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3 years ago

What is the area of the shaded region on the graph shown?

Mathematics

1 answer:

Sindrei [870]3 years ago

5 0

Answer:

As Doris Day said: Good morning to you

Answer 27/2

Step-by-step explanation:

$f(x)=-x^3+5x\\F(x)=-\dfrac{x^4}{4} +\dfrac{5x^2}{2} \\F(2)=\dfrac{-16}{4}+\dfrac{20}{2} =6\\\\F(-1)=\dfrac{-1}{4} +\frac{5}{2} =\dfrac{9}{4} \\g(x)=\dfrac{3x^2}{2}+\dfrac{x}{2}-5\\\\G(x)=\dfrac{x^3}{2} +x^2-5x\\\\G(2)=4+1-10=-5\\\\G(-1)=\dfrac{-1}{2} +\dfrac{1}{4} +5=\dfrac{19}{4} \\\\\int\limits^2_{-1} {(f(x)-g(x))} \, dx =F(2)-G(2)-(F(-1)-G(-1))\\\\=11+\dfrac{5}{2} =\dfrac{27}{2}$

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HhahsecbxhsaBNIMQKBS help?

Yuliya22 [10]

28.6 I think if it not I’m sorry

8 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

kondaur [170]

Answer: A. profit of $4500

Step-by-step explanation:

r(x) = x² + 6x + 10

- c(x) = x² - 4x + 5

(r - c)(x) = 10x + 5

(r - c)(4) = 10(4) + 5

= 40 + 5

= 45

(r - c)(x) represents the profit (in hundreds of dollars) in x months

(r - c)(4) represents the profit (in hundreds of dollars) in 4 months

So, the new store will have a profit of $4500 in 4 months

3 0

3 years ago

Order the numbers from the least to greatest 19/6, 47/14, 83/2 Thx!

ElenaW [278]

I would change the fractions to decimals so that I could see least to greatest.

19/6=3.17

47/14=3.36

83/2=41.5

Least to greatest:

19/6, 47/14, 83/2

7 0

4 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

Solve these system of linear equations:

frutty [35]

1.solve for y
2x+4y=12
 -2x -2x
4y=12-2x
4 4
y=3-1/2x

step2 plug in y and solve for x
2x+8y=24
2x+8(3-1/2x)= 24
2x+24-4x=24
-2x=0
-2 -2
x=0
last step plug in x and solve for y

y=3-1/2x(0)
y=3

5 0

3 years ago