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Alex_Xolod [135]

3 years ago

6

A pair of shoes costs $70.00. How much will the customer pay after 7% sales tax is added to the purchase?

1 answer:

ANEK [815]3 years ago

5 0

Answer:

$74.90

Step-by-step explanation:

If $70 is your original price, you would need to multiply it by 1.07, because that is 107%.

Since the original price is 100% of the price, and sales tax is another 7% of the price, you are multiplying the original price by 107%, again making $74.90.

Do you understand?

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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is...

enot [183]

Answer:

c. $\frac{1}{\pi}$

Step-by-step explanation:

We have been given that the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

We will use derivatives to solve our given problem.

We know that area (A) of a circle is equal to $A=\pi r^2$ .

Let us find derivative of area function with respect to time.

$\frac{dA}{dt}=\frac{d}{dt}(\pi r^2)$

Bring out constant:

$\frac{dA}{dt}=\pi \frac{d}{dt}(r^2)$

Using power rule and chain rule, we will get:

$\frac{dA}{dt}=\pi(2r)* \frac{dr}{dt}$

$\frac{dA}{dt}=2\pi r*\frac{dr}{dt}$ Here $\frac{dr}{dt}$ represents change is radius with respect to time.

We have been given that area of an expanding circle is increasing twice as fast as its radius in linear units. We can represent this information in an equation as:

$\frac{dA}{dt}=2\frac{dr}{dt}$

$2\pi r* \frac{dr}{dt}=2\frac{dr}{dt}$

$2\pi r=2$

$\frac{2\pi r}{2\pi}=\frac{2}{2\pi}$

$r=\frac{1}{\pi}$

Therefore, the radius is $\frac{1}{\pi}$ and option 'c' is the correct choice.

6 0

3 years ago

PLEASE show work also for this one if you wants points.

sammy [17]

I would help you but I’m trying to do my hw too srry maybe next time

7 0

3 years ago

Short on time, please help!

kvv77 [185]

56.3% hope it helped ok

3 0

3 years ago

The sum of the two areas of two circles is the 80x square meters. Find the length of a radius of each circle of them is twice as

Alborosie

Answer:

$r = 4m$ --- small circle

$R =8m$ --- big circle

Step-by-step explanation:

Given

$Area = 80\pi\ m^2$ -- sum of areas

$R = 2r$

Required

The radius of the larger circle

Area is calculated as;

$Area = \pi r^2$

For the smaller circle, we have:

$A_1 = \pi r^2$

For the big, we have

$A_2 = \pi R^2$

The sum of both is:

$Area = A_1 + A_2$

$Area = \pi r^2 + \pi R^2$

Substitute: $R = 2r$

$Area = \pi r^2 + \pi (2r)^2$

$Area = \pi r^2 + \pi *4r^2$

Substitute $Area = 80\pi\ m^2$

$80\pi = \pi r^2 + \pi *4r^2$

Factorize

$80\pi = \pi[ r^2 + 4r^2]$

$80\pi = \pi[ 5r^2]$

Divide both sides by $\pi$

$80 = 5r^2$

Divide both sides by 5

$16 = r^2$

Take square roots of both sides

$4 = r$

$r = 4m$

The radius of the larger circle is:

$R = 2r$

$R =2 * 4$

$R =8m$

3 0

3 years ago

Convert this number expressesed in standard form to scientific notation 28,500,000

Finger [1]

2.85 x 10^7 is the answer

3 0

3 years ago

Read 2 more answers