Answer:
ln (1 + sin^2(x)) + C
Step-by-step explanation:
Note that sin(2x) = 2 sin(x) cos(x).
So, the integrand is rewritten as:
(2 sin(x) cos(x)) / (1 + sin^2(x) ).
Now, make the substitution u = sin(x), so that du = cos(x) dx. Thus, in terms of the variable u, the integrand is
(2 u )/(1 + u^2).
Make another substitution v = 1 + u^2, so that dv = 2 u du, and the integrand in terms of v is
1 / v
Now, we integrate, and then back substitute to write that the indefinite integral is
ln |v| + C = ln |1 + u^2| + C = ln |1 + sin^2(x)| + C + ln (1 + sin^2(x)) +C, since 1 + sin^2(x) + 1 is positive for all real x.
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to evaluate the given integral.
[tex] \displaystyle \rm = \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx[/tex]
[tex] \displaystyle \rm = \int \dfrac{2 \sin(x) \cos(x) }{1 + \sin^{2} (x) } \: dx[/tex]
Now let us assume that:
[tex] \rm \longmapsto u = 1 + { \sin}^{2}(x)[/tex]
[tex] \rm \longmapsto \dfrac{du}{dx} = 2 \sin(x) \cos(x) [/tex]
[tex] \rm \longmapsto dx = \dfrac{1}{2 \sin(x) \cos(x) } \: du[/tex]
Therefore, the integral becomes:
[tex] \displaystyle \rm = \int \dfrac{1}{u} \: du[/tex]
[tex] \displaystyle \rm = \ln(u) + C[/tex]
[tex] \displaystyle \rm = \ln(1 + sin^{2}x ) + C[/tex]
Therefore:
[tex] \displaystyle \rm \longmapsto \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx = \ln(1 + sin^{2}x ) + C[/tex]
(8×1017)÷(2×103)Give your answer in standard form.
a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 27 cm to 17 cm in 30 minutes. at what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 1 cm?
Answer:
3.30=90
17/1=17
90+17=107
Step-by-step explanation:
help!!!!!!! i will pay, 15$ payment method of ur choice
Pls??? I’ll help u if u help me!!!
Answer: the answer is 21
Step-by-step explanation:
Find the greatest common factor of the following numbers.
The following statements are true about the coins Calvin and Sasha have collected.
Calvin and Sasha have the same amount of money.
Calvin has only quarters.
• Sasha has dimes, nickels, and pennies.
Calvin has the same number of quarters as Sasha has dimes.
Sasha has $1.95 in coins that are not dimes.
Exactly how many quarters does Calvin have?
Answer:
bhai sorry bhai Ham Hindi Wale Hain English Nahin samajhte to please Ham bhi a question mat dena Humko is question ka answer Nahin patahai
The amount of money Calvin and Sasha have, is an illustration of equivalent expressions.
Calvin has exactly 13 quarters
From the question, we have:
[tex]\mathbf{Calvin = 0.25Q}[/tex]
[tex]\mathbf{Sasha = 0.05N + 0.01P + 0.10D}[/tex]
Calvin has the same number of quarters as Sasha has dimes.
So, we have:
[tex]\mathbf{Q = D}[/tex]
Sasha has $1.95 in coins that are not dimes.
So, we have
[tex]\mathbf{0.05N +0.01P = 1.95}[/tex]
They have the same amount of money i.e.
[tex]\mathbf{Calvin = Sasha}[/tex]
This gives
[tex]\mathbf{0.25Q = 0.05N + 0.01P + 0.10D }[/tex]
Substitute [tex]\mathbf{0.05N +0.01P = 1.95}[/tex]
[tex]\mathbf{0.25Q = 1.95 + 0.10D }[/tex]
Substitute [tex]\mathbf{Q = D}[/tex]
[tex]\mathbf{0.25Q = 1.95 + 0.10Q }[/tex]
Collect like terms
[tex]\mathbf{0.25Q -0.10Q= 1.95 }\\[/tex]
[tex]\mathbf{0.15Q= 1.95 }[/tex]
Divide both sides by 0.15
[tex]\mathbf{Q= 13 }[/tex]
Hence, Calvin has exactly 13 quarters
Read more about equivalent expressions at:
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1. What is the degree of the polynomial of a quadratic inequality? a. 0 c. 2 b. 1 d. 3 ing cannot be considered as a quadratic ine
Answer:
2
Step-by-step explanation:
Quadratic means degree 2
Help me Pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
I'm not 100%, but d is my answer because in conic sections you're on the negative side and it's the only answer with a negative integer
The circle P has a center at (0, 0) and a point on the circle at (0, 4). If it is dilated by a factor of 4, what is the distance of the radius for circle P'.
A. 16
B. 4
C. 8
D. 1
Needs to be answered quickly
Answer:
16
Step-by-step explanation:
Solve the inequality. Apply properties
Add
Subtract
Multiply
Divide
1/2-1/4x ≥ -1/4
Answer:
x [tex]\leq[/tex] 3
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] - [tex]\frac{1}{4}[/tex]x [tex]\geq[/tex] - [tex]\frac{1}{4}[/tex]
the first step is to subtract [tex]\frac{1}{2}[/tex] from both sides of the equation.
[tex]\frac{1}{2}[/tex] - [tex]\frac{1}{4}[/tex]x [tex]\geq[/tex] - [tex]\frac{1}{4}[/tex]
-[tex]\frac{1}{2}[/tex] - [tex]\frac{1}{2}[/tex]
----------------
-[tex]\frac{1}{4}[/tex]x [tex]\geq[/tex] - [tex]\frac{3}{4}[/tex]
then, divide both sides of the equation by - [tex]\frac{1}{4}[/tex].
x [tex]\leq[/tex] 3
(since we divided both sides by a negative number, to isolate x, the [tex]\geq[/tex] changed to [tex]\leq[/tex].)
Answer:
1/2 - 1/4x ≥ -1/4
multiply both sides by the l.c.m of the both sides(4)
4(1/2 - 1/4x )≥ -1/4 ×4
2 - x ≥ -1
Collect the like terms
-x ≥ -3
Divide both sides by -1
x ≤ 3(when you divide by a negative number the equality changes)
round 2,169,421 to the nearest ten thousand
Answer:
the answer is 2,170,000
Step-by-step explanation:
round the 6 to 7 and make everything behind a zero so it is 2,170,000
Paul mixes nuts worth $1.40 per pound with oats worth $1.70 per pound to get 30 pounds of trail mix worth $1.50 per pound. How many pounds of nuts and how many pounds of oats did he use?
Paul used pounds of nuts and pounds of oats.
The quantity of pounds of nuts and oats used by Paul is 20 and 10 pounds respectively.
According to the question:
Let pounds of nuts used = x Let pounds of oats used = yTotal quantity of trail mix used = 30 pounds and Overall cost of trail mix = 30 × 1.50 = $45.The information above can be used to generate two equations as follows;
1.4x + 1.7y = 45.............eqn(1)x + y = 30.......................eqn(2)Consequently, by solving the equations simultaneously; we have;
Pounds of nuts, x = 20 pounds.Pounds of oats, y = 10 pounds.Read more:
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Can someone please help me?
Answer:
[tex]\huge\boxed{\sf x\° = 31.8\°}[/tex]
Step-by-step explanation:
Using one of the trigonometric ratios.
sin x° = opposite / hypotenuse
Where: opposite = 39, hypotenuse = 74
sin x° = 39/74
x° = sin⁻¹ 39 / 74
x° = 31.8°
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
use the EQUATION of Sine Cosine Tangent rule
Step-by-step explanation:1
1.Do the pythagoras theorem
2.use the equation
i guess you can take it from here
Mark me as brainiest if you find this helpful a bit
3|5x+2|+10=4
Absolute value
Can you find what each of the answers are
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
1. Find Angle A :
[tex]x + 24 = 3x[/tex][tex]3x - x = 2 4[/tex][tex]2x = 24[/tex][tex]x = 12[/tex]Angle A :
[tex]3x[/tex][tex]3 \times 12[/tex][tex]36 \degree[/tex]2. Find Angle B :
[tex]10x - 27 = 7x[/tex][tex]10x - 7x = 27[/tex][tex]3x = 27[/tex][tex]x = 9[/tex]Angle B :
[tex]10x - 27[/tex][tex](10 \times 9) - 27[/tex][tex]90 - 27[/tex][tex]63 \degree[/tex]Find Angle C :
[tex]5x + 1 = 6x - 13[/tex][tex]6x - 5 x = 1 + 13[/tex][tex]x = 14[/tex]Angle C :
[tex]5x + 1[/tex][tex](5 \times 14) + 1[/tex][tex]70 + 1[/tex][tex]71 \degree[/tex]Find Angle D :
[tex]6x + 3 = 4x + 39[/tex][tex]6x - 4x = 39 - 3[/tex][tex]2x = 36[/tex][tex]x = 18[/tex]Angle D :
[tex]4x + 39[/tex][tex](4 \times 18) + 39[/tex][tex]72 + 39[/tex][tex]111\degree[/tex]And it's given :
36° = Angle A = B 63° = Angle B = A 71° = Angle C = H111° = Angle D = ETherefore, the answer will be " BAHE "
Please answer this question
Range: lowest possible y-value to the highest possible y-value
In this case, the graph spans from -4 to 1, taking on all of the y-values between those two points. But, the graph also has a straight line at y=3.
Range: -4 < y <= 1 or {3}
Hope this helps!
Once simplified, which expression is not
equivalent to the other three expressions?
A. 2(4k + 15) - 12(k + 1)
B. 5(2 - k) + 8 + k
C. -2- (9k - 16) + 5k
D. 16 - 2k – 2(k - 1)
Will give brainliest :)
Answer:
C
Step-by-step explanation:
If you look at the constant terms for each of them, ABD is 18, and only C is 14
Find the value of x that makes m
Answer:
X = 20
Step-by-step explanation:
Hope this helps! If you need the explanation, let me know. Pls give brainliest!
Answer:
[tex]{20}^{o} [/tex]
Step-by-step explanation:
hint alternate angles are equal,
the angle portrayed in the diagram are alternate angles ,ie equal,
for an equation equating the two angles then solve for x
ie,
[tex]3x = 2x + 20 \\ 3x - 2x = 20 \\ x = 20[/tex]
Find X and Y, geometry problem.
Answer: x = 45 and y = 10
Step-by-step explanation: in the picture
Please give me a brainliest answer
3
The students in the Park City schools sold raffle tickets for their district.
• The elementary school students sold 2 thousand raffle tickets
The middle school students sold 9 hundred raffle tickets.
The high school students sold 10 times as many raffle tickets as did students in the elementary and
middle schools combined.
How many raffle tickets did the students in the high school sell?
Answer:
29000
Step-by-step explanation:
2000+900= 2900
2900x10= 29000
Jamal is using the distance formula to find the length, d, of the line segment. His work so far is shown. What is Jamal's next step?
Jamal should find the a(midpoint of each leg) b(midpoint of d) c(length of each leg)
by a(adding the x coordinate and y coordinate) b(squaring x coordinate and y coordinate) c(subtracting x coordinate and y coordinate)
.
Answer:
Jamal should find the Length of each leg by Subtracting the x coordinates and the y-coordinates and y-coordinates.
Step-by-step explanation:
Ansewer for Edmentum:)
Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate
What is right triangle?"It is a triangle whose one the angle measures 90°"
What is Pythagoras theorem?"In a right triangle [tex]c^{2} =a^{2} +b^{2}[/tex] where c is the hypotenuse and a, b are other two sides of right triangle."
What is the distance formula?"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] "
For given question,
Jamal wants to find the length of 'd'
For right triangle in the figure, 'd' is the hypotenuse.
Jamal should find the other two sides of the triangle.
And then using Pythagoras theorem, Jamal can find the length of 'd'
So, Jamal need to find the length of each leg by subtracting x coordinate and y coordinate.
Therefore, Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate
Learn more about distance here:
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A bakery sells trays of cookies. Each tray contains at
least 50 cookies but no more than 60. Which of the
following could be the total number of cookies on
4 trays of cookies?
Answer:
56
Step-by-step explanation:
Please help asap!!!!!!!!!!!!!
The fomula is y=mx+b
The number before x is the slope! Rise over run.
The + __ number is the y-intersect. use this number to place a point on the Y line.
'[oij u9jijij[9ojjk2 =
Answer:
hi
Step-by-step explanation:
I don't know it just makes sense
Round 827.4715 to four significant figures
Answer:
827.5( to four significant figures)
2x + 3y = 8 find x intercept
Answer:
(4,0)
4 is the X intercept
Step-by-step explanation:
3y = -2x + 8
3y - 8 = -2x
-2/3y + 4 = x
Find the measure of AD⏜ in ⊙F ?
LESSON Measuring Angles and Arcs
Explain your reason
Answer:
153
Step-by-step explanation:
Angle AFE is 63 and Angle DFE is a 90 degree angle add them both up and you get 153
Please help marking brainliest!!
A bird was sitting 8 meters from the base of an oak tree. It then flew in a straight line 9 meters to reach the top of the tree.
How tall is the tree?
The tree is
meters tall.
Note: Round your answer to the nearest hundredth.
Answer:
wouldn't it be 17 meters?
=========================================================
Explanation:
Draw a right triangle. The horizontal leg is 8 meters. The hypotenuse is 9 meters. The vertical height is unknown, so we'll call it x.
Apply the pythagorean theorem to solve for x
[tex]a^2 + b^2 = c^2\\\\8^2 + x^2 = 9^2\\\\64 + x^2 = 81\\\\x^2 = 81-64\\\\x^2 = 17\\\\x = \sqrt{17}\\\\x \approx 4.1231056\\\\x \approx 4.12\\\\[/tex]
The tree is approximately 4.12 meters tall
Check out the diagram below.
Quick question: Did I do this right?
Answer:
Yes. good job :)
keep up the good work 0u0
Step-by-step explanation:
The local hamburger restaurant is famous for how quickly they can assemble a burger. The restaurant advertises that its constant rate of assembling burgers is t = 11.3h, where t is the total amount of time in seconds and h is the number of hamburgers assembled.
Please fill in the blanks (picture above)
also explain how to solve this
The awnser you can put in for the blanks are-
33.9
56.5
90.4
45.2
55.5
67.8
11.3
22.6
Answer:
The answer should be 22.6, 33.9, 56.5, and 90.4
Step-by-step explanation:
The 11.3 stands for the time it takes to make one burger. The h stands for how many burgers. So for every burger you make, you simply multiply by 11.3