Answer:
36. m = (3/2)n
37. s = 5tv
38. c = 3/d
Step-by-step explanation:
Each of the variations in these problems has its own associated equation. You only need to make use of the given values to find the constant of variation (k) and fill in the equation.
- direct variation: y = kx; k = y/x
- joint variation: z = kxy; k = z/(xy)
- inverse variation: y = k/x; k = xy
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36. The constant for direct variation is the ratio of the given values:
k = m/n = 18/12 = 3/2
Then the equation for the direct variation is ...
m = (3/2)n
___
37. The constant for the joint variation is the expression ...
k = s/(tv) = 8/((4/5)·2) = 8/(8/5) = 8·5/8 = 5
Then the equation for the joint variation is ...
s = 5tv
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38. The constant for the inverse variation is the product of the given values:
k = cd = (1/4)(12) = 3
Then the equation for the inverse variation is ...
c = 3/d
Answer:
k = 7
Step-by-step explanation:
9.1k = 63.7
/9.1 /9.1
k = 7
Check your answer:
9.1k = 63.7
9.1 (7) = 63.7
63.7 = 63.7
This statement is true.
Hope this helps!
Answer:
D
Step-by-step explanation:
I answered it right
Answer:
Step-by-step explanation:
We'll call height h.
The equations of a cone and sphere are:
Cones: 1/3 * base area * h
Spheres: 4/3 π * r³
The base area of a cone would be the area of a circle equation:
π * r² = π * 2² = 4π.
Because you're converting from sphere to cone, you would set their equations equal to each other.
1/3 * 4π * h = 4/3 π * 5³
Next, isolate h.
h = (4/3 π * 5³)/(1/3 * 4π)
h = 125
Hope this helps!
Answer:
a. No
b. Yes
Step-by-step explanation:
a.
x - 4 = 12
x - 4 + 4 = 12 + 4
x = 16
16 ≠ 8
Therefore, the following value given for problem a is not a solution to the given equation.
b. (3 + x)/4 = 3
(3 + x)/4 * 4 = 3 * 4
3 + x = 12
3 + x - 3 = 12 - 3
x = 9
9 = 9
Therefore, the following value given for problem b is a solution to the given equation.