Answer:
A.
Step-by-step explanation:
Gracie’s pool is circular with a diameter of 30 feet and height of 6 feet. How much water can the pool hold?
1 answer:
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Carlos made the mistake that he did not combine like terms (3 x and 2 x) properly and did not use addition property of equality.
<u>Step-by-step explanation:</u>
Carlos did the work as 3 x + 2 x - 6 = 24
We need to find his mistake that he made in above given.
Here, he did not add the like terms (3 x and 2 x)
3 x + 2 x = 5 x
Therefore, his work should be
5 x - 6 = 24
Also, he did not use addition property of equality. It means the equation remains same even though the same number gets added on both sides. It would be
5 x - 6 = 24
+ 6 = + 6
-----------------------
5 x = 30
Dividing 30 by 5, we get answer as '6'. Hence,
= 6
So, stated the above two are the mistakes found in carlos work.
Answer:
6.667 ft/s
Step-by-step explanation:
Given
Height of street light = 15ft
Height of man = 6ft
Speed away from pole = 4ft/s
Let x represents the distance between the man and the pole, and Let y represents the distance between the tip of the man's shadow to the pole.
This forms a similar triangle (see attachment below).
From similar triangles, we have
(y - x)/6 = y/15 ----- Solve equation
15(y - x) = 6 * y
15y - 15x = 6y ---- Collect Like Terms
15y - 6y = 15x
9y = 15x --- divide through by 9
y = 15x/9
y = 5x/3 ---- differentiate with respect to time, t
dy/dt = 5/3 dx/dt
dx/dt represents rate of change of distance per time = 4ft/s
while dy/dt represents rate of movement of his shadow tips
dy/dt = 5/3 * 4
dy/dt = 20/3 = 6.667 ft/s
