50 points each question. Please help. How do I solve?

Answers

Answer 1

[tex]I=\displaystyle \int ^{\pi}_{\tfrac{\pi}3} \dfrac{ \sin x}{1 + \cos^2 x} dx\\ \\\\\text{let,}\\\\~~~~~u=\cos x\\\\\implies \dfrac{du}{dx} =-\sin x\\ \\\implies \sin x~~ dx = -du\\\\\text{When}~~ x = \pi , ~~ u = \cos \pi = -1\\\\\text{When}~~ x = \dfrac{\pi}3 , ~~u = \cos \dfrac{\pi}3 =\dfrac 12\\ \\\\I =- \displaystyle \int ^{-1}_{\tfrac 12} \dfrac{du}{1+u^2}\\\\\\[/tex]

[tex]=\displaystyle \int ^{\tfrac 12}_{-1} \dfrac{du}{1+u^2}~~~~~~~~~~;\left[\displaystyle \int^{a}_b f(x) dx = - \displaystyle \int^{b}_a f(x) dx ,~ b < a\right]\\\\\\=\left[\tan^{-1} u \right]^{\tfrac 12}_{-1}~~~~~~~~;\left[ \ddisplaystyle \int \dfrac{dx}{ 1+ x^2} = \tan^{-1} x + C \right]\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \tan^{-1} 1\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \dfrac{\pi}4 \\\\\\=1.249[/tex]

Related Questions

Please help!! Will give brainliest! :)

Answers

Answer:

f(-2) = -3

Step-by-step explanation:

Step 1. Find equation

Step 2. Plug (-2) into f(x)

m, rise/run = (-2-0)/(0-4) = -2/-4 = 1/2

b, y-intercept = (0, -2)

y = 1/2x - 2

f(-2) = 1/2(-2) - 2

f(-2) = -1 - 2

f(-2) = -3

If you want to cheat, simply look for x = -2 on the graph and see where it touches the line. Then match the y-value and BOOM: (-2, -3), f(-2) = -3

BRAINLIEST please if this helped!

Solve for x:
AD bisects BAC

Okay What is the value of x?

Answers

Answer:

x=75

Step-by-step explanation:

99/66=1.5

30x1.5=45

30+45 =75

4) True or False? Our town is growing with a doubling time of 40 years, so its
population will triple in 120 years.

Answers

Answer:
False

Explain:

Kevin and randy muise have a jar containing 52 coins. all of which are either quarters or nickels. the total value of coins is $6.40. how many of each coin do they have?

Answers

Answer:

19 quarters33 nickels

Step-by-step explanation:

For mixture problems, it is convenient to let the variable represent the quantity of the high-value contributor.

Here, we can let x represent the number of quarters. Then the number of nickels is (52-x), and the total value of the coins is ...

0.25x +0.05(52 -x) = 6.40

0.20x +2.60 = 6.40 . . . . . . . . simplify

0.20x = 3.80 . . . . . . . . . . . subtract 2.60

x = 3.80/0.20 = 19 . . . . divide by the coefficient of x

The number of quarters is 19. The number of nickels is 52-19 = 33.

On the coordinate plane below, what is the length of AB?

Answers

Answer:

Ok so i think you can just count it i dont know; edit : i counted, it turns out the answer is 15 :)

15!!! I hope this helps :)

Triangle ABC and DEF are similar which proportion is true

Answers

The length of DE in centimetres is 12 .

The following proportion can be established as follow:

AB / DE = BC / EF = AC / DF

Therefore,

let's find DE as follows;

AB / DE = BC / EF

4 / DE = 3 / 9

cross multiply

9 × 4 = 3DE

divide both sides by 3

DE = 36 / 3

DE = 12 cm

learn more: https://brainly.com/question/22808925?referrer=searchResults

Explain how to find 398 + 257 with mental math and with the standard algorithm.

Answers

Step-by-step explanation:

If you were to round 398 to the nearest hundred, you would get 400. that's only 2 off of 398. when you add 400 + 257 that would equal 857 because 4 + 2= 6 and then the other two digits on 400 are zeros so 5 and 7 stay the same. with 857, you must now subtract 2 because you added 2 earlier. 857 - 2 = 855.

Suppose that$ 7000 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.

Answers

Answer:

1) 7420

2) 7865.5

Step-by-step explanation:

The Formula for Compound Intertst is Amout(rate/100+1)^number of years

7000(.06+1)^1

7000(.06+1)^2

CAN SOMEBODY HELP ME PLEASE

Answers

Answer:

vertex (3, -1)y-intercept: (0, 8)x-intercepts: (2, 0), (4, 0)

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

Vertex

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

Y-intercept

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

X-intercepts

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

Additional comment

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

A book sold 33,100 copies in his first month of release suppose is represents 7.6% of the number of copies sold to date how many copies have been sold to date?

Answers

Answer:

2515 number of copies sold to date

A cyclist rides 24 miles at an average speed of 9 miles per hour. At what rate must the cyclist cover the next 20 miles in order to bring the overall average speed up to 12 miles per hour? The cyclist must ride at 00 miles per hour.

Answers

Answer:

20 m/hr

Step-by-step explanation:

distance / rate = time

24 miles / 9 miles/hr = 2 2/3 hr

(24 + 20 miles) / 12 miles/hr = 3 2/3 hr

3 2/3 - 2 2/3 = 1 hour to ride the next 20 miles means 20 m/hr

100 POINTS WILL MARK BRAINLIEST DONE BY 9:00 attachment included
Solve the linear equations below. Show ALL your work AND circle the type of solution you found! (10 points)

Answers

Answer:

1. No sol.

2. One Sol. x=4

3. One Sol. w=22 1/2

Step-by-step explanation:

Group like terms:

4+3p=6p-3p+5

Add similar elements (6p-3p=3p):

4+3p=3p+5

Subract 4 from both sides:

4+3p-4=3p+5-4

Simplify:

3p=3p+1

Subtract 3p from both sides:

3p-3p=3p+1-3p

Simplify:

0=1

There is no solution.

One Sol. x=4

Switch sides:

3x-2=10

Add 2 to both sides:

3x-2+2=10+2

Simplify:

3x=12

Divide both sides by 3:

3x/3=12/3

Simplify:

x=4

There is a solution.

One Sol. w=22 1/2

Subtract 7 from both sides:

2/3w+7-7=22-7

Simplify:

2/3w=15

Multiply both sides by 3:

3*2/3w=15*3

Simplify:

2w=45

Divide both sides by 2:

2w/2=45/2

Simplify:

w=22 1/2

There is one sol.

In the figure below, triangle QRS is isosceles, with QR SR.
If mSPQ = 36° and mQRS = 32°, what is mPQR?
A.
118°
B.
138°
C.
133°
D.
128°

Answers

All angles in triangle QRS are equal since it is isosceles, so If mQRS = 32, subtract that from 180. 180-32=148°.
Now divided 148/2 to get 74°.
In triangle SPQ, there is one right angle 90°, and mSPQ 36°
Add 90+36=126 and subtract that from 180 again
180-126=54°
Add 74° and 54° = 128°

The answer is D

Answer:

Step-by-step explanation:

since Δ QRS is isosceles then the base angles are congruent , that is

∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°

the sum of the 3 angles in Δ SPQ = 180° , then

∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°

Then

∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°

Which expression is equivalent to -18a^-2b^5/-12a^-4b^-6
a. 2a^2b^11/3
b. 2a^2b^30/3
c. 3a^2b^11/2
d. 3a^2b^30/2

Answers

Answer:

c. 3a^2b^11/2

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)/(a^c) = a^(b-c)

[tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]

Solve the equation 64x2 − 144 = −23 by using square roots.
x = ±11/8
x = ±3/2
no real solutions
x = ±7/4

Answers

Answer:

The answers are:x = ±7/4x = ±3/2x = ±11/8

yww:)

Answer:

Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Step-by-step explanation:

Step 1: Add 144 to both sides

[tex]64x^2 - 144 = -23[/tex]

[tex]64x^2 - 144 + 144 = -23 + 144[/tex]

[tex]64x^2 = 121[/tex]

Step 2: Divide both sides by 64

[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]

[tex]x^2 = 1.890625[/tex]

Step 3: Square root both sides

[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]

[tex]x =[/tex] ± [tex]1.375[/tex]

[tex]x =[/tex] ± [tex]11/8[/tex]

Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

3v+4(v-2)= -29 solve for v

Answers

Answer:

v = -3

Step-by-step explanation:

1) Expand.

3v + 4v - 8 = -29

2) Simplify 3v + 4v - 8 to 7v - 8.

7v - 8 = -29

3) Add 8 to both sides.

7v = -29 + 8

4) Simplify -29 + 8 to -21.

7v = -21

5) Divide both sides by 7.

v = -21/7

6) Simplify 21/7 to 3.

v = -3

find all the fraction between 0 and 1

Answers

Answer:

Between 0 and 1 there is 12, between 1 and 2 there is 112=3/2, and so on. In fact, there are infinitely many fractions between any two whole numbers. Let's see why. Between 0 and 1 there are also 13, 14, 15, and any number that can be written as 1n where n is some whole number.
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Hope this helped! Have a nice day!
Please give Brainliest when you can.
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-Jaron, King of Carthya.

My book has 120 pages. If I have read half of it how many pages have I read

Answers

60 pages. half of 120 is 60

Answer:60 pages

Step-by-step explanation:

first take away the zero then devide by 2 then add the zero the the number that your left with.

simplify. giving brainliest :D
show steps in a simple way (not to long of an example ty :))

Answers

Answer:

- 3/2 x²y

Step-by-step explanation:

Multiply the numbers and constant separately.

constant means x any y.

( - 2/3 x ) ( 9/4 xy )

- 2/3 * 9/4 * x * xy

= ( - 2/3 * 9/4 ) * ( x * xy )

= ( - (2*9)/(3*9) ) * ( x²y )

= ( - 18/12 )* x²y

= - 3/2 x²y

1. What is the surface area of the sphere below?
12 cm

Answers

Answer:

Using 3.14 for pi

SA =1808.64 cm^3

Using the pi button

SA =1809.557368 cm^3

Step-by-step explanation:

The surface area of a sphere is given by

SA = 4 pi r^2

We are given a radius of 12

SA = 4 pi ( 12) ^2

SA = 4 pi * 144

SA = 576 pi