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]
Which is greater, 4 or v26
Answer:bvvve26
Step-by-step explanation:
Slove the Equation
-8(k + 46) = -5.
(Please include step-by-step)
Answer: look at the picture
Step-by-step explanation: Hope this help :D
Answer:
[tex]{k = - \frac{363}{8} \: \: \: or \: \: - 45 \frac{3}{8} } \\ [/tex]
Step-by-step explanation:
-8(k + 46) = -5
Expand the terms on the right
-8k - 368 = - 5
Add 368 to both sides of the equation
- 8k - 368 + 368 = - 5 + 368
- 8k = 363
Divide both sides by - 8
[tex] \frac{ - 8k}{ - 8} = - \frac{363}{8} \\[/tex]
We have the final answer as
[tex]k = - \frac{363}{8} \: \: \: or \: \: - 45 \frac{3}{8} \\ [/tex]
Hope this helps you
Shannon used 0.4 kilograms of raisins to make 5 bags of trail mix. How many kilograms of raisins, on
average, did she put in each bag?
Answer:
0.08 kilograms
Step-by-step explanation:
0.4 divided by 8 equals 0.08
On Tuesday morning, the temperature was recorded
at 5°C. Over the course of the day, the temperature
dropped 7º. After this drop, what temperature will be
recorded?
A 12° C
B 2°C
C -2°C
D -12° C

Can someone pls give me the answer to this I need it please
Answer:
i believe it's the first one
Step-by-step explanation:
It took a train 2 3/5 hours to travel 87 1/10 miles. What was the train's
average rate of speed?
Step-by-step explanation:
speed = distance/speed
= 871/10 ÷ 13/5
= 871/10 × 5/13
= 67/2 = 33.5miles/hour
Happy Earth Day. Have a wonderful Day! If you answer you must give me ten Earth day Activities to answer. Thank you! (If you don't got 10 things don't answer.)
Answer:
1. Go around an pick up trash around your neighborhood
2. Separate all the recyclables
3. Work on a Garden
4. Plant something
5. Fund teamtrees.org
6. Tell a friend to do something on this list
7. Don't use any fossil fuel or electricity required things (Like your car, walk instead, or your phone)
8. Dont Eat at any fast food or gourmet restaurants.
9. Eat Healthier no factory produced foods
10. Go on Brainly.com and help some one with their question :D
(っ◔◡◔)っ ♥ Hope It Helps ♥ Please Consider giving Brainliest
Answer:
Any 10 earth day activities are:
cleanlinessplantation recycling plasticsAwarenesssanitation programmeinviting other to involve in environment preservationmanagement of sewage and garbage management of pure drinking watergiving training for management of waste .Visiting zoos,national parks for enjoying wildlife.the diameter of jacob's circular table is 6 feet. what is the area,in square feet, pf jacob's tabletop?
Answer:
28.26
Step-by-step explanation:pie x r^2
What is a third-degree binomial?
Answer:
B and DStep-by-step explanation:
Binomial = 2 terms in the expressionThird degree = highest added degree of variables in one term(A) It has 3 terms and highest degree of 4. It is trinomial of degree 4.
No(B) It has 2 terms and highest degree of 3. It is binomial of degree 3.
Yes(C) It has 2 terms and highest degree of 7. It is binomial of degree 7.
No(D) It has 2 terms and highest degree of 3. It is binomial of degree 3.
Yeslf 60% of a number is 90, what is it number? a)30 b)54 c)150 d)180
Can you please help me ASAP.
15x+20y
Step-by-step explanation:
you do 5x3x=15x & 5x4y=20y
simplify fully: 12/5b² ÷ 3/10ab
Answer:
8a/b
.................
Select the three expressions that are equivalent to 2 (4 - 3x) + (5x-2)
Answer:
The answer correct the questions is 11x-10
Answer:
Step-by-step explanation:
2 (4 - 3x) + (5x-2) can be solved in several basic steps. First, distribute multiplication in 2(4 - 3x), obtaining 8 - 6x and (overall) 8 - 6x + 5x - 2.
Combine like terms: -x = -10, or x = 10
A scuba diver was rising back to the surface after taking photos under water. At 2:50 P.M.,
he was at an elevation of 15.3 feet. At 2:55 P.M., the diver’s depth was 3.7 feet. By how
many feet did the diver’s position change from 2:50 P.M. to 2:55 P.M.
Answer:
the answer is 11.6 feet
Step-by-step explanation:
you simply subtract the feet of the depth he was at at 2:55pm from his depth at 2:50pm
y = x/7 -18 What is the value of y when x = 133?
*Please show work. (Is not mandatory but try to*
Answer:
1
Step-by-step explanation:
(133)/7 - 18
133 ÷ 7 = 19
19 - 18 = 1
Answer: y = 1
Step-by-step explanation:
Well if x is 133 then the problem is y = (133/7) -18
and 133/7 is 19
so the problem is y = 19 - 18
and 19 - 18 is 1, so
y = 1
if G is centroid of triangle ABC and AC = 32. Find the length of CE
Answer:
16
Step-by-step explanation:
From the diagram;
AC = 2CE
Given that AC = 32
32 = 2CE
Swap
2CE = 32
CE = 32/2
CE =16
Hence the length of CE is 16
Solve the inequality. -8y_<40 The solution is .
Answer:
Hi! The answer to your question is y [tex]\geq[/tex] -5
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
A map uses a scale of 3/4 in = 80 miles. If two buildings are 60 miles apart in real life, how far apart would they be drawn on the map?
Given:
The scale of a map is [tex]\dfrac{3}{4}\ in=80\ miles[/tex].
The distance between two buildings is 60 miles.
To find:
The distance between the given building on the map.
Solution:
We have,
[tex]\dfrac{3}{4}\ in=80\ miles[/tex]
It means, 80 miles in real life = [tex]\dfrac{3}{4}\ in[/tex] on the map.
1 mile in real life = [tex]\dfrac{3}{4\times 80}\ in[/tex] on the map.
60 mile in real life = [tex]\dfrac{3\times 60}{4\times 80}\ in[/tex] on the map.
= [tex]\dfrac{180}{320}\ in[/tex] on the map.
= [tex]\dfrac{9}{16}\ in[/tex] on the map.
Therefore, the buildings are [tex]\dfrac{9}{16}\ in[/tex] apart on the map.
Need help asapp!!
- x < 5
- x > 5
Answer: it A
Step-by-step explanation: Hope this help :D
What are the 2 largest desert of East Asia? I WILL GIVE YOU THE BRAIBLIEST!!!!!!!!!!!!!!!!!!!
Answer:
Gobi Desert and karakum desert
Step-by-step explanation:
can someone help?? please!
Answer:
cheese
Step-by-step explanation:
cheese is the best answer
I CAN DO IT!
A. Directions: In a 500-m run competition, the following data was recorded. Solve
velocity using the formula, v-d/t, wherein: v=velocity, d=displacement, time
v(m/s)
PLAYERS
Marione
Hannah
William
Princess
Axel
d(m)
500in
500m
500m
500m
500m
t(s)
53
60
55
58
63
Paturo plsss answer now
Answer:
Marione= 500/53= 9.43m/s
Hannah= 500/60= 8.33m/s
William= 500/55= 9.09m/s
Princess= 500/58= 8.62m/s
Axel= 500/63= 7.94m/s
is 5(x+1) the same as 5x+1? Explain your answer.
If the $3.80 large popcorn was on sale for 25% off, what is the discounted price?
Answer:
2.85
Step-by-step explanation:
You will pay $2.85 for a item with original price of $3.80 when discounted 25%. In this example, if you buy an item at $3.80 with 25% discount, you will pay 3.80 - 0.95 = 2.85 dollars.
Answer:
2.85
Step-by-step explanation:
25%= 100÷25=4
3.80÷4 =0.95
25% of 3.80 = 0.95
discounted price:
3.80-0.95
=2.85
plz answer brainliest and 20 points
Answer:
hi
Step-by-step explanation:
41.89° = 41° + (0.89 X 60)' = 41° + 53.4
41°53' to the nearest minute.
eo
Exercise 5b
In AABC, A = 290, B = 36º, b = 15-8 cm.
Find a.
1
Answer:
a
Step-by-step explanation:
the sides across from each other are called_____ sides
Answer: Vertical Angles are the angles opposite each other when two lines cross.
Step-by-step explanation:
Answer:
hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle
Step-by-step explanation:
find the quantity whose 17 % is rupees 8500
Rs 121428.5714 is Answer:
let quantity be x
17% of x=Rs 8500
x=8500×100/7=Rs 121428.5714
i really need help please help me
Answer:
The orginial angle is a right angle (however, the pair of angles would be classified as complementary angles); the value of x is 28.
Step-by-step explanation:
It's important to note that a right angle is always 90°.
90 - 56 = 34
Set up an equation to solve for x:
34 - 6 = x
34 - 6 = 28
28 = x
Now, check if the answer is correct.
Add up both angles' measurements:
56 + (28 + 6) = 90
Mhanifa please help this is due soon !
Answer:
#1Verify the ratios of corresponding sides are same
ΔABC and ΔXYZ
12/18 = 15/25.20.666 ≠ 0.595NoΔDEF and ΔXYZ
10/18 = 14/25.20.555 = 0.555Yes#13Define the scale factor and use it to fid the missing sides
Scale factor is:
k = 9/21 = 3/7The other sides:
42*3/7 = 1835*3/7 = 15