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2 years ago

When Angelina was born, her grandparents deposited $3000 into a college savings account

Mathematics

1 answer:

ASHA 777 [7]2 years ago

8 0

Answer:

$4105.71

Step-by-step explanation:

1. Add 100 to 4%. When you do this, you get 104.

2. Move the decimal in 104 two times to the left. This will result in 1.04

3. Now you need to solve 3,000(1.04^8)

4. 1.04^2 = 1.36856905041

5. 1.36856905041 x 3,000 = 4105.70715122

6. You round 4105.70715122 to the nearest tenth because it's money. This will result in 4105.71

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find the width of radius r if the width w of the shaded region is 2cm and its area is 176cm^2, use 22/7 for pi (its a full circl

arsen [322]

The area of a shape is the amount of space it can occupy.

<em>The value of r is 13</em>

From the question (see attachment), we have:

$\mathbf{A =176}$ --- area of the shaded region

$\mathbf{w = 2}$ --- the width of the shaded region

The area of the complete circle would be:

$\mathbf{A_1 =\pi (r + w)^2}$

The area of the small circle is:

$\mathbf{A_2 =\pi r^2}$

So, the area of the shaded region is:

$\mathbf{A = A_1 - A_2}$

Substitute known values

$\mathbf{176 =\pi (r + w)^2 - \pi r^2 }$

Substitute 2 for w

$\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }$

Expand

$\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }$

Open brackets

$\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }$

Cancel out line terms

$\mathbf{176 =4\pi r + 4\pi }$

Divide through by 4

$\mathbf{44 =\pi r + \pi }$

Factor out pi

$\mathbf{44 =\pi(r+ 1) }$

Divide through by pi

$\mathbf{r + 1= \frac{44}{ \pi} }$

Substitute 22/7 for pi

$\mathbf{r + 1= \frac{44}{ 22/7} }$

Using a calculator, we have

$\mathbf{r + 1= 14}$

Solve for r

$\mathbf{r= 14 -1}$

$\mathbf{r= 13}$

Hence, the value of r is 13

Read more about areas of circles at:

brainly.com/question/23328170

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1 year ago