Answer:
[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]
General Formulas and Concepts:
Alg I
Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Pre-Calc
[Right Triangle Only] Pythagorean Theorem: a² + b² = c²
a is a legb is a legc is hypotenuseTrigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]
Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]
TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]
TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]
Calc
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
IP [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
U-Trig Substitution: x² + a² → x = atanθ
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]
Step 2: Identify Sub Variables Pt.1
Rewrite integral [factor expression]:
[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]
Identify u-trig sub:
[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]
Later, back-sub θ (integrate w/ respect to x):
[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]
Step 3: Integrate Pt.1
[Int] Sub u-trig variables: [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]: [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]: [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]: [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]Step 4: Identify Sub Variables Pt.2
Determine u-sub for trig int:
u = 2θ
du = 2dθ
Step 5: Integrate Pt.2
[Ints] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub: [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]Step 6: Triangle
Find trig values:
[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]
[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]
tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
Leg a = 2
Leg b = 9x
Leg c = ?
Sub variables [PT]: [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents: [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite: [tex]c = \sqrt{81x^2 + 4}[/tex]Substitute into trig ratios:
[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]
[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]
Step 7: Integrate Pt.3
[Exp] Sub variables [TR]: [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute: [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]Under her cell phone plan, Katherine pays a flat cost of $50 per month and
$5 per gigabyte. She wants to keep her bill at $71 per month. How many
gigabytes of data can she use while staying within her budget?
Answer: x = 4.2
Step-by-step explanation:
To keep her bill at $71 per month, she needs to consume 4.2 gigabyte in a month.
A linear equation is in the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the initial value of y.
Let y represent the amount of money paid for x gigabyte.
Given a flat cost of $50 per month and $5 per gigabyte, hence m = 5, b = 50. Therefore:
y = 5x + 50
For a bill of $71 per month:
71 = 5x + 50
5x = 21
x = 4.2
To keep her bill at $71 per month, she needs to consume 4.2 gigabyte in a month.
Find out more on linear equation at: https://brainly.com/question/14323743
Emilia and Joshua shared some money in the ratio 1:6.
Emilia received £15.
How much did Joshua receive?
Answer:
15x6
Step-by-step explanation:
do 15x6 and what that is, is the answer
−15(x−4)=−2 the 15 is one fifth pls help
A car depreciates in value each year. Which of the following is NOT true about the value of the car after t years
Answer:
The car will be worth more in 20 years than the amount it was purchased for.
Step-by-step explanation:
If you look at the graph you see a downward trend, not an upward. That makes it impossible for it to be worth more Hopefully this helps.
Answer: B (top right)
Step-by-step explanation:
Describe the mathematical process for finding the area of a rectangle triangle and circle be sure to included explain the formulas for finding the area if each shape
On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos(A) Triangle X W Y is shown. Angle X Y W is a right angle. The length of hypotenuse W X is y, the length of X Y is a, and the length of W Y is 9. Triangle W X Y is shown. Sides W X and X Y are congruent. The length of W Y is 7. Triangle W X Y is shown. Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y. Triangle W X Y is shown. The length of W X is 10, the length of X Y is 8, and the length of W Y is 16.
Answer:
C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.
Step-by-step explanation:
On which triangle can the law of cosines be applied once to find an unknown angle measure?
The Law of cosines is given as:
a² = b² + c² - 2bccos(A)
From the options given above, the correct option is Option C
C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.
This is because:
Law of Cosines helps us to find an unknown side of a triangle when we are given 2 known sides and 1 angle.
In the above question, we are given angle 76 degree, and the length of two sides: The length of X Y is 5, the length of W Y is 10
The unknown side is the length of W X which is represented as y.
Hence, Option C is the correct option.
Answer:
D
Step-by-step explanation:
I got it right on my program.
Derek has a bird that weighs 3 pounds. Use the double line diagram below to help you determine approximately how many kilograms this bird weighs.
2 lines. The first line is labeled Pounds and has 6 marks, equally spaced apart, and every other mark labeled 3, 5, 7, respectively. The second line is labeled Kilograms and has 6 marks, equally spaced apart, and every other mark labeled, 1, 2, 3, respectively.
(2 points)
1.5 kilograms
3 kilograms
5.5 kilograms
6 kilograms
Answer:
about 1.5 kilograms
Step-by-step explanation:
3 pounds=1.36078 so that is closer to the answer 1.5 kilograms
Answer:
1.5
Step-by-step explanation:
i took the test
HELPPPPOMOGMGOGMGOGKM PLS ANSWER THIS CORRECTLY PLZZZ THIS IS FOR A VERY IMPORTANT TEST YOUWILL GET BRAINLIEST HELP
Answer:
i cant give u the answer but here is an example hope this helps slope = "rise over run" the difference in y values divided by the difference in x values
= 6/-3 = -2 = m. It's negative because as x increases, y decreases
plug that into the point slope formula, with either point. generally use the most simple point
y-h= m(x-k) where m= -2 and (k,h) = (2,-2)
y+2 = -2(x-2)
simply if you want
Y = -2x +4 -2 = -2x +2
or
2x +y = 2
Step-by-step explanation:
Answer:
Your slope is -1
Your y inter is -3
Step-by-step explanation:
Hope this helps you :)
Which quadrants are (-4,5) in
Answer:
Quadrant 2
Step-by-step explanation:
Take a look at the picture I added it should help you on futures questions like this :)
One bottle contains 250 ml of juice. Soham wants 2 liters of juice. How many bottles should he buy?
Answer:
8 bottles
Step-by-step explanation:
Choose the number that correctly completes the ratio table.
Answer:
its 8:9
Step-by-step explanation:
It would be 8 because you can see that the top row multiplies 16 by two in the exact spot where the missing number is.
Please help :( Find X.
Round to the nearest tenth.
use long or synthetic division to find the following quotients
(x^3+2x^2!22x-45)÷(x+5)
Answer:
[tex]\boxed{\textsf{ The quotient is $\sf x^2-3x-7$ and the remainder is (-10).}}[/tex]
Step-by-step explanation:
Here we will be using long division method to find the quotient . Here we need to divide (x³+2x²-22x-45) and (x+5) . So lets divide .
x+5) x³+2x²-22x-45 ( x² -3x -7
x³ + 5x²
- -
______________
- 3x²-22x -45
-3x² -15x
+ +
______________
-7x -45
-7x -35
______________
-10
Quotient = x² -3x -7
Remainder = (-10)
★Hence the quotient is x² -3x -7 and the remainder is (-10) .HELP HELP PLSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
19
Step-by-step explanation:
31 +9 =40
40 by 2 = 20
9-5=4
4 by 4= 1
20-1= 19
The ratio of boys to girls at a movie is 5:4 . If there are 16 girls , how many boys are at the movie?
Answer:
,it's 15. and here's why: if i pick 4,its makes 12 because 3x4=12 and if you put 3 with 5,you get 15 which is the answer.
Step-by-step explanation:
Probability tree diagram
Answer:
?
Step-by-step explanation:
can you explain a little more
arrange in order from least to greatest. -3/5, 7/-10,-5/6
[tex] \frac{ - 3}{5} \frac{7}{ - 10} \frac{ - 5}{6} [/tex]
plzz help!!!
fast!!
it is due in 10 min..
I'll make brailiest whose ans is correct...
Jake and Natalya both have jobs that pay by the hour. The amounts they earned based on various numbers of hours worked are shown in the tables. Which of these statements is correct? Immersive Reader
A. If the amount Abby earns can be described by p=11.75h, where p is her pay and h is the number of hours worked, the Abby earns more per hour than Jake and less per hour than Natalya.
B. If the amount Bobby earns can be described by p=10.75h, where p is his pay and h is the number of hours worked, then Bobby earns less per hour than Jake and Natalya.
C. If the amount Deion earns can be described by p=12.25h, where p is his pay and h is the number of hours worked, the Deion earns more per hour than Jake and Natalya.
D. If the amount Frederica earns can be described by p=12.75h, where p is his pay and h is the number of hours worked, then Frederica earns less per hour than Jake and Natalya.
I need help with 1 through 10
Answer:
1) yes
2) no
3) no
4) no
5) yes
6) yes
7) yes
8) yes
9) circle equation - B
10) circle equation - D
11) 12 people in each team
sorry im not able to answer for 12 , 13 and 14 i have urgent work im so sorry
8. Do the representations below define a function? *
y =
x - 2
Yes, it is a function.
No, it is not a function.
Answer:
Step-by-step explanation:
Yes it is a function. Every x has only 1 y associated with it.
PLZZZZ HELP QUICK
Ted and Katie have saved up a total of $94.00. Ted has saved 6 dollars less than 4 times as much as Katie. How much has Katie saved?
Answer:
22
Step-by-step explanation:
94-6 divided by 4
Answer:
LOOK BELOW IN STEP-BY-STEP
Step-by-step explanation:
First, do $94.00 times 4 which is $376
Then, take away 6 dollars from $376 which is $370
Hope that helped!!!
9.
Jacks Plumbing charges customers $100 per hour for repair jobs. Al's Plumbing charges according to the equation y = 75x + 50, where x = time in hours and y = cost
dollars
Explain why Ars Plumbing charges less than Jacks Plumbing for a 4-hour repair job.
Does Als Plumbing charge less than Jacks Plumbing for all repair jobs? Explain why or why not.
Answer:
As given,
Per hour cost of Jack's plumbing = $100
Also,
Al's plumbing charges = 75x + 50 where x = time in hours .
Now,
Al's plumbing cost for 4 hours:
Here , x = 4
⇒75x + 5 = 75(4) + 50 = 300 + 50 = 350
∴ we get
Al's plumbing cost for 4 hours = $350
Now,
As Jack cost for 1 hour = $ 100
⇒ For 4 hour = 4×$100 = $400
∴ we get
Jack's plumbing cost for 4 hours = $400
As we can see that
$ 400 > $350
⇒Jack's plumbing cost for 4 hours > Al's plumbing cost for 4 hours
Now,
Al's plumbing charges = 75x + 50 where x = time in hours .
For 1 hour
75x + 50 = 75(1) + 50 = 125
Al's 1 hour cost = $125
whereas Jack Plumbing cost for 1 hour = $100
∴ we get
$125 > $100
⇒Al's 1 hour cost > Jack's 1 hour cost
Now,
Al's 2 hour cost
75x + 50 = 75(2) + 50 = 150 + 50 = 200
Al's 1 hour cost = $200
whereas Jack Plumbing cost for 2 hour = $200
∴ we get
$200 = $100
⇒Al's 2 hour cost = Jack's 2 hour cost
Now,
Al's 3 hour cost
75x + 50 = 75(3) + 50 = 225 + 50 = 275
Al's 1 hour cost = $275
whereas Jack Plumbing cost for 3 hour = $300
∴ we get
$275 < $300
⇒Al's 3 hour cost < Jack's 3 hour cost
Als0,
Jack's plumbing cost for 4 hours > Al's plumbing cost for 4 hours
∴ we get
We can not say that Als Plumbing charge less than Jacks Plumbing for all repair jobs.
Because the charge is fluctuating ,
For 1 hour , Aly' charge is grater whereas The 2 hour cost of Jack's is higher.
So, the Correct answer is - No, Al's Plumbing charge is not always less than Jacks Plumbing for all repair jobs.
I need assistance please
Answer:
23
Step-by-step explanation:
6/3 = x-5/9 simplify the first fraction
2= x-5/9 multiply both of the sides
18 = x-5/9 move it around correctly
-x=-5-18 calculate it
-x=-23 the negatives cancel out
x=23
Mr. Tanner bought some boxes of markers with 18 markers in each box. He kept 2 markers and gave the rest to his students. Use the equation below to calculate the number of boxes (b) he bought. 18b – 2 = 214
Answer: 18b-2+2=214 +2
Step-by-step explanation:Add 2 both sides of the equation
Answer:
b = 12; he bought 12 boxes.
Step-by-step explanation:
18b - 2 = 214 (subtract 2 on both sides)
18b = 216 ( divide 18 on both sides to get 'b' alone)
b = 12
Solve each single-step equation. Show your work. -15+n=-9
Answer:
6
Step-by-step explanation:
-15+6 means it goes minus basically its 15-6(-15+6)=-9
Answer:
n=24
Step-by-step explanation:
First add 15 to the right side equaling 24. Therefore n=24
(−4,3),(−2,1),(0,−1),(2,−3) Write a scenario?
Answer:
tergtjmsrhatsfdghb
Step-by-step explanation:
Can someone please help
Answer:
(-4)^10
Step-by-step explanation:
When doing this sort of problem, we multiply the exponents.
This is the power rule.
Find each angle measure to the nearest degree please help
9514 1404 393
Answer:
4°48°Step-by-step explanation:
The inverse cosine function of your calculator is used to find the angle from the cosine value. (Be sure your calculator is set to 'degrees' mode.)
1) A = arccos(0.9976) ≈ 4°
2) U = arccos(0.6691) ≈ 48°
Here is a picture of the Ferris wheel has a radius of 40 m how far does the writer travel in one complete rotation around the Ferris wheel
Answer:
I'm getting points
Step-by-step explanation:
so I can ask questionss
This circle graph shows the results of a survey that asked people to identify their favorite type of music.
What percent of people chose rock or country as their favorite type of music?
A. 9%
B. 35%
C. 45%
D. 55%