Which of the following is equal to 49x2−81?


(7x−9)2

(x+9)(x−9)

(7x+9)(7x−9)

(7x+9)2

Answer:

answer is 3.144

Step-by-step explanation:

Answer:

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]

Step-by-step explanation:

we want to integrate the following integration:

[tex] \displaystyle \int {x}^{2} \cdot {e}^{x} dx[/tex]

notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:

[tex] \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx[/tex]

where u' can be defined by the differentiation of u

now we have to choose our u and v

which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.

since x comes first thus,

[tex] \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} [/tex]

by figuring out the defferentiation of u,we acquire:

[tex] \displaystyle u' = 2x[/tex]

altogether we get:

[tex] \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx[/tex]

by figuring out the parentheses integration

we get:

[tex] \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx[/tex]

now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline

[tex] \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} [/tex]

by figuring out the defferentiation of u

we acquire:

[tex] \displaystyle \: u' = 2[/tex]

altogether we get:

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)[/tex]

by solving parentheses we get

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)[/tex]

by figuring out the integral we get:

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)[/tex]

remove parentheses:

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} [/tex]

at last we of course have to add constant of integration:

[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]

and we are done!

Answer:

[tex]\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Integration

Integration by Parts:                                                                                               [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

Step-by-step explanation:

*Note:

The answer below me is correct, but there is a simpler method of obtaining the answer.

Step 1: Define

Identify

[tex]\displaystyle \int {x^2e^x} \, dx[/tex]

Step 2: Integrate

Use tabular integration.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

A

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

From the question, we are informed that a 2-mile walking trail has a distance marker every 1\4 mile. Hl

The number of markers that are along the trail will be calculated as:

= Length of walking trail / interval of distance marker

= 2 ÷ 1/4

= 2 × 4

= 8

There are 8 markers along the trail.

Answer:

1. B. The bag of candy produced last Monday is different from the standard bag.

2. A. The bag of candy produced last Monday are like the standard bag.

3. B. The bag of candy produced last Monday is different from the standard bag.

Step-by-step explanation:

Given - A company that makes hard candy have a standard bag of hard candy with 150 pieces. The hard candy has three distinct colors red, white and orange and equal proportion of each candy is present in the standard bag. The manager wants to know whether the bags produced last Monday were similar to the standard bag. To test this, they plan to choose a random bag from the batch and compare it with the standard bag. You will have to answer questions below to assist the manager in comparing the two bags.

To find - 1. What is the alternate hypothesis for this exercise?

              2. What is the null hypothesis for this exercise?

              3. After performing the necessary calculations, the chi-square value of the test is 6.7. The cut-off/critical value of chi-square test is 5.991 (for 5% chance).  What is your conclusion about the bags based on this result?

Proof -

1.

The alternate hypothesis is - B. The bag of candy produced last Monday is different from the standard bag.

2.

The null hypothesis is - A. The bag of candy produced last Monday are like the standard bag.

3.

The conclusion is - B. The bag of candy produced last Monday is different from the standard bag.

Answer:

36 degrees

Step-by-step explanation:

I’m pretty sure that’s it

Answer:

The equation of the axis of symmetry is x = 7

Step-by-step explanation:

Mathematically, we have the equation of the axis of symmetry as;

x = -b/2a

where a is the coefficient of x^2 = 1

b is the coefficient of x which is -14

So, the equation of the axis of symmetry will be;

x = -(-14)/2(1) = 14/2 = 7

So the equation of the axis of symmetry is x =7

Answer:

11.3, rounded

Step-by-step explanation:

mean = average. Add them all up, then divide by how many entries/data points you have.

12 + 18 + 9 + 14 + 8 + 7 = 68

There are 6 numbers we added, so 68/6 = 11.3333333

Please let me know if you have questions.

75cm²

Explanation:

10 times 15 is 150 and since it is a triangle you divide in half so the answer is 75. And in this case the 18 is not needed.

Answer:

75cm²

Step-by-step explanation:

The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. But in this case, there are three sides.

To find the area of a triangle with 3 sides given as 10, 15, and 18, we assume that a = 10, b = 15, and c = 18.

Then the semi-perimeter is, s = (a + b + c)/2 = (10 + 15 + 18)/2 = 21.5. We will find the area of the triangle using Heron's formula.

A = √[s(s-a)(s-b)(s-c)]

= √[8(21. 5-10)(21.5 -15)(21. 5-18)]

= √[21.5 × 11.5 × 6.5 × 3.5]

= √(5625)

≈ 7.5

Answer:

10.667 yards

Step-by-step explanation:

Answer:

[tex]9k^{2} - 25k - 44[/tex]

Step-by-step explanation:

Answer:

7,000 - 2,386 = 4,614

Answer:

5,9

Step-by-step explanation:

Answer:

area = 153.94

Step-by-step explanation:

Diameter = 14. Half of 14 is 7, so radius = 7.

Formula for the area of a circle = π * r^2, so π * 7^2 = 153.93804

Answer:

yes i think

Step-by-step explanation:

Answer:

2.83

Step-by-step explanation:

d= Square root of (x2 - x1 )^2 +( y2- y1)^2

from the point given you

x1= -6

y1 = -17

x2 = -8

y2 = -19

by applying the formula

Square root of ( -8 - (-6))^2 + ( -19 - (-17))^2

Square root of (-8+6) + (-19+17)^2

Answer:

Please can you complete the question

Answer:

The answer would be X= -7 .

Step-by-step explanation:

Hope it helps :)

Answer:

78

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(x^2+2)*(1-3x)=-3x^3+x^2-6x+2

now plug in -1

-3(-1)^3+(-1)^2-6(-1)+2=12

hope this helped  

Total Number of words made out of English = 93

Answer:

336m^2

Step-by-step explanation:

base x height + (side1 + side2 + Height)Length

Answer:

4209/10000

Step-by-step explanation:

42.09%=4209/10000

Answer:

X would equal 4

Step-by-step explanation:

5 x 4 is 20. And the equation was 5x + 1 = 21.

So, the answer would equal 20. Hope this helped!! :D

Answer:

x=4

Step-by-step explanation:

Start with your equation: 5x+1=21

Subtract 1 on both sides: 5x=20

Divide by 5 on both sides: x=4

Hope I helped

Answer:

24 + 50 = 74 cm³

Step-by-step explanation:

I split the irregular figure into two separate shapes and found the volume of each and then added the values, I am most certain the answer would be 74 cm³, I apologize if it isn't.

Answer:

The perimeter is 206.

Step-by-step explanation:

When given the area, height and side of the parallelogram, you would use the formula to find the perimeter: P=2a+2*A /h. a = side of the parallelogram, A = area, and h = height. When you plug in everything, you will get 206.

Answer:

C

Step-by-step explanation:

volume of a cone = πr²[tex]\frac{h}{3}[/tex]

so 20² x π x [tex]\frac{35}{3}[/tex] = 14660.76572