Evaluate the function

Find the area of the shaded region.f(x)=4x+3x2−x3,g(x)=0 The area is _____.

Tasya [4]

Answer:

The answer is " $\bold{\frac{7}{2}}$ "

Step-by-step explanation:

Given value:

$\to f(x)=4x+3x^2-x^3\\\\\to g(x)=0$

Find:

area=?

calculation:

$\ Area = \int_{-1}^{0} -(4x+3x^2-x^3) dx + \int_{0}^{1} (4x+3x^2-x^3) dx \\\\$

$= -(2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= -( 2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= ( 2- 1 -\frac{1}{4}) + (2+1- \frac{1}{4})\\\\\\= ( \frac{8-4-1}{4}) + (\frac{8+4-1}{4})\\\\= ( \frac{3}{4}) + (\frac{11}{4})\\\\= \frac{3}{4} + \frac{11}{4}\\\\= \frac{11+3}{4}\\\\= \frac{14}{4}\\\\= \frac{7}{2}\\\\$

7 0

3 years ago

Two sides of a triangle are as follows: 2 centimeters and 5 centimeters. Describe the possible lengths of the third side

Elden [556K]

Answer:

3cm < Third side < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values of third side are

4cm, 5cm,6cm

Step-by-step explanation:

This question can be solved using given by Triangle Inequality Theorem Given below.

Sum of two sides is always greater than value of third side
Difference of two sides is always less than value of third side

Given two sides are 2cm, 5cm

Sum of two sides = (2+5)cm = 7 cm

Difference of two sides = (5-2) = 3 cm

Let the third side be X

thus according to Triangle Inequality Theorem

X < Sum of two sides of given triangle

X < 7cm -----1

X > Difference of two sides

X > 3cm ----1

combining expression 1 and 2 we have

3cm < X < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values are

4c, 5cm,6c

7 0

2 years ago

Suppose the function h(x)=2x-9 is translated up 5 united to become a new function, i(x). what the equation of the new function?

andreyandreev [35.5K]

Option B

i(x) = 2x - 4 is the equation of the new function

Solution:

Given that the function h(x) = 2x-9 is translated up 5 united to become a new function, i(x)

To find: Equation of new function

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.

Adding to the output of a function moves the graph up

Therefore,

Given function is:

h(x) = 2x - 9

Translated up by 5 units

Therefore, new function is:

i(x) = h(x) + 5

i(x) = 2x - 9 + 5

i(x) = 2x - 4

Thus Option B is correct

6 0

3 years ago

Carlos gross pay was 8357.75 for 27 regular hours worked. What is her regular rate of pay?

Alex777 [14]

Answer:

im not sure but i think its 48

Step-by-step explanation:

if you divide the two you get 96. Divide that by the average rate number (2) and get 48.

8 0

3 years ago

Based on this picture, if ∠3 = 50˚then what is m∠8? SHOW WORK PLEASE

zheka24 [161]

The answer is that measure of angle eight is 130°

6 0

3 years ago