The solution of the function [tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex] is - cos t - ¹/₄cos 2t + c.
What is the indefinite integral?An indefinite integral is a function that practices the antiderivative of another function.
It can be visually represented as an integral symbol, a function, and then a dx at the end.
The given function is;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex]
Multiply by sint in the function and simplify;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt[/tex]
Use trigonometric formulas for double angles:
[tex]\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t[/tex]
Substitute the values in the function
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\[/tex]
And now we integrate this trigonometric form.
[tex]\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c[/tex]
Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.
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Find the distance between the points (-8, 9) and (2, 9).
units
Answer:
Distance=√(x2−x1)2+(y2−y1)2
Step-by-step explanation:
How to Find Distance Between Two Points?
Note down the coordinates of the two given points in the coordinate plane as, A(x1,y1 x 1 , y 1 ) and B(x2,y2 x 2 , y 2 ).
We can apply the distance formula to find the distance between the two points, d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]
Enter an equation and an answer to the following question:
What is the original list price if the discount is $25 and the discount rate is 12%?
Answer:
$208.30
Step-by-step explanation:
Discount:Let the original price be $ x
Discount % = 12%
Discount = $ 25
12% of x = 25
[tex]\sf \dfrac{12}{100}*x = 25[/tex]
[tex]\sf x = 25 * \dfrac{100}{12}=\dfrac{25*25}{3}\\[/tex]
= $ 208.30
Evaluate the expression -6³
Answer:
-216
Step-by-step explanation:
please mark as brilliant
2. A small plastic vessel has the shape of a truncated cone as shown. A cubic centimeter is the same as a
milliliter. What is the volume of this cup to the nearest milliliter? Show the work you use to find the answer.
If the height of the frustum of the cone is 10 cm. Then the volume of this cup will be 47 milliliters.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A small plastic vessel has the shape of a truncated cone as shown. A cubic centimeter is the same as a milliliter.
Then the volume of this cup to the nearest milliliter will be
The volume is given as
[tex]\rm V = \dfrac{1}{3} \pi (r_2^2 - r_1^2) h[/tex]
We have
Height (h) = 10 cm = 0.1 m
Radius (r₁) = 3.2 cm = 0.032 m
Radius (r₂) = 2.4 cm = 0.024 m
Then the volume will be
[tex]\rm V = \dfrac{1}{3} \pi (0.032^2 - 0.024^2) \times 0.1\\\\\rm V = 4.7 \times 10^{-5} \ \ m^3[/tex]
Then the conversion of m³ to milliliters will be
4.7 × 10⁻⁵ m³ = 4.7 × 10⁻⁵ × 10⁶ millileters
4.7 × 10⁻⁵ m³ = 47 milliliters
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(4h+5) and (h – 6). find the product
Answer:
4h²– 19h – 30
Step-by-step explanation:
(4h+5)(h-6)
=4h²–24h+5h–30
=4h²–19h–30
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:how\:to\: solve\: }}}[/tex]
➣Given➣ (4h+5) and (h – 6) find the product➣ Let's start !
[tex] \qquad \sf{➛ \: (4h + 5) \times (h - 6)} \\ [/tex]
★ Opening brackets multiplying nd solving
[tex]\qquad \sf{➛( \: 4h \times h) +( 4h \times - 6) + (5 \times h) + (5 \times - 6)}\qquad \\ \sf{➛\: {4h}^{2} - 24h + 5h - 30 }[/tex]
★ arranging like terms and solving gives
[tex]\qquad \sf{➛ \: {4h}^{2} - 19h - 30\bold\green{✓}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hope it helps !
Simplify the expression. Write your answer
the distance of -17 from 0
i have no idea what to do :(((
A paint mixture uses a specific blue to yellow ratio. for every 7 gallons of paint, 2 are blue. enter the ratio of yellow paint to total gallons of paint as a fraction?
Answer:
7:9
Step-by-step explanation:
For very 9 gallons of paint, it needs 7 gallons of yellow.
need help with this
The total numbers of A, B, C, D, and F grades are recorded in the table. What was the probability that a student earned a B? (Write as percent rounded to the nearest tenth)
Answer:
18.7%
Step-by-step explanation:
P(B) = 114/ (61+114+220+175+39) = 0.1872 = 18.7%
what’s the answer to this problem , figure out the area and perimeter of this triangle
Answer:
Area=16.65
Perimeter=26.3
Step-by-step explanation:
To find the area of a triangle, you must multply the length and height and divide by two. An equation like this could help find the area of a triangle: A=2÷(L×W) In your case, 7.4 is the length and 4.5 is the base. Multiply 7.4 and 4.5 together and divide the result by 2.
To find the perimeter, just add 7.4, 6.3, and 12.6 together. 4.5 doesn't get added, only the 3 sides of the triangle do. Don't forget to label the measurements.
Write an algebraic expression for the phrase the quotient of 17 and k
Answer:
[tex] \frac{17}{k} [/tex]
does someone mind helping me with this problem? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate the value of c using Pythagoras theorem ~
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 40 {}^{2} = {24}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: b² = \sqrt{40² - 24²} [/tex]
[tex]\qquad \sf \dashrightarrow \: b= \sqrt{1600-576} [/tex]
[tex] {\qquad \sf \dashrightarrow \: b= \sqrt{1024}} [/tex]
[tex]\qquad \sf \dashrightarrow \: b = 32 \: units[/tex]
The length of "b"
Solution:[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]
[tex] {b}^{2} = {40}^{2} - {24}^{2} [/tex]
[tex]b = 1024[/tex]
[tex]b = \sqrt{1024} [/tex]
[tex]b = 32[/tex]
Hence, the length of "b" is 32.
Solve the system of equations below.
4x – 6y = 30
3x + 7y = 80
x =
, y =
Answer:
The answer is stated above:
x=15
y=5
O
3
o A. -
B. 2
OC
3
mly
O D. -2
Answer:
A. -3/2
Step-by-step explanation:
» Concepts
The slope of a line describes the steepness, or the change in y over the change in x of a line. The formula to find the slope, given two points, is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where we put in the x- and y-coordinates of the two points.
» Application
In this case, we're given two points: (-2, 5) and (4, -4). We have to find the slope of the line containing them, so we must use our aforementioned formula.
» Solution
[tex]\frac{(-4)-(5)}{(4)-(-2)}[/tex] [tex]\frac{-9}{4+2}[/tex] [tex]-\frac{9}{6}[/tex] [tex]-3/2[/tex]Therefore, the answer is A. -3/2.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
B
Step-by-step explanation:
There is two wholes and one half.
Solve for a. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Remark
a is one part of the cosine function. It is termed the adjacent side. The given number (12) is the hypotenuse of a right triangle. The reference angle is given as 25. You have all you need to solve for a
Givens
<B = 25o
AB = 12
a = a
Equation
Cos(B) = adjacent side / hypotenuse
Solution
Cos(25) = adjacent side / 12 Multiply both sides by 12
12*cos(25) = adjacent side
cos(25) = 0.90631
12*0.906331 = adjacent side
10.87 = adjacent side
Answer
a = 10.9
A video store specializes in three types of movies: children's, American West, and horror. It's known that:
60% of children's movies plus 50% of westerns account for 30% of all movies.
20% of children's movies plus 60% of westerns plus 60% of horror movies represent half of all movies.
X, y, z denote children's movies, western movies, and horror movies, respectively. The related system of equations is formed and solved.
[tex]\left\{\begin{matrix} \qquad\qquad\ \dfrac{60}{100}x + \dfrac{50}{100}y =\dfrac{30}{100}(x+y+z)\\ \dfrac{20}{100}x+ \dfrac{60}{100}y+ \dfrac{60}{100}z= \dfrac{1}{2}(x+y+z) \\ \ \ \ x+100=y \end{matrix} \right.\[/tex]
Simplifying the system of equations, we have
[tex]\left\{\begin{matrix} 3x + 2y -3z=0\\ -3x+ y+ z= 0 \\ \ \ \ x+100=y \end{matrix} \right.\ \ \Longrightarrow \ \left\{\begin{matrix} 5x-3z=-200\\ -2x+ z= -100 \end{matrix} \right.\[/tex]
[tex]\ \ \ 5x-3z=-200\\\underline{-6x+3z=-300} \ \Rightarrow \ x=500\\\ \ -x+0= \ 500[/tex]
[tex]y&=500+100=600\\ z&=3(500)-600=900[/tex]
The video store has 500 children's movies, 600 westerns and 900 horror movies.
24r + 48 write the expression in two other ways
Answer:
2(12r + 24)
12(r + 2)
HELP IM ON A TIMER
What is the product?
(x - 3)(2x2 – 5x + 1)
O 2x3 - x2 + 16x + 3
O 2x3 - 11x2 + 16x + 3
O 2x3 - 11x2 + 16x - 3
0 2x3 - x2 + 16x - 3
Answer:
The answer is 2x3 - 11x2 + 16x -3
Please someone help me with my question
Answer:
∠A≅∠Z AB ≅ ZX
∠B≅∠X AC ≅ ZY
∠C≅∠Y BC ≅ XY
ΔCBA ≅ ΔYXZ
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
The radius of a circle is 1 meter. What is the circle's circumference?
Use 3.14 for .
Answer:
6.28
Step-by-step explanation:
D = R x 2
D = 2
2 x 3.14 =
6.28
The volume of a rectangular pyramid is 176 units³. If the length of the rectangular base measures 6 units and the width of the rectangular base measures 11 units, find the height of the pyramid.
Answer:
2.66unit
Step-by-step explanation:
volume=176
l×b
6×11=66
Therefore,176÷66=2.66unit
Stacy recorded the number of minutes she used her
smartphone each day for one week before using an
app that awards points for decreased phone usage,
and for one week after using the app. Stacy's
alternative hypothesis is Ha:X< 114.6.
Before 103 127 87 12495 136 130
After 83 94 1201057598 96
Stacy used a simulation to randomize her data 200
times. She found that the difference between sample
means over 200 trials is approximately normally-
distributed, with a mean of -0.2 and a standard
deviation of 9.1. Which of the following conclusions
is most appropriate?
Phone use did not change.
Phone use increased and then decreased.
Phone use increased.
Phone use decreased.
Using the t-distribution, the most appropriate conclusion for the hypotesis test is given by Phone use did not change.
How to find the value of z-statistic for population mean? (z test statistic)Suppose we're specified that:
The sample mean = [tex]\overline{x}[/tex]
The population mean =[tex]\mu[/tex]
The population standard deviation = [tex]\sigma[/tex]
The sample size = n
Then the z-statistic for this data is found as:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}[/tex]
In this problem, the values of those parameters are as follows:
The sample mean [tex]\overline{x}[/tex] = -0.2
The population mean =[tex]\mu[/tex] = 0
The population standard deviation = [tex]\sigma[/tex] = 9.1
The sample size = n = 200
Hence, the test statistic is given by:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}\\\\\\Z = \dfrac{-0.2- 0}{9.1/\sqrt{200}}\\\\z = 0.31[/tex]
Thus,
t = 0.31.
Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and the conclusion is:
Phone use did not change.
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Rena used the steps below to evaluate the expression (StartFraction (x Superscript negative 3 Baseline) (y Superscript negative 2 Baseline) Over 2 (x Superscript 4 Baseline) (y superscript negative 4 Baseline) EndFraction) Superscript negative 3, when x = negative 1 and y = 2.
Step 1:
Substitute x = negative 1 and y = 2 into the expression.
(StartFraction (negative 1) Superscript negative 3 Baseline (2) Superscript negative 2 Baseline Over 2 (negative 1) Superscript 4 Baseline (2) superscript negative 4 Baseline) EndFraction) Superscript negative 3
Step 2:
Simplify the parentheses.
(StartFraction (2) Superscript 4 Baseline Over 2 (negative 1) Superscript 4 Baseline (negative 1) cubed (2) squared EndFraction) Superscript negative 3 Baseline = (StartFraction (2) squared Over 2 (negative 1) Superscript 7 Baseline EndFraction) Superscript negative 3
Step 3:
Evaluate the power to a power.
StartFraction (2) Superscript negative 6 Baseline Over 2 Superscript negative 3 Baseline (negative 1) Superscript negative 21 baseline EndFraction
Step 4:
Use reciprocals and find the value.
StartFraction 1 Over 2 cubed (2) Superscript 6 Baseline (negative 1) Superscript 21 Baseline EndFraction = StartFraction 1 Over 8 times 64 times (negative 1) EndFraction = Negative StartFraction 1 Over 512 EndFraction
In which step did Rena make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:
step 4
Step-by-step explanation:
Solve for the value of x
Answer: 12
Step-by-step explanation:
Do you still have to do summer school if you fail one class? (serious question please answer, and yes i know its in math i just need an answer!)
Answer:
In some schools yes but it depends is it a required class? if so then you'd have to retake it.
Answer:
well you might not have to do summer school but you might have to take a course during summer for that class you failed or you may have to redo that class in order to get the points needed to pass but also it depends because even though you might not pass that one class you can still pass the grade but you will be in the same class or a lower standard for that subject now i am not sure it honestly all depends on your teacher and school if they want you to go the next grade but they can also talk to teachers in the next grade to help you so that you can still pass but you have to do lower standard work for the class in that next grade
Step-by-step explanation:
hope it helps let me know if you have anymore questions or if you need anymore help understanding or if you need help with work so that you can pass i would be happy to help you
Fior 50 points solve this problem
Which graph represents the solution to the system of inequalities below?
5x-4y>4
x+y<2
B. is the correct graph.
See the attachment.
Answer:
Step-by-step explanation:
Use desmos to graph
B is The correct answer for this question
What is NOT a characteristic of a polyhedron?
A. faces
B. vertices
C. edges
D. lines
In your Own words explain what in algebra the deffintion of
Mode
Median
Range
I will try to give brainliest to person who discribes in own words
Answer:
The mean means average. To find it, add together all of your values and divide by the number of addends. The median is the middle number of your data set when in order from least to greatest. The mode is the number that occurred the most often. The range is the difference between the highest and lowest values.
Step-by-step explanation:
hope this helps
have a good day <3
Answer:
hope this helps!!
Step-by-step explanation:
Mode: Are there two students who have the same number of children (could be zero)? If yes, that’s the mode. If not, there is no mode. Median: Put all five numbers in a row from lowest to greatest. The one in the middle is the median. Range: Take the difference of the greatest minus the lowest and that is the range.
Can anyone help solve this
