Answers
∫ -------------------- dx
x² + 6x + 10
1
∫ -------------------- dx
(x+3)² + 1
Let t = x + 3
dt = dx
1
∫ -------------------- dt
t²+1
1/1 arctan(t/1)
1/1 arctan (x+3 / 1)
=arctan(x+3) + C
Related Questions
5 for $4.45 or 8 for $7.28
Answers
Answer:
5 for $4.45
Step-by-step explanation:
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
Answers
Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Sorry if the picture is scuffed. Pls help fast
Answers
Answer:
C
Step-by-step explanation:
the domain would be all positive real numbers, including zero
Help ASAP Draw a tape diagram representing the following situation. You may need to decide what to present with a variable.
At an athletic banquet, an equal number of athletes were seaterd at each of the 7 large tables, and 24 parents were seated together on the other side of the room. There were 87 guests attending.
Answers
Answer:9
Step-by-step explanation:87-24=63 and 63 divided by 7 equals 9
Solve 1∕4p + 5∕6 = 2∕3 for p.
Question 1 options:
A)
–1∕24
B)
3∕8
C)
–2∕3
D)
6
Answers
Answer:
C) -2/3
Step-by-step explanation:
1/4p = 4/6 - 5/6
1/4p = -1/6
6p = -4
p = -4/6 or -2/3
Solve the equation
2x2 + 12x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Show step by step please!!!!
Answers
Step-by-step explanation:
4+12x=7
12x=7-4
12x=3
X=3/12
X=0.25
Simplify (3^z)^6 in exponent notation
Answers
Answer:
3^6z
Step-by-step explanation:
you multiply 6 and z since they are exponets and one is in a (
Answer:
3 to the power of 6z of 3^6z
Step-by-step explanation:
A line segment has an endpoint at (-7, 11) and (-6, 4), what is the length of
the segment?
Answers
Answer:
d = 5√2 units
Step-by-step explanation:
Let's use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Plug in the values with your endpoints.
d = √[(-6 - (-7))² + (4 - 11)²]
Solve within the parentheses.
d = √[(1)² + (-7)²]
Solve the exponents.
d = √[1 + 49]
Solve within the brackets.
d = √50
Simplify the square root.
25 • 2 = 50
√25 • √2 = √50
5 • √2 = √50
d = 5√2 units
Hope this helps!
Please answer for instant brainliest.
Answers
Answer:
5 T-shirts
or
35 T-shirts
Step-by-step explanation:
Alright so this question is a bit tricky but I will explain to you the steps. What you want to do is take every possible answer and multiply it by $15 (The price of an adult t shirt) and see if the answer you get can be added onto with the price of small t shirts ($10).
In other words you need a multiple of $10 as your answer so you can add $10 onto to that number until you get your total of $2,375.
Lets start with 185 t-shirts.
If we do 185 shirts x $15 per shirt we get $2775
That is way above the total of $2,375 so we know that this cant be the answer.
Next we can do 110 t-shirts.
If we do 110 shirts x $15 this time we get $1650.
Now while this is less than the total this is not a multiple of 10.
To prove this lets take the total amount of money earned ($2,375) and subtract this $1650 from it to see how much in youth shirts they sold.
$2,375 - $1650 = $725
Now we can divide $725 by the rest of the $10 youth shirts and you will see we get 72.5 which is not a whole number so it cant be answer. Since you cant sell someone 25% of a shirt or they probably would be upset.
Moving onto 35 t shirts lets take the same steps.
35 x $15 (price of adult t-shirt)
We then get $525 from this. Lets subtract this total again from the grand total earnings they made from selling both shirts ($2,375)
$2,375 - $525 = $1850.
Now this is a multiple of 10. Meaning you can add 10 into it go get that number and you wont have more or less than it. It will be spot on.
So we can do $1850 divided by $10 to find the total amount of youth shirts sold. We get 185 from this, which is a possible answer.
Lets do the last one.
5 t shirts multiplied by $15
We get $75 from this and now lets subtract again from the grand total.
$2,375 - $75 = $2,300
Now this would work too which is what kind of stumps me but we will go with it. Going off this either 5 t-shirts or 35 t-shirts would work as an answer cause you can have an even number of youth shirts sold with either answer. So I could have done something wrong but I believe based off of this either would be correct but I could be missing something. Someone correct me if I made a mistake.
Anyways I hope this helps :)\
EDIT :
I see what I did wrong here and failed to take into account the total of 220 t-shirts sold. But I believe this can help solve the last 2 answers.
A- g(x)=|x+5|+5
B-g(x)=|x-5|+5
C-g(x)=|x|+5
D-g(x)=|x-5|
Answers
Answer:
if anything, I would say C. I can't see the image too clearly, but I can see what you typed out
Step-by-step explanation:
Carlos, Margaret, and James are playing a board game with a spinner. The spinner goes from 1 to 6. They
start by spinning to see who will go first. (Highest number will go first.)
1. First, Carlos spins a 3. How likely do you think it is that Margaret will get a higher number?
Answers
Probability that Margaret will get a higher number than Carlos is 3/2.
What is probability?Probability is the measure of the likelihood of an event to occur.
Formula of probabilityP(E) = number of favorable outcomes/ total number of outcomes
Where, P(E) is the probability of an event.
According to the question we have,
A spinner goes from 1 to 6.
⇒ sample space = {1, 2, 3, 4, 5, 6}
⇒ Total number of outcomes = 6
Also, Carlos spins 3.
So, the numbers which required to win the game by Margaret are 4, 5 ,6 (greater than 3).
⇒ Total number of favorable outcomes = 3
Therefore,
The probability that Margaret will get a higher number than Carlos = [tex]\frac{3}{2}[/tex]
Learn more about probability here:
https://brainly.com/question/11234923
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Which graph represents the solution to the compound inequality?
–6 < 3x – 12 ≤ 9
A number line with an open circle at 2 with a bold line pointing to the left. A point at 7 with a bold line pointing to the right.
A number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.
A number line with an open circle at negative 6 with a bold line pointing to the left. A point at 9 with a bold line pointing to the right.
A number line with an open circle at negative 6 with a bold line pointing to the right ending at the point at 9.
Answers
Answer:
B) The second one. A number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.
Step-by-step explanation:
B) The second one. A number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.
Answer:
B
Step-by-step explanation:
edge 2022
A garment Stroe bought so shirts cut the rate of
400 per shirts and sold them at a loss of
1600 Find S.p?
Sop=20000
Answers
Answer:
the selling price is 18,400
Step-by-step explanation:
The computation of selling price is shown below:
Given that
The cost price of the shirts is 20,000
And, there is a loss of 1,600
So, the selling price is
= 20,000 - 1.600
= 18,400
hence, the selling price is 18,400
What is the property of 4x+6=18
Answers
Answer: 4x-6= 18
4x=24
x= 24 & 4
x=6
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
I'm not exactly sure of what you mean by property but I think it might be associative property of multiplication?
But to solve for x you would subtract 6 from 18 which gives your 12. Then you divide by 4 to get the x alone and 12/4 is 3.
exact volume of this cylinder
Answers
I am taking this quiz but I'm pretty sure its....c
Answer:
Volume=πr2h=π·42·8≈402.12386
Step-by-step explanation:
5. A length of rope is 20m long. If I cut it into 10 equal length pieces, how long is
each piece? *
what is given
Answers
20m / 10 = 2m
Each piece is 2m long.
Answer:
each piece is = 3 m long
Step-by-step explanation:
20 /10= 2
4x-y=10
y=2
Pls show work will give Brainlyest
Answers
Answer:
give y is equal to 2
substituting the value of y, we get
4x -y = 10
4x=10 +2
4x=12
x=12÷4
therefore x =3
an anthill has a volume of 8792mm^3 of dirt. its radius is 20 mm. what is the height of the cone? explain how you found the height.
Answers
Answer:
Height, h = 21 millimeters.
Step-by-step explanation:
Given the following data;
Volume = 8792mm³
Radius = 20 mm
To find the height;
We know that the shape of an anthill is conical in nature.
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.r is the radius of the base of the cone.h is the height of the cone.Substituting into the equation, we have;
[tex] 8792 = \frac{1}{3} * 3.142*20^{2}*h [/tex]
[tex] 8792 = \frac{1}{3} * 3.142*400*h [/tex]
[tex] 8792 = \frac{1}{3} * 1256.8*h [/tex]
[tex] 8792 = 418.93*h [/tex]
[tex] Height, h = \frac {8792}{418.93}[/tex]
Height, h = 20.99 ≈ 21 mm.
Therefore, the height of the cone is 21 millimeters.
ss of
3. In a class of 50 students, 40 % are girls. Find the number of girls and
number of boys in the class?
Solution:
Answers
Answer:
20 boys in the class
Step-by-step explanation:
40% of 50 is 20
solve all 5 questions for 62 points if they are correct you will be marked brainiest
Answers
Answer:
1.0.003
2.40 minutes
3.a,e
4.a,c,d
5.1/24
Step-by-step explanation:
A newborn turtle has a shell with a 1-inch diameter. The shell keeps a similar shape as the turtle grows. After a year, the shell is 3 inches in diameter. Note: you do not need to know the shape of the shell to complete this question.
1. How many times greater is the volume of the turtle's shell after a year than it was when it was born?
2. How many times greater is the surface area of the turtle's shell after a year than it was when it was born?
Answers
Answer:
I think the volume would be 9 times greater, and the surface area would be 3 times greater
Step-by-step explanation:
Answer:
the volume would be 9 times greater
the surface area would be 3 times greater
Step-by-step explanation:
Because if the shell grows from 1 inch diameter to 3 inch diameter, the surface area will increase 3x more. And the volume I assume is 3x greater because of the height is presumably 3 inches as well.
Please answer this I rlly need help. If you answer correctly, I will mark you as brainliest. Please don't mess around and answer anything and steal points bcuz I rlly need help and I don't have time to be wasting my time so pls be kind and answer pls and ty
Answers
Answer:
A) h= 201-6t
B) Candle B is 290 millimeters tall and burns at 5 millimeters per hour
C) Candle A burns faster because it has a rate of burning that is 1 millimeter faster per hour than Candle B (coefficient in front of t)
D) 58 hours
Step-by-step explanation:
Candle A Went down 24 in 4 hours so thats 6 millimeters per hour.
A) h= 201-6t
Candle A Went down 24 in 4 hours so thats 6 millimeters per hour (how i found the coeffiecient in front of t.)
B) Candle B is 290 millimeters tall and burns at 5 millimeters per hour
(Just interpreted the given equation)
C) Candle A burns faster because it has a rate of burning that is 1 millimeter faster per hour than Candle B, although candle B is still 50% larger than candle A at the beginning of burning.
D) 290=5t
t=58 hours
It would take 58 hours for Candle B to burn down completely, from the given equation.
Name the following segment or point.
Given:
L, M, N are midpoints
Р
M
A
R
N
B
altitude to AC
segment BT
O segment AS
segment BL
Answers
Answer:
should be segment BT, that's what i put and it was right. hope this helps
Step-by-step explanation:
The altitude to the line segment AC is line segment BL.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, L, M, N are midpoints.
We know the altitude of a triangle is a line segment that originates from one vertex of a triangle and bisects the opposite side of the triangle.
By observing the given figure we conclude that the altitude to the line segment AC is the line segment BL.
learn more about the altitude of a triangle here :
https://brainly.com/question/17020135
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Find the value of x if you solve one please say the question number and you dony have to show work
Answers
Answer:
question 1-- x=15
question 2-- x=21
2. x=21
3. x=42
4. x=26
5. x=14
What is a in the parallelogram
Answers
Whats the slope to this.
Giving brainliest. Correct answer
Answers
Answer:
m=-25
Step-by-step explanation:
m=Δh/Δt
(Im choosing for the difference in height and time (Δh and Δt) to be the difference between the data in the first two rows)
m=(4500-5000)/(20-0)
m=-500/20
m=-25
Skylas research Shows at eight empty cans make 1/ 4th pound of aluminum
she
wants to know how many cans it takes to make 5 pounds of aluminum how many kids are there per pound of aluminum
Answers
Answer:
160 cans for 5 pounds of aluminum
Step-by-step explanation:
how many odd _2-digit positive integers can be written using the numbers 2,4,5, and 8?
Answers
Answer:
4 different odd integers: 25, 45, 55, 85
Step-by-step explanation:
Two less than three times a number
Answers
Answer:
3x-2
Step-by-step explanation:
3 times a number is 3x, if we use x as the number
Two less than (3x) is 3x - 2
each of two equal angles is twice the third angle. find the angle of triangle.
Answers
Answer:
45 degrees each and 90 degrees