1) if y = x3 + 2x and dx/ dt = 5, find dy/dt when x = 2. give only the numerical answer. for example, if dy, dt = 3, type only 3.

2)the area a = πr2 of a circular puddle changes with the radius. at what rate does the area change with respect to the radius when r = 5ft?

5π ft2/ft

5 ft2/ft

10π ft2/ft

25π ft2/ft

3)a 25-ft ladder rests against a vertical wall. if the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 20 ft from the wall? answer with 2 decimal places. type your answer in the space below. if your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

a) 70

b) 10π ft²/ft

c) 0.24 ft/sec

Step-by-step explanation:

1) y = x³ + 2x

or

=

at  and x = 2

=

or

= 60 + 10 = 70

2) A = πr² ft²

or

= 2(πr)

at r = 5 ft

= 2(π × 5) ft²/ft

or

= 10π ft²/ft

3) From Pythagoras theorem

Base² + Perpendicular² = Hypotenuse²

Thus,

B² + P² = H²  .............(1)

here, H = length of the ladder

P is the height of the wall

B is the distance from the wall at bottom

or

B² + P² = 25²       ...........(1)  

at B = 20 ft

20² + P² = 25²        

or

P² = 625 - 400

or

P = √225

or

P = 15 ft

differentiating (1) with respect to time, we get

at B = 20 ft, and P = 15 ft

⇒ 2(20)(0.18) + = 0

or

= - 7.2

or

= - 0.24 ft/sec (Here negative sign depicts the ladder slides down)

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y