1. 12 pizzas cost $20. What will 20 pizzas costa
2 answers:
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Answer:
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Answer:
a) The height decreases at a rate of ft/sec.
b) The area increases at a rate of ft^2/sec
c) The angle is increasing at a rate of rad/sec
Step-by-step explanation:
Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.
a) Using pythagorean theorem, we have that . From here, we have that
if we differentiate with respecto to t (t is time), by implicit differentiation we get
Then,
.
We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,
b) The area of the triangle is given by
By differentiating with respect to t, using the product formula we get
when b=7, we know that h=24 and dh/dt = -1/12. Then
c) Based on the drawing, we have that
If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get
or, by replacing the value of db/dt
when b = 7, we have that h = 24, then , then
