The photograph below shows a bouncing ball in front of an illuminated grid. The heights of the ball's bounces make a geometric sequence. What will the height of the next bounce be?A. 0.28812 m
B. 0.2352 m
C. 0.1764 m
D. 0.26724 m
Answers
1.2, 0.84, 0.588, 0.4116
If this is a geometric sequence, then they should have a common ratio. We determine as follows:
0.4116 / 0.588 = 0.7
0.588 / 0.84 = 0.7
0.84 / 1.2 = 0.7
r = 0.7
an = a1(r^(n-1))
an = 1.2 (0.7^(5-1))
an = 0.28812 <--------option A
The photograph below shows a bouncing ball in front of an illuminated grid. The heights of the ball's bounces make a geometric sequence. What will the height of the next bounce be?
A. 0.28812 m
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1/2 pound of cheese
3 sandwiches
To need to divide the 1/2 pound of cheese by 3 sandwiches to get the equal amount of cheese each sandwich must have.
1/2 ÷ 3 = 1/2 * 1/3 = 1/6 pound per cheese
Each sandwich contains 1/6 pound of cheese from the 1/2 pound of cheese available.
Answers
Answer:
rectangular is 114ft and triangular is 112ft
Step-by-step explanation:
Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT
Since VR = length * width and height
VR = 6*x*3
VR = 18x ft³
Also VT = Length *width * Height/2
VT = (7 * x * 4)/2
VT = 28x/2
VT = 14xft³
Since VR = 32 + VT
18x = 32+(14x)
collect like terms
18x-14x = 32
4x = 32
divide both sides by 4
4x/4 = 32/4
x = 8
Volume of the rectangular prism = 18x
Volume of the rectangular prism = 18*8
Volume of the rectangular prism = 144ft³
Volume of the right triangular prism = 14x
Volume of the rectangular prism = 14*8
Volume of the rectangular prism = 112ft³
The volume of the rectangular prism is 144 ft³ and the volume of the triangular prism is 112 ft³.
To find the volume of each figure, we'll use the formulas for volume of a rectangular prism and volume of a right triangular prism. The volume of a rectangular prism is given by the formula V = L × W × H, where L represents the length, W represents the width, and H represents the height.
The volume of a right triangular prism is given by the formula V = (1/2) × L × W × H, where L represents the length, W represents the width, and H represents the height.
Given the information provided, we have:
- For the rectangular prism: L = 6 ft, W = x (unknown), and H = 3 ft.
- For the triangular prism: L = 7 ft, W = x (unknown), and H = 4 ft.
We are also told that the volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism.
Let's set up the equations and solve for the volume of each figure:
Equation for the volume of the rectangular prism:
V_rectangular = L × W × H = 6 × x × 3 = 18x
Equation for the volume of the triangular prism:
V_triangular = (1/2) * L × W × H = (1/2) × 7 × x × 4 = 14x
We are given that the volume of the rectangular prism is 32 cubic feet more than the volume of the triangular prism. So, we can set up the equation: V_rectangular = V_triangular + 32
Substituting the equations for the volumes: 18x = 14x + 32
Simplifying the equation: 4x = 32
Dividing both sides by 4: x = 8
Now, we can find the volume of each figure by substituting the value of x:
Volume of the rectangular prism: V_rectangular = 18x = 18 × 8 = 144 ft³
Volume of the triangular prism: V_triangular = 14x = 14 × 8 = 112 ft³
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Answers
So
(V² - U²) /2s = a
Answers
The variables aren't the same so no they are not alike
HOPE THAT HELPS YOU :-)))
Answers
As the tosses of the 4 coins are independent of each other we multyiply the probs:-
P(4 tails) = 1/2 * 1/2*1/2*1/2 = 1/16
Answers
Answer:
A, B and C
Step-by-step explanation:
In the equation: 3y=27x
Making y the subject of the equation, we have:
The constant of proportionality between y and x is 9.
We want to determine which relationships have the same constant of proportionality 9.
Option A
y=9x
The constant of proportionality is 9.
Option B
2y=18x
Divide both sides by 2 to obtain: y=9x
The constant of proportionality is 9.
Option C
x=3, y=1/3
Substitution into y=kx gives:
1/3=3k
k=9
The constant of proportionality is 9.
Option D
x=6, y=2/3
Substitution into y=kx gives:
2/3=6k
k=2/3*6=4
The constant of proportionality is 4.
Option E
When x=2, y=18
Substitution into y=kx gives:
18=2k
k=9
However, when x=4, y=27
Substitution into y=kx gives:
27=4k
k=6.75
This is not a proportional relation since the constant of proportionality is not equal.
The correct options are A, B and C
The Proportional relationships y = 9x, 2y = 18x, and y = (1/3)x have the same constant of proportionality as the equation 3y = 27x.
The equation 3y = 27x represents a proportional relationship between y and x with a constant of proportionality of 9. To determine which relationships have the same constant of proportionality, we can compare the ratios of y to x in the given options.
A) y = 9x: The ratio of y to x is 9, which is the same as the constant of proportionality in the original equation. So, this option has the same constant of proportionality.
B) 2y = 18x: Dividing both sides of the equation by 2, we get y = 9x, which has the same constant of proportionality. Therefore, this option also has the same constant of proportionality.
D) y = (1/3)x: The ratio of y to x is 1/3, which is different from the constant of proportionality in the original equation. Therefore, this option does not have the same constant of proportionality.
So, the correct answers are A) y = 9x, B) 2y = 18x, and D) y = (1/3)x.
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