What's 80 billion / 3.2 569

An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the

julia-pushkina [17]

Answer:

The rate of decrease is: $43.2mm^3/min$

Step-by-step explanation:

Given

$l = 18mm$

$\frac{dl}{dt} = -0.8mm/min$ ---- We used minus because the rate is decreasing

Required

Rate of decrease when: $l = 18mm$

The volume of the cube is:

$V = l^3$

Differentiate

$\frac{dV}{dl} = 3l^2$

Make dV the subject

$dV = 3l^2 \cdot dl$

Divide both sides by dt

$\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}$

Given that: $l = 18mm$ and $\frac{dl}{dt} = -0.8mm/min$

$\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)$

$\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min$

$\frac{dV}{dt} = -43.2mm^3/min$

<em>Hence, the rate of decrease is: 43.2mm^3/min</em>

8 0

3 years ago

A Train crosses a bridge 100 m in 45 sec at a speed of 60 km/h find a time taken by the train to cross a clock tower

yulyashka [42]

Ans is 351/8.

hope it is helpful

8 0

2 years ago

Lucy and Donavan measured the length of the school garden. Lucy's measurement is 11.3 meters and Donavan's measurement is 113 ce

Zolol [24]

Yes because of u convert 113 centimeters into inches you still get 11.3 but the garden could be a square I think this is right I don't know for sure

8 0

2 years ago

1. Taylor needs to purchase a car. The car Taylor plans to purchase costs $10,000. Taylor has saved $2,000 to use as a down paym

Alexxandr [17]

Answer:

a. The amount Taylor will need to finance is $8,000

b. The amount Taylor pays as interest in one year is $400

Step-by-step explanation:

The given parameters of the financing for the car are;

The cost of the car Taylor plans to purchase, C = $10,000

The amount Taylor has saved to be used as down payment, S = $2,000

The interest rate of the credit Taylor is offered = 5%

The duration given for repayment of the loan = 5 years

a. To purchase the car, the amount Taylor will need to finance, 'P', is given as follows;

P = C - S

∴ P = $10,000 - $2,000 = $8,000

b. The amount of interest on the loan in one year, 'I', is given by the following formula;

$I = \dfrac{P \times R \times T}{100}$

Where;

I = The interest payed

P = The principal amount taken as loan = $8,000

R = The interest rate = 5% APR

T = The time period the interest is applied = 1 year

Plugging in the values, we get;

$I = \dfrac{\$ \, 8,000 \times 5 \times 1}{100} = \$ \, 400$

The interest Taylor will pay on the loan in one year, I = $4,00

7 0

3 years ago

Let g(x) = 2x and h(x) = x^2 + 4. Find the value.(g o h) (0)a) 4b) 8c) 0d) 16

Paul [167]

$\begin{gathered} \text{Given} \\ g(x)=2x \\ h(x)=x^2+4 \end{gathered}$

Solve for (g o h)(x)

$\begin{gathered} (g\circ f)(x)=g\big(f(x)\big) \\ (g\circ f)(x)=g(x^2+4) \\ (g\circ f)(x)=2(x^2+4) \\ (g\circ f)(x)=2x^2+8 \end{gathered}$

Next substitute x = 0

$\begin{gathered} (g\circ f)(x)=2x^2+8 \\ (g\circ f)(0)=2(0)^2+8 \\ (g\circ f)(0)=8 \end{gathered}$ $\text{Therefore, }(g\circ f)(0)=8$

5 0

1 year ago

What's 80 billion / 3.2 569​

What's 80 billion / 3.2 569