(a) Since u = cos(x) gives du = -sin(x) dx, we have
∫ sin(x) cos(x) dx = - ∫ (-sin(x)) cos(x) dx
= - ∫ cos(x) d(cos(x))
= - ∫ u du
= - 1/2 u² + C
= -1/2 cos²(x) + C
(b) Now u = sin(x) gives du = cos(x) dx, so
∫ sin(x) cos(x) dx = ∫ sin(x) d(sin(x))
= ∫ u du
= 1/2 u² + C
= 1/2 sin²(x) + C
(c) Since sin(2x) = 2 sin(x) cos(x), we have
∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx
Substitute u = 2x, so that du = 2 dx, and
∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx
= 1/4 ∫ 2 sin(2x) dx
= 1/4 ∫ sin(u) du
= -1/4 cos(u) + C
= -1/4 cos(2x) + C
(d) Integrate by parts, setting
u = sin(x) ==> du = cos(x) dx
dv = cos(x) dx ==> v = sin(x)
Then
∫ sin(x) cos(x) dx = sin²(x) - ∫ sin(x) cos(x) dx
2 ∫ sin(x) cos(x) dx = sin²(x) + C
∫ sin(x) cos(x) dx = 1/2 sin²(x) + C
The solutions in (b) and (d) are identical, but all 4 are equivalent, and this follows from the identities,
sin²(x) + cos²(x) = 1
cos(2x) = cos²(x) - sin²(x)
2. Find the rank of 4 1 3 3 3
7 -1 6 0 6
2 3 8 2 8
Step-by-step explanation:
please mark me as brainlest
The function f is defined by f(x)= - 1/2x^2
Write down the expression for h(x).
Answer: -1/2 (x-4)^2 + 3
Step-by-step explanation:
Since the graphs both have the same stretch of -1/2x^2, you just need to see how much they were shifted up, down, left, or right. h(x) is shifted up 3 and right 4 of f(x) so h(x) = -1/2 (x-4)^2 + 3
Answer:
[tex]h(x)=-\dfrac12(x-4)^2+3[/tex]
Step-by-step explanation:
Given:
[tex]f(x)= - \dfrac12x^2[/tex]
From inspection of the graph, [tex]f(x)[/tex] has been translated 4 units to the right and 3 units up.
Therefore, [tex]h(x)=f(x-4)+3[/tex]
[tex]\implies h(x)=-\dfrac12(x-4)^2+3[/tex]
Mitchell has been given the option of either paying his $200 bill now or settling it for $204 after 1 month (30 days). If he chooses to pay after 1 month, find the simple interest rate at which he would be charged.
The simple interest rate that he would be of 24.33% a year.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem, considering than an year has 365 days, the parameters are as follows:
[tex]A(t) = 204, A(0) = 200, t = \frac{30}{365}[/tex]
Hence:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]204 = 200\left(1 + \frac{30}{365}r\right)[/tex]
[tex]1 + \frac{30}{365}r = \frac{204}{200}[/tex]
[tex]\frac{30}{365}r = 0.02[/tex]
[tex]r = \frac{365}{30} \times 0.02[/tex]
[tex]r = 0.2433[/tex]
The simple interest rate that he would be of 24.33% a year.
More can be learned about simple interest at https://brainly.com/question/25296782
If x = 7-p and y = 3p + 4, which of the following
expresses y in terms of x ?
step by step please !!
Answer:
Step-by-step explanation:
Answer:
y = -3x + 25
Step-by-step explanation:
You have to find p first.
You can do this by using the x equation and moving the p to the right by adding p to each side to get p + x = 7.
Now, move the x to the left by subtracting x on both sides to get a final answer of p = 7 - x
Then, you can substitute p into the y equation.
So, y = 3(7 - x) + 4.
Distribute to get y = 21 - 3x + 4
Combine like factors to get y = -3x + 25
Hope this helps! :)
Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below.
7, 10, 13, 4, 12, 21, 10, 3
What is the MAD of her data set? What does this tell you about the number of miles biked each day by the bicyclists?
Step-by-step explanation:
4
data-mean/total =4
Arc and sector area question please help
Answer:
A. x = 14Step-by-step explanation:
Angle formed by intersecting chords half the sum of intercepted arc measures.Apply this to the given measures:
56 = 1/2(3x + 10 + 5x - 10)56 = 4xx = 56/4x = 14Correct choice is A
17. Mia has 4 inches of red yard and 2 inches of blue yarn. How many inches of yarn does she
have?
Answer:
6 inches
Step-by-step explanation:
Given:
length of red yarn = 4 inlength of blue yarn = 2 inTo find the total amount of yarn Mia has, add the two lengths together:
total yarn = red yarn + blue yard
= 4 in + 2 in
= 6 in
Sebastian started watching a movie at 17:30.
The movie was 1 hour and 54 minutes long, but part-way
through he paused it for 13 minutes.
What was the time when the movie finished?
Give your answer using the 24 hour clock.
Answer:
19:37
Step-by-step explanation:
1 h and 54 m of the movie + 13 minutes that he paused is 2h and 7 m and adding that to the time it was makes it 19:37 or 7:37 pm
The time when the movie finished is 19:37 if Sebastian started watching the movie at 17:30. The movie was 1 hour and 54 minutes long.
What is the time zone?For legal, commercial, and social purposes, a time zone is a region that observes a uniform standard time. Instead of strictly following longitude, time zones tend to follow the borders between countries and their subdivisions.
It is given that:
Sebastian started watching a movie at 17:30. The movie was 1 hour and 54 minutes long, but part-way through he paused it for 13 minutes.
The total duration of the movie = 1 hour and 54 minutes
The total duration of the movie with 13 minutes pause
= 1 hour and 54 minutes + 13 minutes
= 2 hours 7 minutes
The movie starts at 17:30
Movies will end at 19:37
Thus, the time when the movie finished is 19:37 if Sebastian started watching the movie at 17:30. The movie was 1 hour and 54 minutes long.
Learn more about the time zone here:
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Maria buys 15 sarees. Each saree cost Rs. 525.50 Money spent by Maria is
Answer:
Rs. 7882.5
Step-by-step explanation:
if 1 saree ----->525.50
what about 15------>?
15×525.50÷1 = 7882.5.
I hope this helps
Answer:
Rs 7882.50
Step-by-step explanation:
525.50 x 15 = 7882.50
How do you know that the table and the equation represent the same proportional relationship between x and y
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I need solution of 5
if you have a favorite subject in school what is it
Answer:
My favorite subject in school is ELA because I love to read. Please don't judge I am not a nerd. I just like a good book every once and a while.
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
_____________Gym_______________
how many kilograms are in 3650 grams?
Answer:
Step-by-step explanation:
There is [tex]1000g[/tex] in [tex]1kg[/tex].
Therefore we do:
[tex]3650g = \frac{1kg}{1000g} = \frac{3650g}{1000g}=3.65kg[/tex]
What is the slope?
Find the slope of the line in the graph.
Answer:
0.4 or 2/5
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
Rise(up or down) 2 and run(right or left) 5
The whole equation would be y=2/5x+1
| Find the total surface area of the prism.
3 cm
5 cm
8 cm
4 cm
6 cm
Answer:
8
Step-by-step explanation:
If Olivia makes a smoothie with a ratio 7 strawberries to 2 bananas, how many strawberries would she use with 3 bananas?
Answer:
13
Step-by-step explanation:
7strawberries 2 bananas 3 and she use the 3 bananas
and answer is.13
Answer:
The answer is 13 this is because idek
Hugo began his science experiment with 22 grams of sugar crystals. During the experiment, the change in the mass of the sugar crystals was – 6 grams. What is the final mass of the sugar crystals?
Answer:
16
Step-by-step explanation:22 minus 6 is 16
The final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Hugo began his science experiment with 22 grams of sugar crystals.
During the experiment, the change in the mass of the sugar crystals was – 6 grams.
Let x be the final mass of the sugar crystals.
The value of the x can be found using:
x = 22 - 6
x = 16 grams
Thus, the final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.
Learn more about the arithmetic operation here:
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Mrs. keys has 36 pens. Yesterday she had half that amount plus 2. How many pens did she have?
Answer:
20 pens
Step-by-step explanation:
Half of 36 is 18, along with 2 additional pens.
what is the slope intercept equation of this line
Answer:
B
Step-by-step explanation:
One approach is to plug (2, -2) to every function and only B will work.
Choice A) y = 3x + 4
-2 = 3(2) + 4
-2 = 10
Does not work
Choice B) y = -3x + 4
-2 = -3(2) + 4
-2 = -2
Works
Choice C) y = -1/3x + 4
-2 = -1/3(2) + 4
-2 = -2/3 + 4
-2 = -2/3 + 12/3
-2 = 10/3
Does not work
Choice A) y = 4x - 3
-2 = 4(2) - 3
-2 = 5
Does not work
You can also just take a look at the function and see that its slope is downwards so it has to be negative. Then check the slope using rise/run.
For every 1 to the right it goes down 3, so -3/1 = -3. The only function with a slope of -3 is answer choice B.
HELP ME PLEASEEEEEE
THANK YOUUUUU
Answer:
Step-by-step explanation:
WZ and ZR are perpendicular
WZ and ST are parallel
QT and YS are skewed
Plane WZR and plane SYZ are perpendicular
Step-by-step explanation:
WZ and ZP are perpendicular
WZ and ST are parallel
QT and YS are skewed
Plane WZR and plane SYZ are also perpendicular
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answer:
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so:
[tex]8x+3=19 \longrightarrow x=2[/tex]
[tex]27=-y-5 \longrightarrow y=-32[/tex]
3) A certain medication is prescribed based on the patient's weight at 3mg for
every 20 pounds. How many milligrams of medication would you give a patient
who weighs 180 pounds?
Answer:
27 mg
Step-by-step explanation:
divide 180 by 20 to get 9
then multiply 9 by 3
you should get 27mg
y=3x on a graph
a
b
c
d
Answer:
the answer is D cause of the y x axis
The drama club is selling popcorn so they can earn enough money to travel to their next competition. The table below shows how much money the drama club earns for the amount of popcorn sold. Let p represent the number of bags of popcorn sold. Let t represent the total amount earned, in dollars. Number of Bags of Popcorn Sold p Total Amount Earned t 2 $3 4 $6 6 $9 8 $12 Enter an equation that represents the relationship between the number of bags of popcorn sold and the total amount of money earned.
please
Answer:
t=3/2p
Step-by-step explanation:
We can see the linear pattern between t and p as
p/t = 2/3=4/6=6/9 etc... So t/p=1/(2/3) =3/2 and therefore t=3/2p
Slope
m=(6-3)/4-2m=3/2Equation
y=3/2xOr
t=3/2pcan someone answer this question plsss I'm late
it took him 27 minutes to reach home
plz help me will br
If someone is a chef, then he can cook well.
Jack is a terrible cook.
What us a valid conclusión?
Answer:
he is not a chef
Step-by-step explanation:
Answer: he a bad cook.
Step-by-step explanation:
help me and thanks hans for all the help
II. State the aditional information needed to prove each pair of triangles is congruent indicated by the theorem.
Answer:
Step-by-step explanation:
8) HL ---> Hypotenuse and Leg
It is already given legs are congruent
Hypotenuse: DE = IJ
9) LL -----> This SAS congruent ---> Both legs of the right angled traingle are congruent
AC = YX
10) LA ----> This is AAS congruent.
BE = EI
m TMN = x + 72, m LMN = 166°, and m LMT = 96 + x. Find m LMT. what is the answer to this? ill make you the brainly
Answer: LMT=95
Step-by-step explanation:
combine both problems to equal 166
x+x+72+96=166
Combine like terms
2x+168=166
Subtract 168 from 166
2x=168-166
Divide
X=-2/2
X=-1
Plug in -1 for x
96-1=95
72-1=71
71+95=166
LMT=95