ = -8
Substituting this into y = (-1/2)λ and x = λ, we get:
x = -8 and y = 4
Therefore, the only critical point of f(x,y) inside the triangle is (-8,4).
Next, we need to check the values of f(x,y) at the vertices and along the sides of the triangle.
At the vertices:
f(6,2) = 12
f(0,3) = 0
f(6,0) = 0
Along the line y = (3/2)x:
f(x, (3/2)x) = (3/2)x^2
Using the vertex (6,2) and the x-intercept (4/3, 2), we can see that the maximum value of (3/2)x^2 on this line occurs at x = 4. Therefore, the maximum value of f(x,y) along this line is:
f(4,6) = 24
Along the line y = (-1/2)x + 4:
f(x, (-1/2)x + 4) = (-1/2)x^2 + 4x
Using the vertex (6,2) and the x-intercept (8,0), we can see that the maximum value of (-1/2)x^2 + 4x on this line occurs at x = 8/3. Therefore, the maximum value of f(x,y) along this line is:
f(8/3,10/3) = 80/9
Finally, we need to check the values of f(x,y) at the critical point (-8,4). We have:
f(-8,4) = -32
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Find y such that
∫x^5 dx = ∫ x^y dx
The value of y that satisfies the equation [tex]\int x^5 dx = \int x^y dx[/tex] is y = -1.
We know that the indefinite integral of x^5 dx is (1/6) x^6 + C, where C is
the constant of integration. Therefore:
[tex]\int x^5 dx = (1/6) x^6 + C[/tex]
We want to find y such that [tex]\int x^5 dx = \int x^y dx[/tex]. Using the power rule of integration, the indefinite integral of [tex]x^y[/tex] dx is [tex](1/(y+1)) x^{(y+1)} + C[/tex], where C is the constant of integration. Therefore:
[tex]\int x^y dx = (1/(y+1)) x^{(y+1)} + C[/tex]
For these two integrals to be equal, we need:
[tex](1/6) x^6 + C = (1/(y+1)) x^{(y+1) } + C[/tex]
Subtracting C from both sides, we get:
[tex](1/6) x^6 = (1/(y+1)) x^{(y+1)}[/tex]
Multiplying both sides by (y+1), we get:
[tex](1/6) x^6 (y+1) = x^{(y+1)}[/tex]
Now, we can equate the powers of x on both sides:
[tex]x^6 (y+1) = x^{(y+1)}[/tex]
Using the fact that[tex]x^a \times x^b = x^{(a+b)}[/tex], we can simplify the left-hand side:
[tex]x^(6(y+1)) = x^{(y+1)}[/tex]
Now, we can equate the exponents on both sides:
6(y+1) = y+1
Simplifying, we get:
6y + 6 = y + 1
5y = -5
y = -1
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It is kinda hard but just try it
Answer:
we 1st can get the weight of rat by
1 rat and 1 cat + 1 dog and rat = 30
2 rat + 1 cat + 1 dog = 30
Then 1 rat and cat measure 24 so
2 rat + 24 =30
2 rat + 24 =30 1 rat = 3 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg
so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them
Un terreno de forma rectangular tiene un perímetro de 105 metros. Si el ancho es la mitad del largo, ¿Cuáles son las medidas del terreno? *
Sea "l" la medida del largo del terreno y "a" la medida del ancho del terreno.
De acuerdo con el problema, el ancho es la mitad del largo, es decir, a = l/2.
El perímetro de un rectángulo se calcula sumando las longitudes de sus cuatro lados, por lo que en este caso:
Perímetro = 2l + 2a = 2l + 2(l/2) = 3l
Sabemos que el perímetro es de 105 metros, entonces:
3l = 105
l = 105/3 = 35
Por lo tanto, el largo del terreno es 35 metros. Y, como el ancho es la mitad del largo, entonces:
a = l/2 = 35/2 = 17.5
Por lo tanto, el ancho del terreno es de 17.5 metros.
En resumen, las medidas del terreno son 35 metros de largo y 17.5 metros de ancho.
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There are 30 skittles in a box, for every 5 green there are 7 yellow, how many yellows are there in the box
There are 42 yellow skittles in the box.
Based on the given information, we know that the ratio of green skittles to yellow skittles is 5:7. This means that for every 5 green skittles, there are 7 yellow skittles.
To find out how many yellow skittles are in the box, we need to know how many sets of 5 green skittles there are. We can do this by dividing the total number of skittles in the box (30) by 5 (since there are 5 green skittles for every set).
30 ÷ 5 = 6
This means there are 6 sets of 5 green skittles in the box.
Now we can use the ratio of 5:7 to find out how many yellow skittles there are in each set:
5 green skittles : 7 yellow skittles
Since there are 7 yellow skittles in each set, we can find the total number of yellow skittles by multiplying 7 by the number of sets (6):
7 x 6 = 42
There are 42 yellow skittles in the box.
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Francium is a radioactive element discovered by Marguerite Perey in 1939 and named after her country. Francium has a half-life of 22 minutes.
a) Write an exponential function that models the mass how many grams remain from a 480-gram sample after t minutes.
b) How many grams remain after 2 hours?
After 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
a) To write an exponential function that models the mass of Francium remaining after t minutes, we can use the formula:
N = N0 * [tex](1/2)^{(t / t1/2)}[/tex]
where N is the amount remaining after time t, N0 is the initial amount, t1/2 is the half-life, and (t/t1/2) means raised to the power of t/t1/2.
In this case, the initial amount is 480 grams, the half-life is 22 minutes, and we want to find the amount remaining after t minutes. Therefore, the exponential function that models the mass of Francium remaining after t minutes is:
N = 480 * [tex](1/2)^{t/22}[/tex]
b) 2 hours is equal to 120 minutes. To find how many grams of Francium remain after 2 hours, we can substitute t = 120 into the exponential function we found in part a):
N = 480 *[tex](1/2)^{ (120 / 22) }[/tex] ≈ 4.38 grams
Therefore, after 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
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the top of the farm silo is a hemisphere with a radius of 9ft. the bottom of the silo is a cylinder with a height of 35ft. how many cubic feet of grain can the solo hold? use 3.14 for pi and round your answer to the nearest cubic foot.
To find the total volume of the silo, we need to add the volume of the hemisphere on top to the volume of the cylinder at the bottom.
The volume of a hemisphere is given by:
V_hemi = (2/3)πr^3
where r is the radius of the hemisphere.
Substituting r = 9ft, we get:
V_hemi = (2/3)π(9ft)^3
= 1521π ft^3
The volume of a cylinder is given by:
V_cyl = πr^2h
where r is the radius of the cylinder and h is its height.
Substituting r = 9ft and h = 35ft, we get:
V_cyl = π(9ft)^2(35ft)
= 2673π ft^3
Therefore, the total volume of the silo is:
V_silo = V_hemi + V_cyl
= 1521π + 2673π
= 4194π ft^3
≈ 13160 ft^3
Rounding to the nearest cubic foot, the silo can hold approximately 13160 cubic feet of grain.
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?
Answer: Nori
Step-by-step explanation:
2% of 5000 = 100
1% of 1000 = 10
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
number of meals dispensed. n. 1. 3. 6. 7. amount of pet food remaining . f of n. cups. 21. 15. 6. 3.
based on the table, which function models this situation?
The function that models this situation is f(n) = -3n + 24.
To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).
1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.
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i need help fast!!!!
Answer:
1st choice: 1/4(y - 10) = 2/3
Step-by-step explanation:
the "variable" is y
"is" means "=" (equals sign)
one fourth = 1/4
"difference of" means subtract
Answer: 1/4(y - 10) = 2/3
4 Il y f(x, y) da = Sot Shot Sot Staf (x, y) dxdy x D
Characteristics of the drawing of D, you can choose several answers:
1. It is the region in the first quadrant that is bounded from the right by the line x = 2
2. It is the region in the first quadrant that is bounded above by y = x
3. It is the region in the first quadrant that is bounded from the left by the line x = 0
4. It is the region in the first quadrant that is bounded above by y = x2
5. It is the region in the first quadrant that is bounded below by y = 0
6. It is the region in the first quadrant that is bounded below by y = 2
which of these 6 options is correct?
The correct option is option 3.
How to determine the boundaries of the region?Based on the given integral, region D is in the first quadrant, and its boundaries are not explicitly given. However, we can deduce the boundaries of D by looking at the integrand. Since the integrand is f(x,y), we can see that we are integrating over the entire region D, which means that D must be the rectangle that contains all the other regions mentioned in the options.
Therefore, option 1 is not correct, as D is not bounded from the right by x=2, but rather extends indefinitely to the right. Option 2 is also not correct, as D extends beyond the line y=x. Option 4 is not correct either, as D is not bounded above by y=x^2, but rather extends beyond it. Options 5 and 6 are also not correct, as D extends beyond the lines y=0 and y=2.
Therefore, the correct option is option 3, which states that D is the region in the first quadrant that is bounded from the left by the line x=0. This is correct, as D extends indefinitely to the right, and is bounded from the left by x=0.
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) Nadia buys 4 1/5 pounds of plums. Nadia used a 55 cent coupon off her entire purchase. Her total after the coupon was $3. 23. If c represents the cost per pound for the plums, create and solve an equation to determine the cost per pound for the plums
If c represents the cost per pound for the plums, the cost per pound for the plums is $0.90.
First, we need to determine the total cost of the plums before the coupon was applied.
4 1/5 pounds can be written as a mixed number:
4 1/5 = 21/5
So, the total cost of the plums without the coupon can be found by multiplying the cost per pound (c) by 21/5:
Total cost = c * 21/5
Now we can create an equation to represent the total cost after the coupon was applied:
Total cost - coupon = $3.23
Substituting the expression for total cost:
c * 21/5 - 0.55 = 3.23
To solve for c, we can start by adding 0.55 to both sides:
c * 21/5 = 3.78
Then, we can isolate c by multiplying both sides by the reciprocal of 21/5:
c = 3.78 / (21/5)
c = 0.90
Therefore, the cost per pound for the plums is $0.90.
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Under which
transformation would AA'B'C', the wen 2.
image of AABC, not be congruent to AABC?
a. reflection over the y-axis
b.
rotation of 90° clockwise about the origin
c. translation of 3 units right and 2 units down
d. dilation with a scale factor of 2 centered at
the origin
A function is a rule that assingns each value of independent variable to exactly value of the dependent variable
A function is a rule that assingns each value of independent variable to exactly one value of the dependent variable.
A function is a mathematical concept that relates two sets of values, known as the domain and the range. The domain is the set of independent variables, while the range is the set of dependent variables. A function is a rule that assigns to each value in the domain exactly one value in the range.
For example, if we have a function f(x) = 2x + 3, the domain would be any possible value of x, and the range would be any possible value of 2x + 3. So if we put x = 2, then f(x) = 2(2) + 3 = 7. Therefore, the function assigns the value of 7 to the value of 2 in the domain.
Functions are used in various branches of mathematics, science, and engineering to model and analyze relationships between two or more variables. They are an important concept in calculus, where they are used to study rates of change and optimization problems.
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The mainsail of a boat has the dimensions shown. If the mainsail is a right triangle, what is the exact height of the mainsail shown?
a.) 2√6 feet
b.) 24 feet
c.) 4√78 feet
d.) 2√410 feet
Step-by-step explanation:
use Pythagorean theorem to find the height
c = 38 ft
a = 14 ft
a² + b² = c²
(14)² + b² = (38)²
b² = 1444 - 196
b² = 1248
b = √1248
b = √16 × 78
b = 4√78 feet
#CMIIWDetermine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale.
*
Captionless Image
Yes; 3:5
Yes; 2:3
Yes; 2:5
No they are not similar
Determine whether the two figures are similar: D. No, the two figures are not similar.
What are the properties of quadrilaterals?In Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent;
Ratio = 12/8 = 10/6 = 10/6
Ratio = 3/2 ≠ 5/3 = 5/3
In conclusion, the two figures are not similar because the ratio of their corresponding sides is not proportional.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
rotation 90 degrees clockwise about the origin, ignore the dots i kinda started it then i got lost
When the points are rotated 90 degrees clockwise about the origin, the result is:
I: (1, -3)J: (-1, -5)H: (-3, -3)How to rotate about the origin ?To rotate a point 90 degrees clockwise about the origin, you can use the following rule: (x, y) becomes (y, -x). Let's apply this rule to the given points:
I - (3, 1)
Rotated I: (1, -3)
J - (5, -1)
Rotated J: (-1, -5)
H - (3, -3)
Rotated H: (-3, -3)
So, after a 90-degree clockwise rotation about the origin, the new coordinates of the points are:
I: (1, -3)
J: (-1, -5)
H: (-3, -3)
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Which statement is true about all perfect cubes?
A
A perfect cube represents 3 times the area of a face of the cube.
B
A perfect cube represents the sum of 9 edge lengths of the cube.
A perfect cube represents the volume of a cube with equal integer side lengths.
D
A perfect cube represents the surface area of a cube with equal integer side lengths.
C
An 8-sided solid is labeled with faces 1, 2, 3, skip ,4, 5, 6, skip. what is the sample space for the number solid, and what is the probability of rolling a 1?
The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.
The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.
For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.
Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.
The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.
So, the probability of rolling a 1 is:
P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6
Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\
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Which point on the number line has the least absolute value?
The point with the least absolute value on the number line is always the point zero.
The absolute value of a number is the distance that number is from zero on the number line. Therefore, the point on the number line with the least absolute value is the point closest to zero. This point is located at zero itself, as it is the point on the number line that is equidistant from both the positive and negative numbers.
To further explain, consider the following examples:
- The point 3 is 3 units away from zero, but the point -3 is also 3 units away from zero.
- The point 5 is 5 units away from zero, but the point -5 is also 5 units away from zero.
- The point 0 is 0 units away from zero, making it the point with the least absolute value on the number line.
In conclusion, the point with the least absolute value on the number line is always the point zero.
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Find m∠A. PLEASEEEEEEEEEEE HELP ASAP WILLING TO DO ANYTHING PLEASEEEEEE
I have gotten 113
Step-by-step explanation:
The right angle triangle has three angles and the value of its two angles are 90°and30°.We need to find the third angle which is the sum of 90°and 30°subtract from 180°=60°.60° is vertically opposite to angle C. We'll be having a quadrilateral whose angles add up to 360° .Subtract the sum of the three angles from 360° and you'll get 113°
Use Euler's method with step size 0.5 to compute the approximate y-values yi, y(0.1), y(0,2), of the solution of the initial-value problem y' = 1 – 2x – 2y, y(0) = – 3. y1 = y2 = y3 = y4 =
The approximate values of y at x = 0.1, 0.2, 0.3, and 0.4 are all equal to y1 = y2 = y3 = y4 = 0.5, as we only used the first step of Euler's method.
We can use Euler's method with a step size of 0.5 to approximate the solution of the given initial-value problem as follows:
First, we need to find the slope at the initial point (0, -3):
y' = 1 - 2x - 2y
y'(0, -3) = 1 - 2(0) - 2(-3) = 7
Using Euler's method, we can approximate the solution at x = 0.5:
y(0.5) ≈ y(0) + hy'(0, -3) = -3 + 0.57 = 0.5
Next, we can use the approximate value y(0.5) to approximate the solution at x = 1:
y(1) ≈ y(0.5) + hy'(0.5, 0.5) = 0.5 + 0.5(1 - 2(0.5) - 2(0.5)) = -0.5
Similarly, we can use the approximate value y(1) to approximate the solution at x = 1.5:
y(1.5) ≈ y(1) + hy'(1, -0.5) = -0.5 + 0.5(1 - 2(1) - 2(-0.5)) = -1.25
Finally, we can use the approximate value y(1.5) to approximate the solution at x = 2:
y(2) ≈ y(1.5) + hy'(1.5, -1.25) = -1.25 + 0.5(1 - 2(1.5) - 2(-1.25)) = -2.4375
Therefore, the approximate values of y at x = 0.1, 0.2, 0.3, and 0.4 are all equal to y1 = y2 = y3 = y4 = 0.5, as we only used the first step of Euler's method.
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240:360=?:120 (Please quickly)
Answer:
? equals 80
Step-by-step explanation:
What is a good percentage (in decimal form) to multiply your earning to estimate your paycheck?
To estimate your paycheck, a good percentage to multiply your earning by would be 0.75 or 75%. When calculating your paycheck, it's important to account for taxes, deductions, and other withholdings that may be taken out of your gross pay.
This accounts for taxes, deductions, and other withholdings that are typically taken out of your paycheck before you receive your net pay. For example, if you earn $1,000 per pay period, multiplying by 0.75 would give you an estimated net pay of $750. However, keep in mind that this is just an estimate and your actual net pay may vary depending on your specific tax situation and other factors.
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Tanya made this graph that represents the total cost for each of the three locations. Depending on the number of students that attend. Which function represents the cost of the restaurant 
The functions that represents the cost are
(a) y = 8800, (b) y = 1900 + 4/7x and (c) y = 4800, x ≤ 150; y = 1200 + 24x x > 150
Identifying the function that represents the costFrom the question, we have the following parameters that can be used in our computation:
The graph
The function (a) is a horizontal line that passes through y = 8800
So, the function is
y = 8800
The function (b) is a linear function that passes through
(0, 1900) and (175, 2000)
So, the function is
y = 1900 + 4/7x
The function c is a piecewise function with the following properties
Horizontal line of y = 4800 uptill x = 150Linear function of (150, 4800) and (200, 6000)So, the function is
y = 4800, x ≤ 150
y = 1200 + 24x x > 150
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If the coordinates of two points are P (-2, 3) and Q (-3, 5), then find (abscissa of P) – (abscissa of Q)
The difference between the abscissa of P and Q is 1.
The abscissa of a point is its x-coordinate, or horizontal distance from the origin (usually measured along the x-axis).
In the given problem, the abscissa of point P is -2, which means it is located 2 units to the left of the origin on the x-axis. The abscissa of point Q is -3, which means it is located 3 units to the left of the origin on the x-axis.
To find the difference between the abscissas of P and Q, we simply subtract the abscissa of Q from the abscissa of P:
(abscissa of P) - (abscissa of Q) = (-2) - (-3) = -2 + 3 = 1
Therefore, the difference between the abscissas of P and Q is 1 unit.
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please do both will give brainliest and it's for 72 points
Step-by-step explanation:
Pick any of the two points...I'll use the first two
calculate slope: m = ( y1-y2) / (x1-x2) = (-14 - -5) / (-2 -1) = -9/-3 = 3
equation of a line in slope intercept form is y = mx+ b
so now you have y = 3x + b
sub in any of the x,y points given (8,16) to calculate 'b'
16 = 3 (8) + b
b = -8
so your first line is y = 3x - 8
In a similar fashion, for the second one m = - 5/8 and b = 2
y = -5/8 x + 2
Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Always True.
Line x is perpendicular to line y. Line z crosses lines x and y. Only statements 3 and 4 are true.
∠6 = ∠8 is not true because they both lie on the same plane and makes an angle of 180° and can never be true. ∠6 = ∠1 is also not true because ∠1 is clearly obtuse angle and ∠6 is clearly acute angle so they cannot be equal. Hence, statement a and b are false.
∠7 = ∠3 is always true because they are corresponding angles and corresponding angles are always equal. m∠2 + m∠4 = 180° is also true because they lie on same plane and have common vertex and hence, they are supplementary angles and make a sum of 180°. Hence, statement 3 and 4 is always true.
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