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3 years ago

What is the area of the drumhead on the drum shown below? Round to the nearest 10th.14 inches

1 answer:

5 0

The formula for finding the area of a circle is

a = pi × radius^2

Since the diameter is 14 inches, the radius is 7 inches, so to solve...

a = pi × 7^2
a = 3.14 × 49
a = 153.86

Rounded to the nearest tenth...

153.9 inches^2

You might be interested in

Find the radius of convergence, then determine the interval of convergence

galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.

First aₙ is noted and then aₙ₊₁ is noted.

For ∑ aₙ, aₙ and aₙ₊₁ is noted.

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = β

If β < 1, then the series converges

If β > 1, then the series diverges

If β = 1, then the series inconclusive

Here $a_{k}$ = $\frac{(x+2)^{k}}{\sqrt{k} }$ and $a_{k+1}$ = $\frac{(x+2)^{k+1}}{\sqrt{k+1} }$

Now limit is taken,

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|$

= $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|$

= $\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|$

= $|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}$

= $|{x+2 }|$ < 1

- 1 < ${x+2 }$ < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

#SPJ1

5 0

1 year ago

Read 2 more answers

The given angles Y and Z are supplementary angles. The measure of angle is 50 degrees. The measure of angle is five times the va

Minchanka [31]

Answer:

x is 10°, expression of angle could be

180 - z or 180 - 5x, the value of y is 130° if z is 50°

Step-by-step explanation:

y + z is 180°

x is 50/5 = 10°

z is 50°

y is 180 - z = 180 - 50 = 130°

y can be 180 - 5x or 180 - z

8 0

3 years ago

Solve the Equation 4(2x+1)=5x+9+3x?

Scorpion4ik [409]

8x+4=5x+9+3x

combine:5+3=8x

subtract 8x-8x=0

subtract 4 from 9=5

0=5

4 0

2 years ago

American Eagle is having a 60 % clearance sale on all summer merchandise. The consumer purchased $342.57 of the summer merchandi

Virty [35]

Answer:

$143.88

Step-by-step explanation:

Look at image above...

I did not add this to the picture but to get the new total of $137.03, you need to subtract $205.54 (the 60% off) from the original total.

6 0

2 years ago

A line goes through the points (9,8) and (4,-12). What is the slope of the line? Show your work Write the equation of the line i

RoseWind [281]

The slope of the line is 4

The point slope form of the line can be written as (y - 8) = 4(x - 9)

The slope intercept form of the line is y = 4x - 28

In order to find the slope you will need to use the formula for slope. It is included below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - -12)/(9 - 4)

m = (8 + 12)/(9 - 4)

m = 20/5

m = 4

Now that we have the slope, we can plug it into point slope form along with one of the points.

(y - y1) = m(x - x1)

(y - 8) = 4(x - 9)

Now to get to the slope-intercept form of the line, we can simply manipulate the point-slope form until it is in y = mx + b

(y - 8) = 4(x - 9) ----> Distribute the 4

y - 8 = 4x - 36 -----> Add 8 to both sides

y = 4x - 28

5 0

3 years ago