Answer:
[tex] \displaystyle \sin(x) + x\cos( \alpha ) + \rm C[/tex]
Step-by-step explanation:
we are given
[tex] \displaystyle \int \frac{ \cos ^{2} (x) - \cos ^{2} ( \alpha ) }{ \cos( x) - \cos( \alpha ) } dx[/tex]
we want to Integrate it
notice that, the denominator can be rewritten by using algebraic identity
remember that,
[tex] \displaystyle {a}^{2} - {b}^{2} = ( a + b)(a - b)[/tex]
therefore
rewrite the denominator by using the identity:
[tex] \displaystyle \int \frac{ ((\cos (x) + \cos ( \alpha) ) ( \cos(x) - \cos( \alpha ) ) }{ \cos( x) - \cos( \alpha ) }dx [/tex]
reduce fraction:
[tex] \displaystyle \int \frac{ ((\cos (x) + \cos ( \alpha) ) ( \cancel{ \cos(x) -\cos( \alpha ) ) }}{ \cancel{\cos( x) - \cos( \alpha ) } }dx[/tex]
[tex] \displaystyle \int \cos(x) + \cos( \alpha ) dx[/tex]
recall that,
[tex] \rm\displaystyle \int f(x) \pm g(x)dx =\int f(x) \pm \int g(x)dx[/tex]
by that
we get
[tex] \displaystyle \int \cos(x) dx + \int \cos( \alpha )dx [/tex]
we also know that,
[tex] \displaystyle \int \cos(x) = \sin(x)dx [/tex]
and also the Integration of a constant is always cx
so,
[tex] \displaystyle \sin(x) + x\cos( \alpha ) [/tex]
and of course we have to add constant
[tex] \displaystyle \sin(x) + x\cos( \alpha ) + \rm C[/tex]
Find the sum of 7x + 3 and 4x2 -5.
Answer:
[tex]4x^2+7x-2[/tex]
Step-by-step explanation:
group like terms: [tex]4x^2+7x+3-5[/tex]
subtract 5 from 3: 3-5=-2
[tex]4x^2+7x-2[/tex]
HELP ITS IMPORTANT!!!!
Answer:
its b
Step-by-step explanation:
Please help me out! As soon as possible.
Answer:
Number of hours gardening
Step-by-step explanation:
12g
g = Number of hours gardening
If two lines are parallel and they are defined by the equations, y=4x-5 and y=ax+2, what is the value of a?
Answer:
[tex]a=\dfrac{4x-7}{x}[/tex]
Step-by-step explanation:
The equations of lines are :
y=4x-5 and y=ax+2
From above equations,
4x-5 = ax+2
4x-ax = 5+2
4x-7 = ax
[tex]a=\dfrac{4x-7}{x}[/tex]
So, the value of a is equal to [tex]\dfrac{4x-7}{x}[/tex].
Determine the equation of the circle graphed below.
Answer:
(x + 5)² + (y - 1)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 5, 1) and r = 2, then
(x - (- 5))² + (y - 1)² = 2² , that is
(x + 5)² + (y - 1)² = 4
Answer:
Step-by-step explanation:
hello :
hello:
note : an equatin for the circle is : (x-a)²+(y-b)²=r²
when the center is the point : C(a , b) and the radius r
use this graph : given two points in this circle A(-3,1) and B(-7,1)
1) AB/2 = r = 4/2 = 2
2) the midipoint for the segment AB is the center C
a = (-3-7)/2 and b = (1+1)/2
a= -5 and b= 1 so : C(-5 , 1)
an equation is : (x+5)²+(y-1)²=2²
If it took 4 hours to clean 10 houses, how many houses could be cleaned in 8 hours?
Answer:
20
(10 in 4) x 2
10 in 4 & 10 in 4
10 + 10
4 + 4
20 in 8
Create an equation that models the total number of calories Jonathan consumes,y,based on number of biscuits he eats,x,and the 6 packages of pemmican
An equation that models the considered calorie consumption by Jonathan is y = mx + 6k, where m is the number of calorie per buiscuit, and k is the number of calorie per package of pemmican.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
We're specified that:
x = number of buiscuits Jonathan eastsy = number of calories Jonathan consumes6 = number of packages of pemmican that jonathan consumes.Let we take:
m = number of calories per buiscuit that Jonathan eats.
Then, for x buiscuits, it would be [tex]m \times x[/tex] calories, or in short [tex]mx[/tex] calories.
Let k = number of calories per package of pemmican, then:
for 6 packages of pemmican, it would be [tex]6 \times k[/tex] calories, or in short [tex]6k[/tex] calories.
Thus, total calories Jonathan consumes = y = calories from x buiscuits + calories from 6 packages of pemmican.
or, we get:
[tex]y = mx + 6k[/tex]
Thus, an equation that models the considered calorie consumption by Jonathan is y = mx + 6k, where m is the number of calorie per buiscuit, and k is the number of calorie per package of pemmican.
Learn more about forming equations here:
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help if correct will give brainiest
Answer:
x
Step-by-step explanation:
Answer:
the answer is Z all you have to do is move it left 4 times and then up 6 times
write an equivalent expression in standard form.
(2x + 5)(x + 1)
The equivalent expression in standard form is 2x² + 7x + 5.
What is Expression?An expression is combination of variables, numbers and operators.
To write the expression in standard form, we need to simplify it by multiplying the two factors using the distributive property of multiplication:
(2x + 5)(x + 1) = 2x² + 2x + 5x + 5
Combining like terms, we get:
(2x + 5)(x + 1) = 2x² + 7x + 5
Therefore, the equivalent expression in standard form is 2x² + 7x + 5.
To learn more on Expressions click:
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answer this question!!! :)
Answer:
X = 1
Step-by-step explanation:
You first divide each side by 3 leaving you with X+5 = 6. Then you take the 5 to the other side leaving you with X=6-5 as the 5 changes from positive to negative. So 6-5=1 so X=1
Hope this helped
-A3miz
Age:13
Write a congruence statement for the pair of triangles. Name the postulate it theorem that justifies your statement.
Answer:
B
Step-by-step explanation:
This is not a math question ofc... but I want to know if y’all guys like anime?
1.Yes
2.No
3.why.....
UM YES! My favorite is Attack On Titans
Find the diameter of a circle with a circumference of 63 feet. Round your answer to the nearest hundredth.
The diameter is about__
feet.
Answer:
20.05feet
Step-by-step explanation:
Given data
Circumference= 63feet
The expression for circumference is
C= 2πr
substitute
63= 2*3.142*r
63= 6.284r
r= 63/6.284
r=10.025
Hence the diameter is
=10.025*2
=20.05feet
Expand logarithm equation
Answer:
[tex] log_{2}(x) + log_{2}(y) + log_{2}(z)[/tex]
Step-by-step explanation:
[tex]5 log_{2}(xyz)^{ \frac{1}{5} } \\ \\ = 5 \times \frac{1}{5} log_{2}(xyz) \\ \\ = log_{2}(xyz) \\ \\ = log_{2}(x) + log_{2}(y) + log_{2}(z)[/tex]
how many solutions does 2(4x+5)=8x+8
Answer:
Step-by-step explanation:
Its no soluction.
select all expressions that are equivalent to 3x - 2 (x - ) - 1
A.) -9 + x
B.) x + 7
C.) 3x - 2x - 8 - 1
D.) 3x - 2x + 8 - 1
Answer:
a
Step-by-step explanation:
Jenny counted the coins in her bank.
She had 4 times as many nickels as dimes.
She had 8 more quarters than nickels.
She had 52 dimes.
How many quarters did Jenny have in her bank?
A.
21
B.
64
C.
200
D.
216
Answer:
Step-by-step explanation:
its d cause there is actually 208 nickles and if u ad 8 more it gives u 216.
Answer: D.
Step-by-step explanation:
52x4=208
Since we know she has 4 times as many nickels as dimes(52), we just have to multiply 52x4 to get 208 nickels
208+8=216
We know that she has 8 more quarters than nickels(208) so we have to add 8 to 208 to get 216 quarters
I hope this helps
Hopefully it's brainlist
solve the system below.
options:
a. (1,-4)
b. (-4,1)
c. (-1,5)
d. (-1,4)
Answer:
1 and - 4is the correct answer
Rate this 1-10
PLEASE BE HONEST
When I think of you happiness hits me
It did until you played my heart the wrong way at least
But nah that's alright I will deal with you.
I feel du.mb for allowing you to do this to me
I get sad, mad, depressed, and pis.sed everytime
I no longer want you, you hurt me I hurt you
Never again will I make this mistake
Good job making a happy guy mad
This is why I dont trust girls with my heart
So dont break me next time we guys are fragile
If you dont think so do this to another guy
I will not allow you to be like this ever again
Dont play with me next time
But this will not bother me because I dont care
I am going to my old ways of barely any emotions
I wont let this get to me, Good bye my queen
Answer:wow
Step-by-step explanation:
This is honestly amazing 10/10
The parabola is swached vertically by a factor of 5.
Answer:
answer below
Step-by-step explanation:
I think you mean "squashed" or "stretched" vertically by a factor of 5.
f(x) is the original parabola equation
g(x) = 5f(x) is vertically stretched by a factor of 5
(x,y) -> (x , 5y)
in a random School sampling of 50 middle school students it was found that 18 students bring their lunch to school everyday if there are 942 students in the school predict how many bring their lunch to school each day
Answer:
340
Step-by-step explanation:
We can see in the sample that 18/50 people bring lunches to school. If we divide 18 by 50 we get 0.36 now we know that 36% of people bring their lunches in the sample. Now we take that number and multiply it by 942.
0.36*942= 339.12 which we can round to 340
Tressa is traveling by boat from Texas to Florida and she creates a function f(t)= 20t + 15 to show how many miles she has traveled f(t) from her mom’s house in Texas after (t) hours have passed. Which of the following represents the distance the boat has traveled from its original position? please I need help with this
Answer:
20t
Step-by-step explanation:
15 is where the boat started so 20t is how much the boat traveled from the origional position of 15
The 20t distance the boat has traveled from its original position.
Given that,
She creates a function f(t)= 20t + 15,
To show how many miles she has traveled f(t) from her mom’s house in Texas after (t) hours have passed.
We have to determine,
Which of the following represents the distance the boat has traveled from its original position.
According to the question,
She creates a function f(t)= 20t + 15 .
To show how many miles she has traveled f(t) from her mom’s house in Texas after (t) hours have passed.
Then,
Her mom’s house in Texas after (t) hours have passed.
The 15 is where the boat started
And 20t is the boat traveled from the original position of 15.
Hence, The 20t distance the boat has traveled from its original position.
To know more about Motion click the link given below.
https://brainly.com/question/25129327
A football team had a total of 33 players. One third of the players were seniors. How many players were underclassmen?
Answer:
22
Step-by-step explanation:
1/3 of 33=11
11=number of seniors
2/3 of 33=22
22+11=33
22=number of underclassmen
plz can i get brainliest:)
WRITE THE RATIO: A cookie recipe calls for 1 cup of flour to make 24 cookies. Create a proportion to show how many cups of flour are needed to make 36 cookies
Answer:
1&(1/2) or 1.5 or 3/2 cups flour needed for 36 cookies
Step-by-step explanation:
Flour : Cookie ratio (Flour needed to make particular cookie) = 1 : 24
1 cup flour make 24 cookies, so 1/2 cup floor make 12 (half) cookies.
So, 1&(1/2) or 1.5 or 3/2 cups would make 24 + 12, ie = 36 cookies
AlternativelyMultiplying numerator & denominator of fractional ratio 1 : 24 with 1.5 each
(1 x 1.5) : (24 x 1.5)
It implies 1.5 : 36 flour cookie ratio
find the area of the figure. use 3.14 for pi
Answer:
100
Step-by-step explanation:
14-12=2
10-6=4
4x2=8
divid it by 2 cos itza triangl
8/2=4
the smallr square
4x4=16
biggr square
10x8=80
4+16+80=100
Answer:
answer =100 ft²
Step-by-step explanation:
......hope it helps
There about fifteen hundred players in the nfl in a survey of a random sample of 50 players three players were hurt how many players in the nfl would be excpected to get hurt
Answer: 90 players.
Step-by-step explanation:
Since we are informed that in a survey of a random sample of 50 players, 3 players were hurt. This gives a fraction of 3/50 for those that are hurt.
Therefore, in a survey of 1500 players, the number of players expected to be hurt will be:
= 3/50 × 1500
= 90
x-2y=4 in slope intercept form
Answer:
y = 1/2x - 2
Step-by-step explanation:
Slope intercept form:
y = mx + b
x - 2y = 4
-2y = -x + 4
2y = x - 4
y = 1/2x - 2
Which of the following is equivalent to the expression shown below
Answer:
v^3/2
Step-by-step explanation:
(sqrt(v))^3
sqrt(v)^3
v^3/2
The library had 202 shelves of books. Each shelf had 14 books. Librarians checked out 907 books to students. How many books does the library have remaining? PLZ WORTH 25 POINTS
Answer:
1921 books remaining.
Step-by-step explanation:
This library is fairly organized, so each shelf only has 14 books. Now with 202 shelves, we multiple the shelves by the amount of books per shelf.
202x14=2,828
Now, with 2828 books in the library before being checked out, we need to find out how many books left after the students came.
2828-907=1,921
The answer is 1,921 books remaining.
Hope this helps!
When Larry tried to teach his dog Allegra to speak, he gave him 1 sausage - and he barked once. When he
gave him 2 sausages, he barked twice. Then he gave him 3 sausages, and he barked three times.
Larry predicted that Allegra would bark four times if he gave him 4 sausages.
What type of reasoning did Larry use to make his prediction?
A. Deductive reasoning
B. Inductive reasoning
C. Indirect reasoning
D. Circular reasoning
In case of : Allegra barking n = 4 times, when given 4 sausages - Inductive Logic is used.
Given : Allegra barks once & twice & thrice, when Larry gives him 1 & 2 sausages respectively.
So, later he assumes that he would bark 4 times, if given four sausages
Deductive Reasoning is when conclusion related to particular is drawn, based on general universal. Eg : All men are mortal, Ram is a man. Ram is mortal. Inductive Reasoning is when a generalised conclusion is drawn, based on specific case. Eg : Law of gravity based on apple falling. Allegra's case of barking n times for n sausages (1, 2,3 ...) is further generalised for other positive numbers & hence 4. Indirect Reasoning relates two events. If A is true leads to B is true, then B is false implies A has also been false. Circular Reasoning is a logical fallacy of beginning with an already assumed true statement.To learn more, refer https://brainly.com/question/2848937?referrer=searchResults