Answer:
10 years
step-by-step explanation:
First, divide 7.5 by 100, you should get 0.075, then multiply 0.075 by 2000, you should get 150, thats how much interest he gains each year, now subtract 2000 from 3500 to see how much he needs to get to 3500, you should get 1500, now divide 1500 by 150, you should get 10, which is how many years he will need to get to 3500 from 2000
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
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
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.
Simplify. (−1+2i)(3−5i)
Choices
7+i
−3+i
7+11i
−13+11i
Answer:
The answer is 7 + 11i
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
3/2 p - 14 = p + 13
Please help
Answer:
p=54 hope this helps
Step-by-step explanation:
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
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'
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: ∅.
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:
Can someone help me please??
Answer:
the perimeter is just the distance around the shape so 7+10+15+8+8+2=50
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
Which stamens is true
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 $5.35 in nickels and quarters. If she has 13 more quarters than nickels, how many of each coin does she have?
(Scroll Down for Answer!)
We know that n = q - 13.
The value equation is
5n + 25q = 535 (we work in cents)
Now substitute for n and get
5(q - 13) + 25q = 535
5q - 65 + 25q = 535
30q = 600
q = 20 so that
n = 7
Step-by-step explanation:
Use the expression 7.6s+(45÷9)−15 to answer 9–10.
9.
Which part of the expression represents a quotient? Describe its parts.
10.
Which part of the expression represents a product of two factors? Describe its parts.
9. The part of the expression that represents a quotient is
10. The part of the expression that represents a product of two factors is
Answer:
45 ÷ 9, 7.6s
Step-by-step explanation:
9) A quotient is a result of dividing a quantity by another quantity. We see that 45 ÷ 9 is a form of division. We could say that 45 is divided into 9 parts. 45 ÷ 9 can also be written in fractional form: [tex]\frac{45}{9}[/tex]. Lastly, we see that the quotient would be 5.
10) A product is a result of multiplying a quantity by another quantity. We see that 7.6s is a simplified form of multiplication that actually represents 7.6 × s.
7.6 is a known numerical value. It is the coefficient of the variable x, which we do not know the value for.
Questão 11 - Um investidor aplicou
a quantia de R$ 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.
search correct answer which expression is equivalent to the polynomial?
8mil 133yd 2ft - 5mil 107 yd 2ft =
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°
change improper fractions: 6 × 1/4 =
Answer:
[tex]1 \frac{1}{2}[/tex]
What is the decimal multiplier to decrease by 7.4%
Answer:
0.074
Step-by-step explanation:
convert 7.4% to a decimal.
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 :)
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:
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░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob
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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.
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
I had to raise the number to49 pls help
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:
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.
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
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