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2 years ago

What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit.

Mathematics

2 answers:

Aleonysh [2.5K]2 years ago

5 0

Answer:

75% of the area of the circle is 6 square units.

Step-by-step explanation:

Given:

Circumference of a circle = 10 units

Now we have to find the radius of the circle, then we have to find the area of the circle.

Circumference of a circle = 2*π*r [π = 3.14]

2*3.14*r = 10

6.28r = 10

Dividing both side by 6.28, we get

r = 10/6.28

r = 1.59

Now let's find the area of the circle.

The area of the circle = π*r^2

= 3.14*1.59*1.59

The area of the circle = 7.94, which is 100 %

Now we have to find the 75% of the area of the circle.

75% = 0.75

75% of the area of the circle = 0.75*7.94

= 5.95

To round off to the nearest whole number, we get 6 square units.

Zolol [24]2 years ago

3 0

Circumference = 2 pi r = 10

r = 10 / 2 pi

75% of the error = 0.75 * pi * (10 / 2pi)^2

= 5.968 square unts

6 to nearest square unit

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frutty [35]

Answer:

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

$g(x) =e^{x^3}$

we know that $\frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)$

$g'(x) =e^{x^{3}}(3 x^{2})$

$g'(x) =3 x^{2} e^{x^{3}}$

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

$m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}$

using the equation of line:

$(y-y_1)=m(x-x_1)$

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

$(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\$

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

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2 years ago

What is the largest two-digit number that is a multiple of 5 and 10 at the same time?

alexandr402 [8]

Answer:

Step-by-step explanation:

90/10= 9

90/5= 18

No number larger than 90 would work.

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2 years ago

A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater

BartSMP [9]

Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
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h = 5/x² (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
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C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
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