Answer:
Start off by expanding the square:
x^6 -2x³ + 1.
Now, we can integrate it in dx:
∫x^6 - 2x^3 + 1 dx = ∫x^6 dx - 2∫x^3 dx + ∫1 dx = (x^7)/7 - 2((x^4)/4) + x = (x^7)/7 - (x^4)/2 + x.
That's the result!
[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^3)^2dx[/tex]
[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^6+2x^3)dx[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^{6+1}}{6+1}+2\dfrac{x^{3+1}}{3+1}[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+2\dfrac{x^4}{4}[/tex]
[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+\dfrac{x^4}{2}[/tex]
for 0 ≤ θ < 2 π what are the solutions to sin^2(θ) =2sin^2(θ/2)
Answer:
Option A: [tex]\{0,\frac{\pi}{2},\frac{3\pi}{2}\}[/tex]
Step-by-step explanation:
[tex]sin^2(\theta)=2sin^2(\frac{\theta}{2}), [0,2\pi)[/tex]
[tex]sin^2(\theta)=2sin^2(\frac{\theta}{2})[/tex]
[tex]sin^2(\theta)=2sin(\frac{\theta}{2})sin(\frac{\theta}{2})[/tex]
[tex]sin^2(\theta)=2(\sqrt{\frac{1-cos(\theta)}{2}})(\sqrt{\frac{1-cos(\theta)}{2}})[/tex]
[tex]sin^2(\theta)=2(\frac{1-cos(\theta)}{2})[/tex]
[tex]sin^2(\theta)=\frac{2-2cos(\theta)}{2}[/tex]
[tex]sin^2(\theta)=1-cos(\theta)[/tex]
[tex]1-cos^2(\theta)=1-cos(\theta)[/tex]
[tex]-cos^2(\theta)=-cos(\theta)[/tex]
[tex]cos^2(\theta)=cos(\theta)[/tex]
[tex]cos^2(\theta)-cos(\theta)=0[/tex]
[tex]cos(\theta)[cos(\theta)-1]=0[/tex]
[tex]cos(\theta)=0[/tex]
[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}[/tex]
[tex]cos(\theta)-1=0[/tex]
[tex]cos(\theta)=1[/tex]
[tex]\theta=0[/tex]
Therefore, the solutions contained within the interval are [tex]\{0,\frac{\pi}{2},\frac{3\pi}{2}\}[/tex]
Helpful Tips:
Half-Angle Formula: [tex]sin(\frac{\theta}{2})=\pm\sqrt{\frac{1-cos(\theta)}{2}}[/tex]
Pythagorean Identity: [tex]sin^2(\theta)+cos^2(\theta)=1,sin^2(\theta)=1-cos^2(\theta),cos^2(\theta)=1-sin^2(\theta)[/tex]
[tex]\sin^2 \theta = 2 \sin^2 \left(\dfrac{\theta}2 \right)\\\\\implies \sin^2 \theta = 1- \cos 2 \cdot \dfrac{\theta}2\\\\\implies \sin^2 \theta = 1- \cos \theta \\\\\implies 1-\cos^2 \theta = 1 - \cos \theta \\\\\implies -\cos^2 \theta - \cos \theta = 0\\\\\implies \cos^2 \theta - \cos \theta = 0\\\\\implies \cos \theta( \cos \theta -1) = 0\\\\\\\text{Now,}\\\\\cos \theta = 0\\\\\implies \theta = n\pi + \dfrac{\pi}2\\\\\text{For n = 0,1 and}~ [0.2\pi)\\\\[/tex]
[tex]\theta = \dfrac{\pi}2, \dfrac{3\pi}2[/tex]
[tex]\text{Again,} \\\\\cos \theta -1= 0\\\\\implies \cos \theta = 1\\\\\implies \theta = 2n\pi\\\\\text{For n= 0 and}~ [0,2\pi)\\\\\theta = 0\\\\\text{Combine solutions,}\\\\\theta = 0, \dfrac{\pi}2, \dfrac{3\pi}2[/tex]
Graph the line of the equation 8x/5 - 2y = -8 using its slope and y-intercept
Answer:
[tex]y=\frac{4}{5}x+4[/tex]
Step-by-step explanation:
You'll need to get this equation in slope-intercept form by solving for y. I do a little extra here to get it in the correct form, but I think it's pretty clear. Let me know if I need to clarify.
[tex]\\\\\frac{8x}{5}-2y=-8\\\\-2y=-\frac{8x}{5}-8\\\\2y=\frac{8x}{5}+8\\\\y=\frac{4}{5}x+4[/tex]
Once it's in slope-intercept form, both the slope and the y-intercept are readily available so you can easily graph it. I graphed both of them in the attached image so you can see that they are the same line.
A sports store has jerseys representing the seven Canadian NHL teams and the eight Canadian CFL teams. Five of these jerseys have to be chosen for display in a store window. The store owner decides to choose three NHL and two CFL jerseys. These jerseys will be arranged in a row in the store window.
The number of displays that can be made by choosing the jerseys and then arranging them in the window is
A. 4900
B. 11 760
C. 117600
D. 1411 200
The answer key says the right Answer is (C), I just don't know how to get there.
Answer:
possible arrangements
CCNNN
CNCNN
CNNCN
CNNNC
NCCNN
NCNCN
NCNNC
NNCCN
NNCNC
NNNCC
Ten ways to arrange the window
for any one of these there are
NHL
7 ways to fill the first position
6 ways to fill the second
5 ways to fill the third
7•6•5 = 210 ways to select the NHL jerseys
CFL
8 ways to fill the first position
7 ways to fill the second
8•7 = 56 ways to select the CFL jerseys
210•56 = 11760 ways to select a set of 5 jerseys
11760•10 = 117 600 possible ways to arrange the window
When a number is subtracted from 24 and the difference is divided by that number, the result is 3. What is the value of the number?
a) 2
b) 4
c) 6
d) 12
e) 24
Classify the Triangle by its sides and angles. 140° Right Scalene Right Isosceles Equilateral Obtuse Isosceles Acute Isosceles Obtuse scate Acute Scalene
Answer: Obtuse Isosceles.
Explanation: Two angles are congruent, which means the triangle is isosceles. One angle is over 90°, which means the triangle is obtuse.
3. Which of the following is a rational
number that is not an integer?
A-2
C 0
B -0.5
D 4
Step-by-step explanation:
-0.5 cause decimals and fraction are not included
[F r e e] [p o i n t s]
:0
Answer:
Ayo
Step-by-step explanation:
Thanks bro
Find the arc length for arcs of circles as follows:
radius: 12 inches
central angle: radians
- - -
Answer:
≈ 11.78 in
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{\frac{\pi }{4} }{2\pi }[/tex] ( cancel 2π on numerator/ denominator )
= 15 × [tex]\frac{\pi }{4}[/tex]
= [tex]\frac{15\pi }{4}[/tex]
≈ 11.78 in ( to 2 dec. places )
3(y+8)=2y-6 what is y=
Answer:
y = -30
Step-by-step explanation:
3 (y + 8) = 2y - 6
3y + 24 = 2y -6 Distribute the 3
y + 24 = -6 Subtract 2y on both sides
y = -30 Subtract 24 on both sides
State whether the system is consistent or inconsistent. If it is consistent, then state whether the graphs' equations are dependent or independent. State the number of solutions.
If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
Select the table representing a linear function. (Graph them if necessary.)
Check the picture below.
The perimeter of a rectangular field is 314 m.
If the width of the field is 72 m, what is its length?
Answer:
85m
Step-by-step explanation:
Perimeter of a rectangle = 2(l+b)
b=72m, l=?
perimeter =314m
314=2(l+72)
314/2= l+72
157=l+72
l=157-72
l=85m
Evaluate.
{3+[−5(2−4)÷2]}⋅3
−27
−13
18
24
2-4 is -2 and -5 times -2 is 10 divided by 2 is 5 and 5 +3 is 8. and 8 times 3 is 24. PEMDAS
Answer:
→24
Step-by-step explanation:
Evaluate: {3+[−5(2−4)÷2]}⋅3
= {3+[-5(2-4)÷2]}.3
= {3+[-5(-2)÷2]}.3
= {3+[10÷2]}.3
= {3+[10÷2]}.3
= {3+[10÷2]}.3
= {3+[10/2]}.3
= {3+[5]}.3
= {3+5}.3
= 8.3
= 8*3
= 24 Ans.
.I want a way to solve such a problem
Answer:
Step-by-step explanation:
The answer is 65. You just add the number of computer towers that fall into that category. So your sum would look like this:
Divisor: 5+ 12 + 21 + 15 + 12 = 65
The question does not ask you to do any more than figure out what you will be dividing by. Thank goodness it does not ask what you will be dividing into which is a whole lot more complicated problem.
The area
of this figure
is square inches.
20 in
28 in
30 in.
7 in
25 in.
Answer:
946 square Inches
Step-by-step explanation:
First, you should split up the shape into parts.
1st part 28x7
2nd part 30x25
We are multplying simply because
Area = Length x Width
Now that we have split up the parts lets multply them and add them togeher.
28 x 7 = 196
30 x 25 = 750
196 +750 = 946
So the area of this figure is 946 square inches.
The diagram shows the distance between my home, H. and two towns, A and B.
It also shows information about journey times.
What is the average speed of the journey from my home to town A?
I do not know English :33333
HELPPP!! DUE NOWWWW!
Lucy recently joined a fitness club, she had to pay an initial fee to join. Lucy will also pay an extra fee per class she takes there. The equation below represents the relationship.
f(x)=20+3x
Identify the false statement
A. Lucy paid $3 per class.
B. f(x) represents the total amount Lucy paid.
C. x represents the cost of classes.
D. The initial fee was $20
Answer: C
Step-by-step explanation: x represents the number of classes, not the cost of classes.
What are the coordinates of B
Answer: (-7,-5)
Step-by-step explanation:
Because when you mark point M and A if you mirror point M and A on the x Axis then you will get (-7,-5)
i need help with this
Answer:
Yes Jeff is the correct answer
Step-by-step explanation:
Guys this is another one. But it’s a different one
Complete the statement to describe how to convert ounces to pound to find the weight in pounds blank the number of ounces by the unit rate ounces per pound
Answer: you would multiply and the other one is 1536
Step-by-step explanation:
Have nice night
The population of certain city is projected to grow at the rate of r(t) = 400 1+ people/ 24 +7 year in interval (Osts 5) t years from now. The current population is 60 000. What will be the population 5 years from now?
The population 5 years from now would be 60482
The population growth rate is given as:
[tex]r(t) = 400(1 + \frac{2t}{24 + t^2})[/tex]
The value of t, 5 years from now is represented as:
t = 5
Substitute 5 for t in the function r(t).
So, we have:
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 5^2})[/tex]
Evaluate the exponent
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 25})[/tex]
Evaluate the products
[tex]r(5) = 400(1 + \frac{10}{24 + 25})[/tex]
So, we have:
[tex]r(5) = 400(1 + \frac{10}{49})[/tex]
Divide 10 by 49
[tex]r(5) = 400(1 + 0.204)[/tex]
This gives
[tex]r(5) = 400(1.204)[/tex]
Expand
[tex]r(5) = 481.6[/tex]
The current population is given as 60000.
So, the population (P) 5 years from now would be
[tex]P = 60000 + 481.6[/tex]
[tex]P = 60481.6[/tex]
Approximate
[tex]P = 60482[/tex]
Hence, the population (P) 5 years from now would be 60482
Read more about population functions at:
https://brainly.com/question/20115298
Please look for the question in the picture.
Answer:
C and B
Step-by-step explanation:
20%=1/5 so D+1/5D
1.2 = 120%
ACTIVITY 2 Continued
> Solve each problem.
Kathy works after school to finish assembling the 82 favors needed for the school
dance. When she starts at 3:15 PM, she counts the 67 favors already assembled.
She works until 4:30 PM to finish the job.
How many favors can Kathy assemble each minute?
Answer:
.2
Step-by-step explanation:
3:15 to 4:30 is 75 minutes
she had to assemble 15 since there were already 67 made
divide 15/75
.2 per minute
Help help help math math
Answer:
yes
Step-by-step explanation:
x increases by 2, and y increases by 3 consistently
Answer:
No
Step-by-step explanation:
please mark me brainliest
How many terms does the expression 14 + 9 have? What are they? Explain how you know.
Answer:
23, so 1. i know because i added 14+9 and got 23. im sorry if you meant like a definition term, please comment if thats what you meant. because i'll help you then.
Step-by-step explanation:
Find the expected value of the winnings from a game that has the following payout probability distribution: Skip Payout ($) 1 2 5 8 10 Probability 0.35 0.2 0.1 0.2 0.15 Expected Value = [?] Round to the nearest hundredth.
Answer:
$4.35
Step-by-step explanation:
The expected value of a random variable X, often denoted as E(X), indicates the probability-weighted average of all possible values/events. The general formula of expected value is
[tex]\mathrm{E(\textit X \mathrm)} = \displaystyle\sum_{\mathclap{i=1}}^{k} \ X \times P(X) \\ \\ \\ = X_{1} \times P(X_{1}) \ + \ X_{2} \times P(X_{2}) \ + \ X_{3} \times P(X_{3}) + \ \cdots \ + X_{k} \times P(X_{k})[/tex].
Therefore, the expected value of the winnings from a game is
[tex]\mathrm{E(\textit X \mathrm)} \ = \ 1 \times 0.35 \ + \ 2 \times 0.2 \ + \ 5 \times 0.1 + \ 8 \times 0.2 \ + 10 \times 0.15 \\ \\ = \ 4.35 \ \ (\mathrm{nearest \ hundredth})[/tex].
what does it mean to square a value/ expression
Squaring a number means multiplying the same number by itself.
For example,
[tex]\\2 \cdot 2 =2^2\\\\a\cdot a =a^2~~ \\\\ (a+1)(a+1) =(a+1)^2 \\\\ (x^{10}+1)(x^{10}+1) =(x^{10}+1)^2[/tex]
A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold
Answer:
225 children tickets, 450 adult tickets and 500 student tickets were sold
Can somebody, anybody please helppp
Simplifiy the expression.
x^2 + 3x - 28/ x^2 - 7x + 12
show your work! (this part is REALLY important) thanks(:
Answer:
Step-by-step explanation:
3x3 then 4 x v ?
Lella will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an additional $0.14 per mile driven. The
second plan has an initial fee of $51 and costs an additional $0.10 per mile driven