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4 years ago

Find the area of a semicircle

Mathematics

2 answers:

Furkat [3]4 years ago

6 0

Answer:

18pi, or 56.52

Step-by-step explanation:

To start off, if you were to find the area of any whole circle, you would use the formula: pi x radius^2 = area of circle

However, since this is a semi-circle (half of a whole circle) you would divide the whole expression by 2, and then solve:

(pi x radius^2)/2 = area of semi-circle

(pi x 6^2)/2 = area of semi-circle

(36 x pi)/2 = area of semi-circle

18 x pi = area of semi-circle

18 x 3.14 = area of semi-circle

56.52 = area of semi-circle

Inessa [10]4 years ago

6 0

The area of a circle is

$\pi \: {r}^{2}$

So the area of a semicircle would be half of that, or

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

So just plug in the radius, six, to get this

$18\pi$

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Solving a percent mixture problem using a linear equationSamantha vEspelTwo factory plants are making TV panels. Yesterday, Plan

Alborosie

ANSWER

Number of panels produced by plant B: 20000

EXPLANATION

First we have to name the variables. We're looking for the number of panels produced by plant B and also we don't know the number of panels produced by plant A.

Let x be the number of panels produced by plant A and y the number of panels produced by plant B.

We know that plant A produced 7000 fewer panels than plant B. This as an equation is:

$x=y-7000$

To solve this we need to find another equation, because we have two variables.

The other equation is the one with the defective panels. The total number of defective panels produced by both plants is 860, and we know that represents the 2% of produced panels from plant A and 3% of produced panels from plant B. To find the number that represents that percentage we divide the percentage by 100 and multiply by the total amount. For the 2% of plant A this is:

$\frac{2}{100}\cdot x=0.02x$

And the 3% of plant B is:

$\frac{3}{100}\cdot y=0.03y$

So the second equation is:

$0.02x+0.03y=860$

Since we only want to find y, which is the number of panels produced by plant B, we can use the substitution method. Substitute the first equation into the second - in other words, replace x in the second equation by y - 7000:

$0.02(y-7000)+0.03y=860$

To solve for y, first apply the distributive property of multiplication:

$\begin{gathered} 0.02y-0.02\cdot7000+0.03y=860 \\ 0.02y-140+0.03y=860 \end{gathered}$

Add like terms:

$\begin{gathered} (0.02y+0.03y)-140=860 \\ 0.05y-140=860 \end{gathered}$

Add 140 on both sides of the equation:

$\begin{gathered} 0.05y-140+140=860+140 \\ 0.05y=1000 \end{gathered}$

And divide both sides by 0.05:

$\begin{gathered} \frac{0.05y}{0.05}=\frac{1000}{0.05} \\ y=20000 \end{gathered}$

This result means that <em>plant B produced 20000 TV panels in total.</em>

7 0

1 year ago

(05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 9 inches and the height is

Aneli [31]

The area at the top of the plate is 63 inches squared

4 0

4 years ago

Read 2 more answers

(No links) HELP ME THIS IS THE LAST QUESTION

Volgvan

Part 1

<h3>Answer: (x+5)(x+10) - 50 = 126</h3>

Other answers are possible.

-------------

Explanation:

The old width was 5, but then it increases to x+5. The old length was 10, but now it's x+10.

The area of any rectangle is length times width.

So the area of the larger rectangle is (x+5)(x+10). Subtract off the old area of 5*10 = 50 and we get (x+5)(x+10) - 50 as the area of the L shape. Set this equal to 126 to finish setting up the equation. This is one possible answer out of many others. This is because we could expand out the (x+5)(x+10) into x^2+10x+5x+50 or simplify that to x^2+15x+50, as two possible options.

==========================================================

Part 2

<h3>Answer: x = 6</h3>

-------------

Explanation:

Solve the equation we set up in the previous part

(x+5)(x+10) - 50 = 126

x^2+10x+5x+50-50 = 126

x^2+15x = 126

x^2+15x-126 = 0

Apply the quadratic formula from here

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(15)\pm\sqrt{(15)^2-4(1)(-126)}}{2(1)}\\\\x = \frac{-15\pm\sqrt{729}}{2}\\\\x = \frac{-15\pm27}{2}\\\\x = \frac{-15+27}{2} \ \text{ or } \ x = \frac{-15-27}{2}\\\\x = \frac{12}{2} \ \text{ or } \ x = \frac{-42}{2}\\\\x = 6 \ \text{ or } \ x = -21\\\\$

Another method you could use is factoring, so you could say:

x^2+15x-126 = 0

(x-6)(x+21) = 0

x-6 = 0 or x+21 = 0

x = 6 or x = -21

The issue with this is that it may take a while to do this trial and error approach.

Whichever method you used, you'll end up with two solutions. One of those solutions doesn't make sense though. We can't have a negative length or distance value, so we ignore x = -21.

The only practical solution is x = 6

If x = 6, then the old height goes from 5 to x+5 = 6+5 = 11

If x = 6, then the old length goes from 10 to x+10 = 6+10 = 16

The new larger rectangle is 11*16 = 176 sq ft, in which we subtract off the 50 sq ft to get 176-50 = 126 sq ft, and this matches with the 126 given to us. Therefore, the answer is confirmed.

8 0

3 years ago

If g(x)=2(x-4), find the value of x if g(x)=20

Softa [21]

Answer:

32.64

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles a

dimaraw [331]