Answer:
A
Step-by-step explanation:
Two sides of a triangles sum must be larger than the third side.
Answer:
46
Step-by-step explanation:
a + 4(b - 3)
Substitute the values for a and b.
10 + 4(12 - 3)
Subtract inside the parenthesis.
10 + 4(9)
Multiply.
10 + 36
Add.
46
Answer:
The answer is 3.703 repeating
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Step-by-step explanation:
Answer:
Step-by-step explanation:
This situation models a right triangle. The hypotenuse is the ladder which has a given length of 25 meters. Let's call the ground (the base of the triangle) x, and the vertical wall (the height of the triangle) y. Pythagorean's Theorem tells us that
This is our main formula.
We are given that the rate the distance between the bottom of the ladder and the wall is increasing at 3.5 m/min. This is the rate of change of x, or dx/dt. We are wanting to find the rate of change of the distance between the top of the ladder and the ground, dy/dt, when y = 7. Let's find the derivative of our equation first, then fill in what we are given:
From our given, we can fill in the dx/dt, and the y. We are looking for dy/dt, but we are missing what the x value is. Let's find that by going back to Pythagoreans Theorem and filling in y to find x:
and
so
x = 24
Now let's fill in our derivative:
and
and
so
Within the context of our problem, this means that the height of the ladder is decreasing at a rate of 12 m/min. The negative value lets us know that the height is decreasing, not that the height is negative.