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3 years ago

Find the length of arc AD. Use 3.14 for .

Mathematics

1 answer:

Alexxandr [17]3 years ago

6 0

Answer:

Length of arc AD = 15.7 cm

Step-by-step explanation:

Length of arc = $\frac{\theta}{360}(2\pi r)$

Here, θ = Central angle subtended by the arc

r = radius of the circle

From the picture attached,

Central angle subtended by arc AD = 360° - (180° + 66.4°)

= 113.6°

Length of arc AD = $\frac{(113.6)}{360}(2\pi )(7.9)$

= $\frac{113.6}{360}(2)(3.14)(7.9)$

= 15.655 cm

≈ 15.7 cm

Length of arc AD = 15.7 cm

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Answer:

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Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

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And remember that the sum of these three angles must be equal to 180.

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Let's take these equations

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If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

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Combine like terms;

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Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

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The amount will be equal to $1348.07. The correct option is A.

<h3>What is compound interest?</h3>

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

$\rm A = P(1+\dfrac{r}{n})^{nt}$

Compound Interest Formula:

A = Account Balance

P = Principle/Initial Amount

r = Rate of Interest (decimal)

n = Number of times compounded (per year)

t = Number of Years

Given Information

Account Balance = ?

It is given that the balance after 15 years in a savings account earns 2% interest compounded bi-monthly when the initial deposit is 1000.

This is because we are gaining money, so the multiplier should be greater than 1. We already added 1, which is 100% so you simply add the 0.02 for the extra 2%.

Number of times compounded per year = 6

This is because it is being compounded bi-monthly, or once every 2 months. 12 months divided by 2 months is 6 months, so 6 times a year.

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Solve by plugging the given values into the formula.

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Therefore, the amount will be equal to $1348.07. The correct option is A.

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