11.09.2021

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY MIND A cup has the shape of a right circular cone. The height of the cup is 16 cm, and the radius of the
cm opening is 4 cm. Water is being poured into the cup at a constant rate of 3 cm. At what rate, in
cm per second, is the water level rising when the depth of the water in the cup is 6 cm? (The volume of a cone of height h and radius r is given by V=1/3pir^2h.

1. 1/64pi
2. 3/pi
3. 4/3pi
4. 9/4pi

. 0

Step-by-step answer

09.07.2023, solved by verified expert
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3.  PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Step-by-step explanation:

Volume of a cone:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

(where r is the radius and h is the height)

Given:

h = 16 cmr = 4 cm

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Therefore, substitute PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42 into the volume formula to find the volume of the cone in terms of h:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Differentiate with respect to h:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Volume is increasing at a constant rate of 3cm/s:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Use the chain rule to find PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

When h = 6:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

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Mathematics
Step-by-step answer
P Answered by Specialist

3.  \dfrac{4}{3 \pi}

Step-by-step explanation:

Volume of a cone:

V=\dfrac13\pi r^2h

(where r is the radius and h is the height)

Given:

h = 16 cmr = 4 cm

\implies r=\dfrac14h

Therefore, substitute r=\frac14h into the volume formula to find the volume of the cone in terms of h:

\implies V=\dfrac13\pi \left(\dfrac14h\right)^2h

\implies V=\dfrac{1}{48}\pi h^3

Differentiate with respect to h:

\implies \dfrac{dV}{dh}=3 \cdot \dfrac{1}{48} \pi h^2=\dfrac{\pi h^2}{16}

Volume is increasing at a constant rate of 3cm/s:

\implies \dfrac{dV}{dt}=3

Use the chain rule to find \dfrac{dh}{dt}

\implies \dfrac{dh}{dt}=\dfrac{dV}{dt}\times\dfrac{dh}{dV}

\implies \dfrac{dh}{dt}=3\times\dfrac{16}{\pi h^2}

\implies \dfrac{dh}{dt}=\dfrac{48}{\pi h^2}

When h = 6:

\implies \dfrac{dh}{dt}=\dfrac{48}{\pi \cdot 6^2}=\dfrac{4}{3 \pi}

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years

Mathematics
Step-by-step answer
P Answered by PhD

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

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