(b) simplify (5ab^2)^2

Recall some identities:

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

and from the first identity, you can establish that

cos(2x) = 2 cos²(x) - 1

So, rewrite the integrand as much as possible in terms of cos(x) :

[tex]\sin^3(x) \cos(2x) = \sin(x) \sin^2(x) (\cos^2(x)-\sin^2(x)) \\\\ \sin^3(x) \cos(2x) = \sin(x) (1-\cos^2(x)) (2\cos^2(x) - 1)[/tex]

Then in the integral, substitute u = cos(x) and du = -sin(x) dx. With some rewriting, you end up with

[tex]\displaystyle \int_1^2 \sin^3(x) \cos(2x) \,\mathrm dx = -\int_{x=1}^{x=2} (1-\cos^2(x))(2\cos^2(x)-1) (-\sin(x)\,\mathrm dx) \\\\ = -\int_{u=\cos(1)}^{u=\cos(2)} (1-u^2)(2u^2-1)\,\mathrm du \\\\ = \int_{\cos(1)}^{\cos(2)} (1-3u^2+2u^4) \,\mathrm du \\\\ = \left(u-u^3+\frac25u^5\right)\bigg|_{\cos(1)}^{\cos(2)} \\\\ = \left(\cos(2)-\cos^3(2)+\frac25\cos^5(2)\right) - \left(\cos(1)-\cos^3(1)+\frac25\cos^5(1)\right) \\\\ = \boxed{\cos(2) - \cos^3(2) + \frac 25 \cos^5(2) - \cos(1) + \cos^3(1) - \frac25 \cos^5(1)}[/tex]

Answer:

larger number is -0.514

Step-by-step explanation:

-0.514 is greater than -0.5148 by 0.0008

Answer:  138.16 cubic feet (choice H)

This volume is approximate and occurs when you use pi = 3.14

==========================================================

Work Shown:

r = 2 ft = radius

h = 11 ft = height

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*11

V = pi*4*11

V = pi*44

V = 44pi .... exact volume in terms of pi

V = 44*3.14

V = 138.16 .... approximate volume and the final answer

Answer:”H”

Step-by-step explanation: just trust the process

The value of b for which the quadratic equation x² - bx + 16 = 0 have exactly two different integer solutions is b > 8

An equation is an expression that shows the relationship between two or more numbers and variables.

A quadratic equation is in the form:

y = ax² + bx + c

Where a, b and c are constants.

Given the equation:

y = -4x² + 24x - 35

From the graph of y = -4x² + 24x - 35, the axis of symmetry of the parabola is at x = 3

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

411 #

Step-by-step explanation:

solution :

Let x = the number of adult tickets sold

Let x + 61 = the number of student tickets sold

x + x + 61 = 761

2x = 700

x = 350

x + 61 = 411

mark me brain list

Answer:

x = 5

Step-by-step explanation:

x^2/(x + 5) = 25/(x+5)      Subtract the right side from both sides.

x^2/(x + 5) - 25/(x + 5) = 0

x^2 - 25

=======   = 0

x + 5

(x + 5)(x - 5)

============= = 0

(x + 5)

Cancel x + 5 in the numerator and denominator.

x - 5 = 0

x = + 5

Does it check?

x^2/(x + 5) = 25/(x + 5)

x = 5

5^2/(10) = 25/10

25/10 = 25/10 Yes it checks.

Answer:

This is 3.747*11/sqrt(5)=18.4

the interval is (49.9,86.7), the SE added to and subtracted from the mean.

It is B

                          Thank You

Answer:

Statement is?

Step-by-step explanation:

As soon as you finish the question!

Answer:

64

Step-by-step explanation:

Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.

Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.

Answer:

112

Step-by-step explanation:

1 bag- Has 14 marbles in all

So if you multiply 14 times 8 total bags you get 112.

Step-by-step explanation:

Correct option is

A

50

n(AΔB)=n(A∪B)−n(A∩B) [As n(A∪B)=n(A)+n(B)−n(A∩B)]

=n(A)+n(B)−2n(A∩B)

=50+20−2(10)=50

Answer:

3*3*3

3^3

Step-by-step explanation:

27 = 9*3

    = 3*3*3

    = 3^3

The formula for the volume of a cube is V = a^3.

We know the volume is 125 cubic inches.

125 = a^3

Take the third square root

5 = a

The length of each edge is 5 inches

Answer:

So the length of the edge of a cube with a volume of 125 is 5 inches

Step-by-step explanation:

All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power.

So if we take the edge of the cube to be of length x, then:

Volume=x3

125=x3

5=x

Answer:

x=10

Step-by-step explanation:

10 a 8 son dos, entonces 14 ax es 4

Answer:

La explicación sería:

//////////////////////////

=> 9 * 2 + 4/2 = 20

=> 18 +2 =20

=> 20 =20

//////////////////////////

=> 5*2 + 8/2 = 14

=> 10 +4 =14

=> 14 =14

//////////////////////////

=> 3*2 + 10/2 = x

=> 6 + 5 = x

=> 11 = x

Answer:

8/5 = x

Step-by-step explanation:

6 = 5x - 2

~Add 2 to both sides

8 = 5x

~Divide 5 to both sides

8/5 = x

Best of Luck!

[tex]\\ \sf\longmapsto 8\dfrac{1}{2}\div \left(4\dfrac{4}{5}-7\dfrac{7}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{24}{5}-\dfrac{77}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div\left(\dfrac{48-77}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{29}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\times \dfrac{10}{29}[/tex]

[tex]\\ \sf\longmapsto \dfrac{17(10)}{2(29)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{170}{58}[/tex]

[tex]\\ \sf\longmapsto \dfrac{85}{29}[/tex]

[tex]\\ \sf\longmapsto 2\dfrac{27}{29}[/tex]

Answer:

Step-by-step explanation:

The positive difference is the result of subtraction of the smaller number from the greater number.

The positive difference of 4 4/5 and 7 7/10 is:

Now division:

Answer:

3.   15

6.   4

Step-by-step explanation:

Put  3 instead of x

3.    5x

     = 5 × 3

    = 15

6.   12 ÷ x

     = 12 ÷ 3

     = 4

Answer:

When X is 3 it will be

5(3)=15

Then for the second one it will be 12/3

The answer is 4

Hope I helped

Answer:

keep can run millions at 30 friends all for 10 minutes for what purpose for running running of the steelers versus the dynasties of running of the

Answer:

3.16 miles

Step-by-step explanation:

Hi there!

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

We're given that the campsite is located at (1,7) and the checkpoint station is located at (4,6). We must calculate the distance between them. Plug these points into the formula:

[tex]d=\sqrt{(x_2-1)^2+(y_2-7)^2}\\d=\sqrt{(4-1)^2+(6-7)^2}\\d=\sqrt{(3)^2+(-1)^2}\\d=\sqrt{9+1}\\d=\sqrt{10}\\d\approx3.16[/tex]

Therefore, the distance between the campsite and the checkpoint is 3.16 miles when rounded to the nearest hundredth.

I hope this helps!

Answer:

Her monthly income is Rs. 21000

Step-by-step explanation:

15000 x ( 1 + 40 % )

= 15000 x 140 %

= 21000

Answer:

See the image for solution

Hope it helps

Have a great day

Answer:

y = -1/2x - 1

Step-by-step explanation:

A line that is parallel to another will have the same slope. All we need to do is find the new y-intercept. We can do that by using the slope intercept form equation [ y = mx + b ].

1 = -1/2(-4) + b

1 = 2 + b

-1 = b

Now we can input the information we know and solved for back into the formula.

y = -1/2x - 1

Best of Luck!

Answer:

The answer will be 4(x+5)=60

Answer:

[tex]\frac{49}{75}[/tex]

Step-by-step explanation:

y= [tex]\frac{11}{15}[/tex]-[tex]\frac{2}{25}[/tex]

y= [tex]\frac{49}{75}[/tex]

Answer:

49/75

Step-by-step explanation:

y + 2/25 = 11/15

now, we could do it like the other answer and do fraction arithmetic, or we try and multiply everything out to eliminate the fractions :

15y + 30/25 = 11

375y + 30 = 275

375y = 245

y = 245/375 = 49/75

the same result, of course, but a slightly different way to get there.

9514 1404 393

Answer:

  (c)  -0.5

Step-by-step explanation:

Starting from standard form ...

  ax +by = c

and solving for y, we get the slope-intercept form ...

  y = (-a/b)x +c/b

The coefficient of x is the slope: -a/b.

For your equation x+2y=16, the slope is -1/2 = -0.5.

Number of balls should fit inside the bin are 216 balls.

Given:

Radius of spherical ball = 16 cm

Height of cylinder = 210 cm

Diameter of opening = 150 cm

Find:

Number of  balls should fit inside the bin

Computation:

Volume of sphere = [tex][\frac{4}{3}] [\pi ][r^3][/tex]

Volume of sphere ball = [tex][\frac{4}{3}] [\pi ][16^3][/tex]

Volume of sphere ball = 17164.19 cm³

Radius of cylinder = Diameter of opening / 2

Radius of cylinder = 150 / 2

Radius of cylinder = 75 cm

Volume of cylinder = [tex][\pi ][r^2][h][/tex]

Volume of cylinder = [tex][\pi ][75^2][210][/tex]

Volume of cylinder = 3,712,500 cm³

Number of balls should fit inside the bin = Volume of cylinder / Volume of sphere ball

Number of balls should fit inside the bin = 3,712,500 / 17,164.19

Number of balls should fit inside the bin = 216.293

Number of balls should fit inside the bin = 216 balls (Approx.)

Learn more:

https://brainly.com/question/13338592?referrer=searchResults

Answer:

Step-by-step explanation:

I don't know

Answer:

Step-by-step explanation:

[tex]Remember:\\(a+b)(a-b)=a^2-b^2\\\\(6+5i)(6-5i)=6^2-(5i)^2=36-(-1)*25=36+25=61\\[/tex]