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Vlad [161]
3 years ago
14

A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best desc

ribes the change in the radius of the original circle?
Mathematics
1 answer:
kogti [31]3 years ago
3 0
Area of a circle is directly proportional to the square of radius of the circle while the circumference is proportional to the radius of the circle. This means that if the radius of a circle is increased x times, then its area will be increased to x^2 times the original area, and the circumference will increase to x times the original circumference.

Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.

We can calculate exact area and circumference of a circle from its radius using the following equations:

Area of circle = (pi/4)*r^2

Circumference of circle = 2*pi*r

Where r is the radius of the circle.

I know this is a lot, sorry.
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10=4y <br>I keep help pleasee​
uranmaximum [27]

Answer:

y=5/2

Step-by-step explanation:

10=4y divide four by both sides to get y by itself  10/4=4y/4 so that equals 10/4=y  reduce it so 5/2=y

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Graphing in Point-Slope Form y−y1=m(x−x1) <br> ​<br> Graph the equation y+7=−45(x−4) ?
nevsk [136]

Answer:

<h2>The graph is in the attachment.</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

<em>m</em><em> - slope</em>

<em>(x₁, y₁)</em><em> - a point on a line</em>

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

We have the equation in a point-slope form:

y+7=-\dfrac{4}{5}(x-4)

y-(-7)=-\dfrac{4}{5}(x-4)

Therefore we have one point: <em>(4, -7)</em><em>.</em>

<em>Convert to the slope-intercept form:</em>

y+7=-\dfrac{4}{5}(x-4)              <em>use the distributive property</em>

y+7=-\dfrac{4}{5}x+\left(-\dfrac{4}{5}\right)(-4)

y+7=-\dfrac{4}{5}x+\dfrac{16}{5}

y+7=-\dfrac{4}{5}x+3\dfrac{1}{5}          <em>subtract 7 from both sides</em>

y=-\dfrac{4}{5}x-3\dfrac{4}{5}

Put <em>x = -1</em><em> </em>to the equation:

y=-\dfrac{4}{5}(-1)-3\dfrac{4}{5}=\dfrac{4}{5}-3\dfrac{4}{5}=-3

Therefore we have the second point <em>(-1, -3)</em>.

3 0
3 years ago
Cos^3a-sin^3a/cosa-sina
KIM [24]

Answer:

1 + cosa sina

Step-by-step explanation:

\frac{cos^3a-sin^3a}{cosa-sina}

cos³a - sin³a ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

cos³a - sin³a

= (cosa - sina )(cos²a + cosa sina + sin²a)

= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]

Then

\frac{cos^3a-sin^3a}{cosa-sina}

= \frac{(cosa-sina)(1+cosasina)}{cosa-sina} ← cancel (cosa - sina) on numerator/ denominator

= 1 + cosa sina

8 0
2 years ago
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