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A circular oil slick is expanding at a rate of 3m/min. How fast is the area of the oil slick changing when the diameter is 48 me

olga55 [171]

Answer:

$48\pi \:m/min$

Step-by-step explanation:

Diameter = 48 m

Therefore radius r = 48/2 = 24 m

$Area \: of \: circular \: oil \: slick \\ A = \pi {r}^{2} \\ differentiating \: w \: r \: to \: t \: on \: \\ both \: sides \\ \\ \frac{dA}{dt} = \frac{d}{dt} (\pi {r}^{2} )\\ \\ \frac{dA}{dt} =\pi \frac{d}{dt} {r}^{2} \\ \\ \frac{dA}{dt} =\pi \times 2{r}\\ \\ \frac{dA}{dt} =2\pi {r} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =2\pi \times {24} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =48\pi \: m \: per \: min$

6 0

3 years ago

The amount in a savings account after x years is represented by A = P(1 + r)* Suppose A = 2100(1.04)* models the amount in your

koban [17]

Answer:

B. The rate of increase is 4%

D. 2100 represents the initial deposit.

Step-by-step explanation:

Look at the equation modeling the savings account.

A = 2100(1.04)

1.04 represent the percent the current account is of the previous one.

That is a 4% increase, which remains the same, so B is one of the correct answers.

2100 was the original deposit, so D is correct as well.

Knowing this, B and D are correct.

7 0

3 years ago

The graph is of a function in the form p(t)=a*b^t. What is the function.

Vladimir [108]

Answer:

Exponential Function

Step-by-step explanation:

An exponential function has the graph $f(x) = ab^x$

A parabola has the graph $f(x) = a(bx-h)^2+k$

A linear has the graph $y=mx+b$

5 0

3 years ago

How does the order of steps in solving an equation relate to order of operations

Akimi4 [234]

If you dont follow the right steps in the right order or properly, you won't end up with the right answer:
For example 3 x 5 + 7
If you do multiplication then add you get 22 which is correct.... but!!
If you add then do multiplication you get 36 which isn't right

Remember always follow PEMDAS
P-Parenthesis
E-Exponents
M or D- Multiplication or division (go left to right)
A or S- Addition or Subtraction (go left to right)

5 0

4 years ago

For questions 6 – 10, find the unknown side length. number 10

Sergeu [11.5K]

Answer: $\begin{gathered} s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \\ s\text{ = 14.142 \lparen decimal approx.\rparen} \end{gathered}$

Explanation:

10) Given:

hypotenuse = 20

angle = 45°

To find:

length of s

angle = 45

opposite = side opposite the angle = s

To find the value of s, w will apply sine ratio (SOH)

$sin\text{ 45 = }\frac{opposite}{hypotenuse}$ $\begin{gathered} sin\text{ 45 = }\frac{s}{20} \\ s\text{ = 20sin45} \\ sin\text{ 45 = }\frac{\sqrt{2}}{2} \\ \\ s\text{ = 20}\times\frac{\sqrt{2}}{2} \\ s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \end{gathered}$ $\begin{gathered} s\text{ = 20sin45} \\ s\text{ = 20\lparen0.7071\rparen} \\ s\text{ = 14.142 \lparen decimal approximation\rparen} \end{gathered}$

3 0

1 year ago