Answer:
[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{ \sin(x + a) }{ \sin(x) } dx[/tex]
we can rewrite the denominator by using algebraic identity given by:
[tex] \displaystyle \rm\sin( \alpha \pm \beta ) = \sin( \alpha ) \cos( \beta ) \pm \cos( \alpha ) \sin( \beta ) [/tex]
thus substitute:
[tex] \displaystyle \int \frac{ \sin(x ) \cos(a) + \cos(x) \sin(a) } { \sin(x) } dx[/tex]
we should rewrite integrand as sum therefore we can use sum integration formula
[tex] \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } + \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]
use sum integration formula:
[tex] \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]
reduce fraction:
[tex] \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]
rewrite:
[tex] \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) } { \sin(x) } \cdot \sin( a) dx[/tex]
use trigonometric indentity:
[tex] \displaystyle \rm\int \cos(a) dx + \int \cot(x) \cdot \sin( a) dx[/tex]
use constant integration formula
[tex] \displaystyle \rm\int \cos(a) dx + \sin(a) \int \cot(x) dx[/tex]
use integration rules:
[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right)[/tex]
and finally we of course have to add constant of integration
[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C[/tex]
And we are done!
[tex]\text{Note:I used integration by substitution to figure out }\\\displaystyle \int \cot(x)dx \:\text{part}[/tex]
help would be nice right about now:)))
Answer:
6x+4=52
-4 -4
6x=48
/6 /6
x=8
Step-by-step explanation:
i hope this helps :)
Solve these equations: |x-6|=-10
Answer:
I got x= -4 as the answer. I hope it helps
Calculate the expected value of playing a lottery ticket game where each ticket costs $5, and the chance of having winning ticket is one in one million, and the payout for having a winning ticket is 4.9 billion dollars. Round the expected value to the nearest cent.
Answer:
$4895
Step-by-step explanation:
P(winning) = 1 / 1000000 = 0.000001
P(not winning) = 1 - 1/1000000 = 0.999999
Winning amount = 4,900,000,000 - 5 = 4899999995
Amount lost = - 5
__ X: - 5 _________ 4899999995
P(X) : 0.999999 ___ 0.000001
Expected value E(x) = Σx * p(x)
E(x) = - 5(0.999999) + 4899999995(0.000001)
E(x) = - 4.999995 + 4899.999995
E(x) = 4895
Hence, expected value is 4895
Rami designed a small pond for a restaurant. The diagram below shows the measurements of the pond. How many cubic feet of water are needed to fill the pond?
Answer:
426
Step-by-step explanation:
Consider the net of a prism below. Describe the prism that the net models.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the net of the prism is not shown.
However, I will give a general explanation on how to determine the net of the three popular prisms.
(1) Rectangular prism.
It is made up of 6 rectangles
(2) Triangular prism
It consists of 3 rectangles and 2 triangles
(3) Square prism
It is made up of 6 squares
See attachment for the net of each prism
What are vertical angles called?
Answer:
They are called vertical angles but are also known as "Vertically Opposite Angles"
Step-by-step explanation:
can i get brainliest im 1 away from ranking up
Answer:
"Vertical" refers to the vertex
Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.
Step-by-step explanation:
The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down. They are also called vertically opposite angles.
I'M SO SORRY IF WRONG FORGIVE ME the internet gave me this
Answer:
2x + 2x + x - 8 = 4 (x + 2)
x = 16
Step-by-step explanation:
Because that's a square, the perimeter would be 4s where s is the measure of the side:
2x + 2x + x - 8 = 4 (x + 2)
To solve, refer below:
2x + 2x + x - 8 = 4x + 8
5x - 8 = 4x + 8
5x = 4x + 8 + 8
x = 16
80% of the tickets sold at a water park were child tickets. If the park sold 720 tickets in all, how many child tickets did it sell?
Answer:
576 child tickets were sold.
Step-by-step explanation:
Since you know the amount of tickets that were sold and the percentage of the tickets that were child tickets, you have to multiply the number of tickets sold by that percentage to find the answer:
720*80%= 576
According to this, the answer is that 576 child tickets were sold.
help me pls very much appreciated luvs <33
Answer:
18
Step-by-step explanation:
Since this is a multiple choice question, I will employ the guess and check method - meaning I will check each answer one by one.
Variable x = dimes = $0.10
Variable y = quarters = $0.25
Set up a system of equations:
x + y = 38
x(0.10) + y(0.25) = 6.80
Plug in each choice into the second equation. You can find the number of quarters that correspond to each number of dimes by using the first equation.
20 dimes:
20 + y = 38
y = 18
20(0.10) + 18(0.25) = 6.80
2 + 4.5 = 6.80
6.5 does not equal 6.80
Because dimes (x) are worth less than quarters (y), this result tells us the answer will be less than 20 dimes as with 20 or more we have less than $6.80. Another example just to show this is true:
38 dimes:
38 + y = 38
y = 0
38(0.10) + 0(0.25) = 6.80
3.8 + 0 = 6.80
3.8 does not equal 6.80.
Since x is worth less than y, we need more of y rather than x. Adding more x will only mean we will get a lower price. Adding more y will mean we get a higher price which is what we need. So only solve for x that is less than 20.
6
6 + y = 38
y = 22
6(0.10) + 32(0.25) = 6.80
0.60 + 8 = 8.60
8.60 does not equal 6.80.
This result is higher than what we wanted (6.80) which means we need more x. Now we only have to solve for x numbers that are greater than 6 and less than 20.
18
18 + y = 38
y = 20
18(0.10) + 20(0.25) = 6.80
1.8 + 5 = 6.8
6.8 does equal 6.8.
Correct!
please helppppppppppp
Answer:
RQ = 5 cm
ST = 8 cm
Find the value of x. Round to the nearest tenth.
help please!
integrate the following:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2a) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
Answer:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
notice that you can simplify the integrand
recall that,
[tex] \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1[/tex]
thus substitute:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx[/tex]
remove parentheses:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx[/tex]
[tex]\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
factor out 2:
[tex]\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
we can use algebraic identity i.e
a²-b²=(a+b)(a-b) to factor the denominator
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
reduce fraction:
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx[/tex]
[tex] \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx[/tex]
distribute:
[tex] \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx[/tex]
use sum integration formula:
[tex] \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx[/tex]
recall integration rules:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) [/tex]
and we of course have to add constant of integration
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
what is the slope of a line passing through (-3,-7) and (1,4)
solution,
slope(m) = y2-y1/ x2-x1
= 4+7/1+3
=11/4
I hope this is correct, the formula can be wrong so pls double check if u have formula.
i need help on my math problem
Answer:
420 cubic inches. Or 420 inches cubed
Step-by-step explanation:
V = l * w * h
12 * 7 * 5 = 420
Answer:
7*5*12= 420
Step-by-step explanation:
Volume of a rectangular prism would be Length * width * height.
so the length = 12 inches
the width = 5 inches
and the height = 7 inches
Plug those in and you get 420 inches cubed :)
The graph shows the population of a city from 1900 to 2000. What is the average rate of change of the population between 1950 and 1980?
Please help! I attached a photo of the graph.
Answer:
-15
Step-by-step explanation:
in 1950 it was 45 and in 1980 it was 30 so it is -15
The average rate of change can be define as the value of something is changing with respect to another thing is tinging. The average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.
Given information-The given graph shows the population of a city between the year 1900 to 2000.
Average rate of change-The average rate of change can be define as the value of something is changing with respect to another thing is tinging.
Form the given graph,
The year 1950 is between the year 1940 and year 1960. The value at the y axis where the population (in thousand) shown is 45,000 for the year 1950.
The year 1980 is shown in graph at the x axis and the value of the population in the y axis is 30,000.
Thus the population is decreasing from year 1950 to 1980. The difference in the population of the year 1950 and 1980 is,
[tex]d=45000-30000[/tex]
[tex]d=15000[/tex]
Thus the change in the population between 1950 and 1980 is 15,000.
Average rate of change of the population between 1950 and 1980 -
As the population and the year both are changing. The rate of change for the population with respect to the year can be calculating by dividing the difference of the population between two year to the total years between the 1950 to 1980.
There is total 30 year from 1950 to 1980, thus the average rate of change is,
[tex]A(x)=\dfrac{15000}{30} \\ A(x)=500[/tex]
Thus the average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.
Learn more about the average rate of change here;
https://brainly.com/question/2530409
9multiply root 3 by 3 root 5
Answer:
[tex] \frac{9 \sqrt{3} }{3 \sqrt{5} } \\ = \frac{3 \sqrt{3} }{ \sqrt{5} } [/tex]
Hope it helps!
Find the missing measurement round answer to nearest tenth
Answer:
hope this helps you out five is a little harder to read sorry
Help me with this question pls
T.J. invests $8,100 in an account
that earns 7.2% compound interest.
If T.J. does not make any additional
deposits or withdrawals, how much
interest will he earn after 7 years?
Answer:
I don't know
Step-by-step explanation:
if don't know
please show work
Max has a collection of 99 dimes and pennies worth $4.41. How many pennies does he have?
Answer:
61 pennies
Step-by-step explanation:
d + p = 99
0.1d + 0.01p = 4.41
d = 99 - p
0.1(99 - p) + 0.01p = 4.41
9.9 - 0.1p + 0.01p = 4.41
-0.09p = -5.49
p = 61
Answer: 61 pennies
What is the measure of RMN( don’t understand how to get the answer) PLZZZ HELP.
Answer:
RMN+117°=180
RMN=63°
Angle RMN is on the straight line with <117 in which the sum of angle on a straight line add up to 180 so we subtract 117 from 180 to get RMN
Translate algebra expressions take away 2 from 8 times f
Answer:
Algebraic Expression:
[tex]8f - 2[/tex]
Answer:
(8f)-2
Step-by-step explanation:
8 times f is multiplication, take two away is subtraction.
evaluate 4^3+3x5-8Captionless Image
Answer:
71
Step-by-step explanation:
64+3×5-8
64+15-8
79-8
71
Answer:
71
Step-by-step explanation:
4^3 = 64 + 15 = 79 - 8 = 71
Give me my brainllest
The triangle and the trapezoid share a 15 inch base and height of 10 inches.
The area of the trapezoid is less than twice the area of the triangle. Find the value of x. Explain your reasoning.
Can the area of the trapezoid be exactly twice the area of the triangle? Explain your reasoning.
Answer:
15 ; yes
Step-by-step explanation:
Base = 15 inches
Height = 10 inches
Area of triangle = 1/2* base * height
Area of triangle = 0.5 * 15 * 10
Area of triangle = 75 in²
Area of trapezium < 2(75)
Area of trapezium, A
A = 1/2*(x+b)h
x = top base ; b = bottom base ; h = 10
1/2*(x + 15)10 < 150
5x + 75 < 150
5x < 150 - 75
5x < 75
x < 15
Hence, Area of trapezoid :
A = 1/2 * (15 + 15)10
A = 1/2 * (30)10
A = 1/2 * 300
A = 150
Hence, Area of trapezium can be twice the area of triangle.
2(75) = 150
The following table of values represents a...
A) Linear Function
B) Quadratic Function
C) Exponential Function
D) Rational Function
Answer:
C: Exponential function
Step-by-step explanation:
This is an exponential function. While the terms decrease steadily, they do not decrease by subtraction of any common difference. Definitely not a linear function (y = mx + b) or a quadratic (ax^2 + bx + c) either.
Which of the following has zero width and an infinite length? A. a point B. a line segment C. a line D. a plane
Answer:line
Step-by-step explanation: the section between any two points on a line is called a line segment a line segment can be very long or very short or somewhere in between the difference between a line and a line segment is that a line segment has two endpoints and a line goes on forever
Can you guys help me with a math problem
If Jacob had an allowance for 20 every 2 weeks how much money will he have saved up after 17 months
Please help I am on a timer
Answer:
680.. that is if we are only doing 4 weeks = a month but yeah :)
Step-by-step explanation:
Answer:
about 680
Step-by-step explanation:
17 months rounds up to 68 weeks so divide by 2 and it would make 34 since jacob is getting the allowance every two weeks then multiply it by 20 which makes 680
i don't know if this is correct but I hope it helps
Find c.
Round to the nearest tenth:
8 cm
82
55°
b
c = [? ]cm
Law of Sines:
sin A
sin C
sin B
b
Please help asap
Answer:
9.7cm
Step-by-step explanation
According to the sine rule;
a/sinA = c/sinC
8/sin55 = c/sin82
Cross multiply
csin55 = 8sin82
c(0.8192) = 8(0.9903)
c = 8(0.9903)/0.8192
c = 7.9221/0.8192
c = 9.67
Hence the value of c to the nearest tenth is 9.7cm
What is the equation?
Answer:
76
Step-by-step explanation: and explain
Answer:
Step-by-step explanation:
hello : here is an solution
what is the length of RU?
Answer:
Length of RU is 20 units.
Step-by-step explanation:
In ΔRSt and ΔRUT,
ST ≅ TU [Given]
RT ≅ RT [Reflexive property]
∠RTS ≅ ∠RTU [Both the angles are the right angles]
ΔRTS ≅ ΔRTU [By SAS property of congruence]
Therefore, RS ≅ RU [By CPCTC (corresponding parts of the congruent triangles are congruent]
8x = 6x + 5
8x - 6x = 5
2x = 5
x = 2.5
Length of RU = (6x + 5)
= 6(2.5) + 5
= 15 + 5
= 20
Length of RU is 20 units.