26-4s=9s
⇔26=9s+4s
⇔26=13s
⇔s=2
Answer:
s = 2
Step-by-step explanation:
26 - 4s = 9s
add 4s to 4s and 9s
that equals 13
26/13 = 13s/13
s = 2
What is the resulting integral?
Answer:
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Antiderivatives - Integrals
Integration Constant C
U-Substitution
U-SolveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx[/tex]
Step 2: Identify Variables
Find the variables u-solve using u-substitution.
U-Substitution
[tex]\displaystyle u = 1 + \sqrt{x}[/tex]
[tex]\displaystyle du = \frac{1}{2\sqrt{x}}dx[/tex]
U-Solve
[tex]\displaystyle x = (u - 1)^2[/tex]
[tex]\displaystyle dx = 2\sqrt{x}du[/tex]
Step 3: Integration
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{x})^5}} \, dx[/tex][Integral] U-Solve: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{(u - 1)^2})^5}} \, 2\sqrt{x}du[/tex][Integral] Simplify: [tex]\displaystyle 2\int {\frac{2\sqrt{x}}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int {\frac{\sqrt{x}}{u^5}} \, du[/tex][Integral] U-Solve: [tex]\displaystyle 4\int {\frac{\sqrt{(u - 1)^2}}{u^5}} \, du[/tex][Integral] Simplify: [tex]\displaystyle 4\int {\frac{u - 1}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle 4[\int {\frac{u}{u^5}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Simplify: [tex]\displaystyle 4[\int {\frac{1}{u^4}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\int {u^{-4}} \, du - \int {u^{-5}} \, du][/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4[\frac{u^{-3}}{-3} - \frac{u^{-4}}{-4}] + C[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\frac{-1}{3u^3} + \frac{1}{4u^4}] + C[/tex][Brackets] Multiply: [tex]\displaystyle \frac{-4}{3u^3} + \frac{4}{4u^4} + C[/tex]Back-Substitute: [tex]\displaystyle \frac{-4}{3(1 + \sqrt{x})^3} + \frac{4}{4(1 + \sqrt{x})^4} + C[/tex]Combine: [tex]\displaystyle \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
What is 6 less than a number t is 7?
Answer:
t-6=7
Step-by-step explanation:
Answer:
6-t=7
Step-by-step explanation:
Match each pair of points a and B to point C such that ABC equals 90°
I don't really get what you mean
(d) Chris chooses a card at random, replaces it, then chooses a
cards she chooses has the letter M printed on it.
(e) Graham chooses a card at random and does not replace it. He continues until he chooses a card with the letter M
printed on it. Find the probability that this happens when he chooses the 3rd card.
Question 2
Percy throws a fair dice until he gets a five.
...
:
20
(a) Work out the probability that Percy gets the five on his first throw.
(b) Find the probability that he has to throw the dice exactly twice to get the five.
(c) Calculate the probability that he will have the throw the dice more than twice to get a five.
Answer:
Step-by-step explanation:
I'm assuming you have 26 cards each with a different letter on it.
(d) Prob(Not M, Not M , M)
= 25/26 * 25*26 * 1/26
= 625/17576
or 0.036 to nearest thousand
(e) Prob(Not M, Not M, M) without replacement
= 25/26*24/25*/1/24
= 1/26
or 0.038 to nearest thousandth.
2(a)
1/6.
(b)
5/6 * 1/6
= 5/36.
(c)
5/6 * 5/6
= 25/36
a farmer sells 7.6 kg of apples and pears at the Farmers Market. Two-fifths of this weight is Apple's, and the rest is pairs. How many kilograms of pears does she sell at the Farmers Market?
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A and B
Step-by-step explanation:
what is the answer to 1\2÷3
Answer:
1/6
Step-by-step explanation:
1/2÷3
1/2×1/3
1×1/2×3
1/2×3
1/6
Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them?
Answer:
0.35 pounds in each cheesecake
Step-by-step explanation:
Number of individual blueberry cheesecakes = 15
Pounds of blueberries = 5 1/4 pounds
How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them?
= 5 1/4 ÷ 15
= 21/4 ÷ 15
= 21/4 × 1/15
= (21*1)/(4*15)
= 21/60 pounds
Equivalent to 0.35 pounds in each cheesecake
Can somebody help me? I need help ;-;...
Answer:
Bottom left
Step-by-step explanation:
Dots are on the inside and outside of the line as well as being on the line
Identifica el cuadrante en el cual se encuentra el ángulo 2.200
Answer:your
Step-by-step explanation:
mom
Thomas lives more than 0.55 km and less than 0.75 km from his school.
Thomas lives from his school?
A. 0.06 km
B 0.50 km
c. 0.60 km
D. 1.30 km
Which choice could be the distance Thomas lives from his school?
One year a surf board maker had $3.5 million in sales. In later year,
sales y (in millions) increased by about 15% each year. Which function
models the amount of money the maker will have after t years?
Answer:
I need help with this one
Step-by-step explanation:
PLS ANSWER 10 POINTS!!
Answer:
the answer is 58°
Step-by-step explanation:
90 - 32 = 58
If another sample of size 100 is taken, what is the probability that its sample mean will
be greater than 2.56 in?
Answer:
I don't know the answer to this but
Suppose we draw a sample of size n=16 from this population and want to know how likely we are to see a sample average greater than 22, that is P( > 22)? So the probability that the sample mean will be >22 is the probability that Z is > 1.6 We use the Z table to determine this: P( > 22) = P(Z > 1.6) = 0.0548.
Step-by-step explanation:
What is the probability that a data value in a normal distribution is between a
z-score of -0.37 and a z-score of 1.22? Round your answer to the nearest
tenth of a percent.
A. 54.3%
B. 52.3%
C. 51.3%
D. 53.3%
Answer:
53.3%
Step-by-step explanation:
It's the correct answer that's why
plz help. I Need help with it
Answer:
O that easy just flip the sign for example - becomes + becomes-
this is an is simple trick I learn hope it helps you.
Step-by-step explanation:
so k goes to -3 j goes to -2
norma had 3/8 birthday cake left over from her party she ate 3/4 of the cake for lunch. how much did she eat at lunch?
Answer:
1/12
Step-by-step explanation:
Fraction is the representation of the parts of a whole number. The amount of cake ate by Norma in the lunch is 9/32 parts.
Given-Total cake left over by the Norma after the party is 3/8.
Total cake she ate for the lunch is 3/4.
The value of the whole cake is given in the fraction parts. To solve this the fraction should be understood.
What is fraction?Fraction is the representation of the parts of a whole number.
As the one whole of cake was there earlier. The 3/8 part of the cake is,
[tex]=\dfrac{3}{8}[/tex]
As she ate the 3/4 part of the left over cake in the lunch. Suppose the part of cake she ate is x. Therefore the part of cake she ate at lunch is,
[tex]x=\dfrac{3}{8} \times\dfrac{3}{4}[/tex]
[tex]x=\dfrac{9}{32}[/tex]
Hence, the amount of cake ate by Norma in the lunch is 9/32 parts.
Learn more about the fraction here;
https://brainly.com/question/1301963
Which of the following best describes the difference between simple and compound interest?
Simple interest is easier to calculate than compound interest.
Simple interest earns interest on the previous interest earned only.
Compound interest earns interest on the principal plus any previous interest earned.
Compound interest earns interest on the principal only.
Answer:
Compound interest earns interest on the principal plus any previous interest earned.
Step-by-step explanation:
compound interest gets its name because the interest keeps on 'compounding' which means earning interest on interest
The correct best describes the difference between simple and compound interest is,
⇒ Compound interest earns interest on the principal plus any previous interest earned.
Option 3 is true.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
To defined best describes the difference between simple and compound interest.
Now, We know that;
Compound interest pays interest on your previous balance plus your previous earned interest; simple interest pays interest only on your original balance.
Hence, The correct best describes the difference between simple and compound interest is,
⇒ Compound interest earns interest on the principal plus any previous interest earned.
Learn more about the Interest visit:
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In ΔVWX, w = 680 cm, ∠X=80° and ∠V=32°. Find the area of ΔVWX, to the nearest 10th of a square centimeter
Answer:
56
Step-by-step explanation:
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The area of the triangle.
= 1/2 x base x height
The area of the triangle is 105760 cm².
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In ΔVWX.
w = 680 cm
∠X=80°
∠V=32°
This means,
∠W + ∠X + ∠V = 180
∠W = 180 - 112
∠W = 68°
This means,
68° = 680
1° = 10
Now,
∠X=80°
x = 800 cm
∠V=32°
v = 320 cm
Now,
V
/ | \
(x) / | \ (w)
/ | \
W M X
(v)
680² = VM² + (320/2)²
462400 = VM² + 25600
VM² = 436800
VM = 661 cm
Thus,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 320 x 661
= 160 x 661
= 105760 cm²
Learn more about triangles here:
https://brainly.com/question/25950519
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(Middle schoolers!)
If you need help with Draw Inferences from Data I have everything you need!
Just ask the question then come to me and I can answer it for you!
This is for do you know/how do you understand!
Answer:
Ok! tysm!
Answer explanation:
What is 70000% + 8100000
Answer:
8100700
Step-by-step explanation:
I used a calculator
Could you pls mark me brainliest I only need one more
Answer:
8100700
hop i helped look at my drawing
Step-by-step explanation:
You have 12 gallons of punch. You estimate that each guest will drink 3 cups. Do you have enough punch for 60 guests?
Answer:i got 1 2 3 4 5 6 7 8 shooters ready to gun you down
Step-by-step explanation:
1, write a ratio in all three forms, to compare the days without games to the days in a year?
Answer:
1. 363 to 2
2. 363:2
3. 363/2
Step-by-step explanation:
1. First of all, there are 365 days in a year.
* Note that the question says there are only 2 days where sports aren't played.
2. As said in the question there are 3 ways to write a ratio: a to b; a : b; a/b. Now, let's think that what are a and b in this scenario? a= says without games= 2; and b= days in a year= 365.
3. Now fill in the variables with the numbers for each form of a ratio.
a. 363 to 2
b. 363:2
c. 363/2
someone plz help no links stg
Calculate: Find the perimeter of a triangle with sides 11 inches, 5 inches, and 13 inches. Show your work.
Answer:
29
Step-by-step explanation:
P=a+b+c=11+5+13=29
help with math pretty easy will give 5 star and brainlyist
Answer:
area = 96 units²
Step-by-step explanation:
area = 16 x 12 x 0.5 = 96 units²
How do you find out if a number is an integer or not?
Answer:
Integers are any whole number negative or positive
Step-by-step explanation:
can you help me pls it's only 3 question's
Answer:
1. 0.8 2. 1.25 3. 27.5
Step-by-step explanation:
Number 1 is 4/5
Number 2 is just 5/4
And I think number 3 is 22/4 which is 5.5 then times 5 which is 27.5.
Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin. What is the correct set of image points for triangle X’Y’Z’?
X’(1, 1), Y’(-4, 3), Z’(1, 5)
X’(1, 1), Y’(–3, –4), Z’(–1, –5)
X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Answer:
When a figure is rotated counterclockwise about the origin, its original coordinates of point P (x,y) will now be positioned as P' (-y,x).
X (1,-1) --> X' (1,1)
Y (3,4) --> Y' (-4,3)
Z (5,-1) --> Z' (1,5)
The correct set of image points for triangle X'Y'Z' is X'(1,1), Y'(-4,3), and Z'(1,5).
Step-by-step explanation:
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
If a point A(x, y) is rotated 90° counterclockwise the new point is A'(-y, x).
Triangle XYZ is rotated 90° counterclockwise, the new coordinate is X'(1, 1), Y'(-4, 4) and Z'(1, -5)
Find out more on Transformation at: https://brainly.com/question/26092237
Which equation describes the function in the table below?
Answer:
A
Step-by-step explanation:
So, first we have to eliminate answers, let us check A first. If we simplify this equation, it's basically saying Y is equal to 1.3 times X plus 10. So, 0 x 1.3 = 0 plus 10 = 10. Now we check the rest of the table. 5 x 1.3 = 6.5 + 10 = 16.5. 10 x 1.3 + 10 = 23. 15 x 1.3 + 10 = 29.5, and 20 x 1.3 = 26 + 10= 36. The math matches with the table so we're done.