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Klio2033 [76]
3 years ago
13

The radius of a circle is 2 miles. What is the circle's

Mathematics
1 answer:
4vir4ik [10]3 years ago
5 0

Answer:

12.56

Step-by-step explanation:

4 ×3.14 to get 12.56

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Calculate the total area of the shaded region.
LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

7 0
2 years ago
Two cars traveling toward each other are 250 miles apart. Car a is traveling 15 miles per hour faster than car
Anon25 [30]

Let car  b be travelling at x  mph.  as they are travelling towards each other their speed of approach is (x + x + 15 ) mph.  So we have the equation

speed = distance / time

2x + 15 =  250 / 2

2x = 125 - 15 = 110

x = 55 mph

Car b travels at 55 mph and car a travels at 70 mph  Answer

3 0
3 years ago
What is an equation of the line that passes through the points (1, -7) and (-4, 8)?
melomori [17]
<h2>Answer:    y + 7  =  -3 (x - 1)</h2>

Step-by-step explanation:

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                                       

                                          =  (- 7 - 8) ÷ ( 1 - (- 4))

                                         =    - 15  ÷  5

                                         =  - 3

We can now use the point-slope form to write the equation for this line:

        y - y₁ = m(x - x₁) where (x₁ , y₁) = (1, -7)

             y - (-7) =  -3 ( x  -  1)

              y + 7  =  -3 (x - 1)

3 0
3 years ago
Which statements are true? Check all that apply.
Dvinal [7]

Answer:

3is the answer because t

s apply

Step-by-step explanation:

3 0
2 years ago
A French restaurant used 848,540 ounces of cream last year. This year, due to a menu update, it used 40% less. How much cream di
Vsevolod [243]

Answer:

339416

Step-by-step explanation:

848,540 * 40/100 = 339416

4 0
3 years ago
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