Answer:
A:42 B:$4.20
Step-by-step explanation:
A: 84x1.5=126 126/3=42
B: 42x10=420=$4.20
1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
8x − 4/x(x2 + 1)2
2. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
2x3 - 16x2 - 39x + 20/x2 - 8x - 20 x dx
3. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
x2/x4 - 42x2 - 343 x dx
Answer:
Step-by-step explanation:
1.
To write the form of the partial fraction decomposition of the rational expression:
We have:
[tex]\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}[/tex]
2.
Using partial fraction decomposition to find the definite integral of:
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx[/tex]
By using the long division method; we have:
[tex]x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }[/tex]
[tex]- 2x^3 -16x^2-40x[/tex]
[tex]x+ 20[/tex]
So;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}[/tex]
By using partial fraction decomposition:
[tex]\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}[/tex]
[tex]= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}[/tex]
x + 20 = A(x + 2) + B(x - 10)
x + 20 = (A + B)x + (2A - 10B)
Now; we have to relate like terms on both sides; we have:
A + B = 1 ; 2A - 10 B = 20
By solvong the expressions above; we have:
[tex]A = \dfrac{5}{2}[/tex] [tex]B = \dfrac{3}{2}[/tex]
Now;
[tex]\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}[/tex]
Thus;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}[/tex]
Now; the integral is:
[tex]\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx[/tex]
[tex]\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}[/tex]
3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.
Please check to the attached image below for the solution to question number 3.
8.
Andrew has $76.50. Elijah has $94.30. How much more money does Elijah have than
Andrew
Answer:
$17.80Step-by-step explanation:
This is a fairly simple question. All we need to do is find the difference between the two amounts.
$94.30 - $76.50 = $17.80
A Recipe for cakes uses 12 cups of flour and 4 eggs. What is the ratio
Answer:
3 to 1 is the ratio
hope it helped
Answer:
12:4
Step-by-step explanation:
I do not know if this question is complete, but if it is, the ratio is 12:4. The reason is that for every 12 cups of flour, there are 4 eggs.
Which expression is equivalent to y^3-2y^2+y
Answer:
the first one i did it yesterday
The cost of an item is $0.30 per ounce. If total cost of the item is $3.60, how many ounces are in the item?
Answer:
Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce
Answer:
12 ounces
Step-by-step explanation:
3.60 = .3x
divide by .3 on both sides
12 = x
200z + 50 = 8000 solve this problem
Answer:
39.75
Step-by-step explanation:
First, subtract 50 from both sides
200z + 50 - 50 = 8000 - 50
200z = 7950
Then isolate the variable by dividing both sides by 200
200z/200 = 7950/200
z=39.75
can u find all the angles plz?
Answer:
The two sides we know are O pposite (300) and A djacent (400).
SOHCAH TOA tells us we must use T angent.
Calculate Opposite/Adjacent = 300/400 = 0.75
Find the angle from your calculator using tan-1
:)
Answer:
1 = 88 2 = 42 3 = 113
Step-by-step explanation:
2 is 42 because it is the opposite angle and then you subtract 42 and 50 from 180 to get 88 for #1 and you subtract 42 and 25 from 180 to get 113 for #3.
In general, how tall are giraffes? stat or not stat
Answer:
18 feet tall
Giraffes are the tallest land animals. Female giraffes are up to 14 feet tall and weigh up to 1,500 pounds. Meanwhile, males are up to 18 feet tall and can weigh 3,000 pounds.
Meet Forest, the tallest giraffe in the world
(CNN) A male giraffe living in a zoo in Australia has been crowned the tallest of them all, hitting a giddy 5.7 meters (18 feet, 8 inches). Isn't that cool?!
( just so you know some of this information was with the help of google)
Brainliest?
Dennis wants to save $189 for a trip to an amusement park. He sets aside $14 of his allowance at the end of each week. How many weeks will it take him to save enough money for the whole trip?
Answer:
x = 13.5 weeks
Step-by-step explanation:
Since he wants to save $189 in total, that will be on one side of the equation by itself. You have to set this up in a y = mx + b equation. The y will be the 189. Since the word "each" goes with the number 14, that will be your m value. There is no value for b.
189 = 14x is your equation. The only step after setting up the equation is to divide 189 by 14. This gives you 13.5. Dennis will have to save up for 13.5 weeks.
Work out 4/7 + 2 1/3
It's 61/21. That's the answer.
Find the equation of the parabola with a focus at the point (2,5), and a directrix of y = 3.
Answer:
1,3
Step-by-step explanation:
Two of the angles in a triangle measure 55° and 28°. What must be the measure of the third angle?
The measure of the third angle is
Work Shown:
Let x be the third angle
For any triangle, the three angles always add to 180 degrees
x+55+28 = 180
x+83 = 180
x = 180-83
x = 97
How do break down what is the percentage of change in cost of the pizza
One of the largest cookies made on record had a diameter of 78.75 feet. What was the circumference of the cookie?
Answer:
247.4
Step-by-step explanation:
- you can either use pi*diameter or 2pi*radius
- [tex]\pi (78.75) = 247.4[/tex]
Find the solutions to the equation below.
Check all that apply.
6x2 + 7x -5 = 0
A. x = 1/3
B. x = 5
c. x = -5/3
D. x = -1/3
E. x = 1/2
F. x = -2
Answer:
A and C
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero
What is 0.12 times 105
Pls help
Answer:
12.6
Step-by-step explanation:
Use long multiplication to evaluate.
Answer:
12.6
Step-by-step explanation:
0.12*105=12.6
Please help. Brainliest to correct answer.
What equation is graphed in this figure?
A dollhouse uses a scale factor of 1/12 The perimeter of a square room in
the dollhouse is 36 inches. What is the length of the full-size room?
Please explain also thanks
Answer:
really phoung. lol its me maham
Step-by-step explanation:
is 0.75 repeating irrational or rational
Answer:
This is a rational decimal and is not a repeating decimal.
Step-by-step explanation:
Whoever answers gets brainlist!
Answer:
1 ST ONE
Step-by-step explanation:
Answer:
No, because its racional
In a proof of the Pythagorean theorem using similarity, what allows you to state that the triangles are similar in order to write the true proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction?
the geometric mean (altitude) theorem
the geometric mean (leg) theorem
the right triangle altitude theorem
the SSS theorem
Answer:
C: the right triangle altitude theorem
Step-by-step explanation:
In proof of the Pythagorean theorem using similarity, the right triangle altitude theorem allows us to state that the triangles are similar.
What is geometric mean(altitude) theorem?We know that the geometric mean (altitude) theorem states that the altitude is equal to the geometric mean of the two segments.
We know that the geometric mean (leg) theorem states that a leg is the geometric mean between the hypotenuse and the leg's projection on it in every right triangle.
We know that the right triangle altitude theorem states that If we draw an altitude in a right triangle from the vertex which contains the right angle to the opposite side, the triangles on both sides of the altitude are congruent, and the entire triangle is congruent as a result.
We know that the SSS theorem If the three sides of one triangle are equal to the three sides of the other, then the two triangles are congruent.
How to tackle the problem?Here, we have to find the specific theorem which demonstrates the equality of proportionate values in the Pythagorean theorem. From the above theorems, we can conclude that our required theorem is the right triangle altitude theorem.
Therefore In proof of the Pythagorean theorem using similarity, the right triangle altitude theorem allows us to state that the triangles are similar. So, option C is correct.
Learn more about the right triangle altitude theorem here -
https://brainly.com/question/4470400
#SPJ2
Find 43.3% of 488.Round to the nearest hundredth.
Answer:
211.30
Step-by-step explanation:
488 times 43.3 divided by 100
211.304
rounded to 211.30
Answer:
211.30
Step-by-step explanation:
big brain big brain
David has 4 bales of hay for his 13 cows. What is an equivalent ratio of cows to bales of hay
Answer:
13 : 4
Step-by-step explanation:
13 : 4
he has 13 cows and he has 4 bales of hay so 13:4
you can't simplfy it so its still 13 : 4
What is the sum of (5x2 + x - 3) and (-4x2 - x +9) ?
Answer:
[tex]x^{2} + 6[/tex]
Step-by-step explanation:
Pick A B or C. Explanation would be helpful
Answer:
c
Step-by-step explanation:
A rectangular garden is divided into four sections. Some dimensions are shown in the diagram, and the distance from
point A to point Cis 16 ft.
12 it
8
15 ft
What is the distance from point A to point B in feet?
A. 8ft B.7ft c.9ft D.6ft
Answer:9 ft
Step-by-step explanation:
The requried measure of the AB is given as 7ft. Option B is correct.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
From the diagram, applying Pythagoras' theorem to the right rectangle,
BC² = 15² - 12²
BC² = 81
BC = 9
Now,
AC = 16
AB + BC = 16
AB + 9 = 16
AB = 7 ft
Thus, the requried measure of the AB is given as 7ft. Option B is correct.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ2
You and a friend are playing a game using a spinner divided into 4 equal sections, numbered 1 through Which of the following would not be a fair game? You win the pointer points at 1 or 2; otherwise, your friend wins. You win the pointer points at an even numberotherwise, your friend wins. You win if the pointer points at any number except 3; otherwise, your friend All of the above games are fair.
Answer:
You win if you spin any number except 3, otherwise your friend wins
Step-by-step explanation:
Because the spinner is divided into equal sections, there is an equal probability of spinning any number. In this case, you win by spinning a 1, 2, or 4, and your friend only wins by spinning a 3. The probability of you winning is 34, while the probability of your friend winning is only 14.
If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
“I think of a number, add 3 to it and multiply the result by 7."
E
Learning Task 2. Give the reciprocal of the given fractions below.
Write your answer in your notebook.
6
1.
6.
2
8.
7
2. 7
7.
1
2
8
3.
8.
4
4
33-
5
als -|- ||-|-
5
4. 41
9.
5
6
5.
1
10. 1
54
5
5
A
Reciprocals represent two numbers whose product is one. Multi-6/8
The correct format of the options are
(1) 6/8 (6) 2/7
(2) 7/2 (7) 1/8
(3) 33[tex]\frac{4}{5}[/tex] (8) 4/5
(4) 41 (9) 5/6
(5) 54[tex]\frac{1}{5}[/tex] (10) 1/5
Answer:
Reciprocal are those number which when multiplied by the original number gives 1 as the result. eg [tex]\frac{6}{8}[/tex] reciprocal is [tex]\frac{8}{6}[/tex], on multiplication [tex]\frac{6}{8}[/tex]*[tex]\frac{8}{6}[/tex] =1
Reciprocal of the following are as follows
(1) [tex]\frac{8}{6}[/tex]
(2) [tex]\frac{2}{7}[/tex]
(3) 33[tex]\frac{4}{5}[/tex] =[tex]\frac{ 33*5 + 4}{5}[/tex] = 169/5 => reciprocal = 5/169
(4) 1/41
(5) 54[tex]\frac{1}{5}[/tex] => [tex]\frac{54*5 +1}{5}[/tex] = 271/5 => 5/271
(6) 7/2
(7) 8
(8) 5/4
(9) 6/5
(10) 5
