Step-by-step explanation:
Area = l × b
= 9ft × 8ft
= 72ft²
Answer:
72 feet
Step-by-step explanation:
8 (length) • 9 (width) = 72 sq ft
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
Please help I need help ASAP????!!!!!!!!!
Answer:
3x
Step-by-step explanation:
if __ + 3 = 15 and x=4 then you need to find what plus 3 = 15.
12+3 = 15, and to get from 4 to 12 you multiply by 3
3x + 3 = 15! hope that helps
Find the sum or difference. 9/12 - 7/12 *
Answer:
Bro this is hard answer is 0.17 or 2/12
Step-by-step explanation:
9/12 - 7/12
9 - 7 first since they both have 12 as their denominator
2 is the answer so you get 2/12
To find the sum or difference of 9/12 - 7/12, you can follow these steps:
Convert both fractions to have a common denominator. In this case, the common denominator is 12, so you can rewrite both fractions as follows: 9/12 - 7/12 = (9/12) - (7/12) = (9 - 7)/12 = 2/12Simplify the fraction if possible. In this case, you can simplify 2/12 to 1/6 by dividing both the numerator and denominator by 2: 2/12 = (2/2) / (12/2) = 1/6The sum or difference is 1/6.So the answer is 1/6.
Please give me brainliest for more high quality answers! - longstretch
What is the decimal multiplier to decrease by 7.4%
Answer:
0.074
Step-by-step explanation:
convert 7.4% to a decimal.
Similar triangles and slope
Line r is parallel to line c
Which angle is congruent
Answer:
C. ∠5Step-by-step explanation:
Angle 3 makes alternate interior angle pair with angle 5
∠3 ≅ ∠5Answer:
C. ∠5
Step-by-step explanation:
Angle 3 makes alternate interior angle pair with angle 5
∠3 ≅ ∠5
Which stamens is true
Use the expression 7.6s+(45÷9)−15 to answer 9–10.
9.
Which part of the expression represents a quotient? Describe its parts.
10.
Which part of the expression represents a product of two factors? Describe its parts.
9. The part of the expression that represents a quotient is
10. The part of the expression that represents a product of two factors is
Answer:
45 ÷ 9, 7.6s
Step-by-step explanation:
9) A quotient is a result of dividing a quantity by another quantity. We see that 45 ÷ 9 is a form of division. We could say that 45 is divided into 9 parts. 45 ÷ 9 can also be written in fractional form: [tex]\frac{45}{9}[/tex]. Lastly, we see that the quotient would be 5.
10) A product is a result of multiplying a quantity by another quantity. We see that 7.6s is a simplified form of multiplication that actually represents 7.6 × s.
7.6 is a known numerical value. It is the coefficient of the variable x, which we do not know the value for.
if Kendra has $5.35 in nickels and quarters if she has seven more quarters and nickels how many of each coin does she have ?
Kendra has $5.35 in nickels and quarters. If she has 13 more quarters than nickels, how many of each coin does she have?
(Scroll Down for Answer!)
We know that n = q - 13.
The value equation is
5n + 25q = 535 (we work in cents)
Now substitute for n and get
5(q - 13) + 25q = 535
5q - 65 + 25q = 535
30q = 600
q = 20 so that
n = 7
Step-by-step explanation:
For the linear function, y increases by a
of 3 each time x increases by 1.
For the exponential function, y increases by a(n)
of 3.
Answer:
The linear equation is:
y = 3*x
when x = 1
y = 3*1 = 3
when x = 2
y = 3*2 = 6
Then as x increases one unit, y increases 3 units.
Then the correct statement would be something like:
"For the linear function, y increases by a sum of 3 each time x increases 1"
The exponential function is:
y = 3^x
When x = 1
y = 3^1 = 3
When x = 2
y = 3^2 = 3*3
when x = 3
y = 3^3 = 3*3*3
So when x increases by 1, we multiply the previous value of y by 3.
Then the correct sentence is something like:
"For the exponential function, y increases by a factor of 3".
Answer: for the linear function y increases by a difference
for the exponential function y increases by a(n) ratio.
Step-by-step explanation:
Which of the following statements are true? Select all that apply.
63=3*3*3*3*3*3
025=2x5
45=4*4x4x4x4x4
03=3*3*3*3
023=4*4*4
52=5*5
Answer:
a
Step-by-step explanation:
Questão 11 - Um investidor aplicou
a quantia de R$ 500,00 em um fundo
de investimento que opera no regime
de juros simples. Após 6 meses o
investidor verificou que o montante
era de R$ 560,00. Qual a taxa de
juros desse fundo de investimento?
Answer:
A taxa de juros desse fundo de investimento é de 24% ao ano.
Step-by-step explanation:
Esta é uma questão que envolve juros simples.
A quantidade de juros acumulados depois de t anos é dado por:
[tex]J = P*r*t[/tex]
Em que P é o investimento inicial, r é a taxa de juros, é t é o tempo, em anos.
O montante é dado por:
[tex]M = J + P[/tex]
Um investidor aplicou a quantia de R$ 500,00.
Isso significa que [tex]P = 500[/tex]
Juros acumulados:
Montante era de R$ 560,00, o que significa que [tex]M = 560[/tex]
Então, a quantidade de juros acumulados é dada por:
[tex]M = J + P[/tex]
[tex]J = M - P = 560 - 500 = 60[/tex]
Taxa de Juros:
6 meses é meio ano, o que implica que [tex]t = 0.5[/tex]
Então
[tex]J = P*r*t[/tex]
[tex]60 = 500*r*0.5[/tex]
[tex]250r = 60[/tex]
[tex]r = \frac{60}{250}[/tex]
[tex]r = 0.24[/tex]
A taxa de juros desse fundo de investimento é de 24% ao ano.
I was climbing a ladder in my backyard and I felt closer to god but then I thought god is us all too.
Answer:
What are you trying to say
Step-by-step explanation:
Answer:
Wow, Thats really touching. I kind of dont know what to say but.
Step-by-step explanation:
░░░░░▐▀█▀▌░░░░▀█▄░░░
░░░░░▐█▄█▌░░░░░░▀█▄░░
░░░░░░▀▄▀░░░▄▄▄▄▄▀▀░░
░░░░▄▄▄██▀▀▀▀░░░░░░░
░░░█▀▄▄▄█░▀▀░░
░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob
▄░▐░░░▄▄░█░▀▀ ░░
▀█▌░░░▄░▀█▀░▀ ░░
░░░░░░░▄▄▐▌▄▄░░░
░░░░░░░▀███▀█░▄░░
░░░░░░▐▌▀▄▀▄▀▐▄░░
░░░░░░▐▀░░░░░░▐▌░░
░░░░░░█░░░░░░░░█
427 diveided by 3 do you have any aneswerers
Answer:
142.333....
Step-by-step explanation: just use a calculator
Answer:
142.34
Step-by-step explanation:
427 ÷ 3 = 142.34
good luck, i hope this helps :)
search correct answer which expression is equivalent to the polynomial?
I had to raise the number to49 pls help
Simplify. (−1+2i)(3−5i)
Choices
7+i
−3+i
7+11i
−13+11i
Answer:
The answer is 7 + 11i
Step-by-step explanation:
Can someone help me please??
Answer:
the perimeter is just the distance around the shape so 7+10+15+8+8+2=50
Help me with this, please!
Answer:
....
Step-by-step explanation:
The answer is a, yes yes
.....
Step-by-step explanation:
The answer is A yes. yes
change improper fractions: 6 × 1/4 =
Answer:
[tex]1 \frac{1}{2}[/tex]
3/2 p - 14 = p + 13
Please help
Answer:
p=54 hope this helps
Step-by-step explanation:
Please help me
Explain how to solve the equation and how to check the
solution.
40 = 8y
Answer:y=5
Step-by-step explanation:
To find out what y is you have to do the inverse to 'undo' the equation.
So instead of multiplying y by 8 you have to divide 40 by 8.
40÷8=5
So y=5
You can check your answer by putting 5 where y is.
40=8×5
Hope this helps :)
Answer:
Use the inverse operation to isolate the variable. Undo multiplication by dividing by 8 on both sides of the equation. Simplify by completing the divisions, 40 ÷ 8 = 5, and 8 ÷ 8 = 1. The solution is y = 5. Check the solution by substituting 5 for y in the original equation, and then simplify. 8 × 5 = 40 and 40 = 40 is a true statement, so 5 is the solution.
Step-by-step explanation:
On edge 2021
Testing:
H0:μ=54.5
H1:μ<54.5
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
Calculate the test statistic, rounded to 2 decimal places.
t=
Answer:
t = -1.54.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
H0:μ=54.5
This means that [tex]\mu = 54.5[/tex]
Your sample consists of 48 subjects, with a mean of 54.1 and standard deviation of 1.8.
This means, respectively, that [tex]n = 48, \mu = 54.1, \sigma = 1.8[/tex]
Test statistic
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{54.1 - 54.5}{\frac{1.8}{\sqrt{48}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is t = -1.54.
PLEASE HELP ME ASAP??!!!!!!!!
9514 1404 393
Answer:
(d) ∅
Step-by-step explanation:
Subtracting y from both sides gives ...
4 = -5
There is no value of y that will make this true. There is no solution to the equation.
The solution set is the null set: ∅.
PLEASE HELP
Which element should you not include in a summary for a book review?
a brief description of setting
the story's ending
explanation of theme
how the main conflict is resolved
ANSWER THIS PLZZ I WILL GIVE TOP COMMENT :)!!!!!
Answer:
D, -42 multiply 6 on both sides
D. because when it is multiplied, the inequality is no longer true.
I need help please ASAP?!!!!
Answer:
no real numbers will make this equation true
Step-by-step explanation:
if you square both sides, you'll get sqrt(-49). this will get you an imaginary number (7i) which is not a real number.
Solve for x
70°
*
20
triangles
Answer:
x = 90°
Step-by-step explanation:
a triangles angles are equal to 180°
so if we have one that is 70° and one that is 20° what s x?
70° + 20° = 90°
180° - 90° = 90°
x = 90°
HELP NEEDED QUICK WILL GIVE BRAINLY
Question 3 (02.03)
Figure EFGH is reflected about the y-axis to obtain figure E’F’G’H’:
Which statement best describes the relationship between the two figures?
1.Figure EFGH is congruent to figure E’F’G’H’.
2.Figure EFGH is bigger than figure E’F’G’H’.
3.The measure of angle H is equal to the measure of angle E’.
4.The measure of angle H is equal to the measure of angle G’.
Answer:
1
Step-by-step explanation:
Figure EFGH is congruent to figure E'F'G'H'
8mil 133yd 2ft - 5mil 107 yd 2ft =
Describe the slope of the line. Then find the slope using two points.
helppp step by step explanation
Answer:
Step-by-step explanation:
Hi,
Describe the slope: This is a horizontal line. Slope measures the steepness of a line, since this is a horizontal line with no change whatsoever, the slope must be 0.
Calculate: (-1,-2) (3,-2)
Change in y over change in x
-2 - (-2) = 0
3 - 1 = 2
0/2 = 0
The slope is 0
Hope this helps <3