Related Rates
1 answer:
Answer:
- 0.382 m/min
- 8 1/3 ft/s
Step-by-step explanation:
1. The rate of change of volume is ...
V = πr^2h
V' = πr^2h'
h' = V'/(πr^2) = (3 m^3/min)/(π(5 m)^2) = 0.12/π m/min
h' ≈ 0.382 m/min
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2. In the attached, ∆PCM ~ ∆MXS, so we can write the proportion ...
x/9 = s/15 . . . . where x = BX and s = BS in the diagram
Multiplying by 15 gives ...
s = (15/9)x = (5/3)x
Then the rate of change is ...
s' = (5/3)x' = (5/3)(5 ft/s)
s' = 8 1/3 ft/s
The tip of the shadow is moving at 8 1/3 feet per second.
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Answer:
Given the equation: 9(x+1) = 25+x
Distributive property of multiplication over addition states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately i,e,
Then, by using distributive property on LHS in the given equation we have;
9x+9 =25 +x
Subtract 9 from both the sides;
9x+9-9=25+x-9
Simplify:
9x = 16+x
Subtract x from both the sides we get;
9x-x=16+x-x
Simplify:
8x=16
Divide both sides by 8 we have;
On Simplify:
x =2
Therefore, the value of x for the equation 9(x+1) = 25+x is, 2