Answer: Last Option
Step-by-step explanation:
By definition the sum of the internal angles of a triangle must always be equal to 180 °.
This means that:
Now we solve the equation for the variable x
We subtract 12 in both barks of the equation
Divide by 3 on both sides of the equation
Finally the measure of angle ABC is: (56-5)° = 51°
Answer:
2 inches per hour
Step-by-step explanation:
2 1/2 hours is equivalent to 150 minutes.
Set up a proportion; let x equal inches of rain
=
Cross multiply -> 150x=300
Divide both sides by 150 to get -> x=2
Answer:
The tip of the man shadow moves at the rate of
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y =
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
----(1)
We are given . Plug in the equation (1), we get
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
