If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]
Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:
[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]
and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].
So, we can write the given integral as
[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]
Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get
[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]
A park has a rectangular shape. One side of the park is 175 23 meters long and the
other is 67.5 wide. Find the area of the park. (Round to the nearest hundredth if
necessary)
Answer:
Step-by-step explanation:
The area of a rectangle is length x width.
Given:
length = 175.23m
width = 67.5m
Area = 175.23m x 67.5m = 11828.025[tex]m^{2}[/tex]
A 20-ounce bottle of lotion costs $3.95. How much does each ounce cost?\
Answer:
$0.20
Step-by-step explanation:
3.95/20 = 0.1975
0.1975 would round up to 0.20
Answer:
$0.1975
Step-by-step explanation:
Do $3.95 divided by 20 so you can find the proportion of 1 ounce
If log_10(x) = 3 + log_10(y), then find x/y
Answer:
1000Step-by-step explanation:
[tex]log_{10}x = 3 + log_{10}y[/tex][tex]log_{10}x - log_{10}y = 3[/tex][tex]log_{10}(x/y) = 3[/tex][tex]x/y = 10^3[/tex][tex]x/y = 1000[/tex]Answer:
x/y = 10^3 = 1000
Step-by-step explanation:
The rules of logarithms tell you ...
log(x/y) = log(x) -log(y)
__
Here, we have ...
log(x/y) = log(x) -log(y)
= (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)
Taking the antilog, we get ...
log(x/y) = 3
x/y = 10^3 = 1000
_____
Additional comment
The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).
In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).
Using the Addition Method, find the value of y in
the system of equations 2x1= 3y – 5 and 5x + 6y =
28
Answer:
28?
Step-by-step explanation:
Westford Lake was originally blue because it only had 810 algae plants. Then towns and farms cropped up by the lake. This caused 9,772 more algae plants to grow, which turned the lake green. How many algae plants are now in Westford Lake?
Answer:
10,582 algae plants
Step-by-step explanation:
10,582 algae plants. You have to add 810 and 9,772 to get 10,582 algae plants.
What is the range of possible sizes for side x?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The value of third side should be lesser than the the sum of other two sides ~
[tex]\qquad \sf \dashrightarrow \:x < 2.8 + 2.8[/tex]
[tex]\qquad \sf \dashrightarrow \:x < 5.6[/tex]
and, value of third side should also be greater than the difference of other two sides ~
[tex]\qquad \sf \dashrightarrow \: x> 2.8 - 2.8[/tex]
[tex]\qquad \sf \dashrightarrow \:x > 0[/tex]
Now, combine the two inequalities, we will get ~
[tex]\qquad \sf \dashrightarrow \:0 < x < 5.6[/tex]
I hope you got the required Answer ~
Which equation represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2h equatWhich equation represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2ion represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2
Answer:
(c) f(x) = 500(5^x)
Step-by-step explanation:
An exponential function is one that has the independent variable (x) in the exponent. The initial value of an exponential function (or any function) is the value when x=0.
__
Examine the ChoicesYou are looking for a function with x in the exponent, and with an initial value of 500. Eliminate answer choices that don't have x in the exponent. Evaluate the remaining choices for x=0 and see which gives you a value of 500.
f(x) = 100(5)^x ⇒ f(0) = 100·1 = 100 ≠ 500
f(x) = 100(x^5) . . . not an exponential function
f(x) = 500(5)^x ⇒ f(0) = 500·1 = 500 . . . . . the function you're seeking
f(x) = 500(x^2) . . . not an exponential function
Answer:
a
Step-by-step explanation:
(a) A color page prints 20 pages in 7 minutes. How many pages does it print per minute?
(b) it takes 55 pounds of seed to completely plant a 7- acre field. How many acres can be planted per pound of seed?
If needed round to nearest hundredth.
Answer:
A. 20 / 7 = 3 (or 2.85)
B. 55 / 7 = 8 (or 7.85)
Brainliest is appreciated!
_ daintysword.mp4
Answer:
A.3
B.8
Step-by-step explanation:
this is the answer
Use E to decode the coded message matrix
Answer:
D because I was doing it for a while and I know it
Liz records the amount of rainfall in her backyard. It rained 3/8 inch for 4 days in a row.
Which shows the amount of rainfall after 4 days?
A : 1 4/8
B : 1 5/8
C : 1 6/8
D : 1 7/8
Find the measure of the indicated arc
Step-by-step explanation:
we need the length of the arc ?
the length of the arc fully around the circle (360°) is the circumference of the circle : 2×pi×r
and the arc length for 123° is then
2×pi×r×123/360
but we would need r to calculate that. you did not provide that.
the only other thing that comes to mind is : the arc angle is indeed the angle at the center of the circle and is 123°.
i don't know how else to help you, as i cannot think of anything else you might need there.
Joe collects toy cars and marbles. Whenever he collects 4 cars, he also collects 12 marbles. How many marbles does he collect after collecting 20 cars? What rule is being used?
Answer; 60
Step-by-step explanation:
solution:
here,
4 cars = 12 marbles
1 car = 12/4. = 3 marbles
then,
20 cars = 3(20) marbles
= 60 marbles
We can make this into a fraction 4/12 = 20/x
Then, we will solve for x
4x = 240 cross multiply
x = 60
Joe collects 60 marbles after collecting 20 cars.
The Multiplicative Inverse Property is being used.
Which of the following expressions is equivalent to……
Answer:
Box 4
Step-by-step explanation:
negative divided by negative is positive so both negatives cancel out and u get (5/6) / (1/3)
CAN SOMEBODY HELP ME SOLVE THIS EQUATION
Step-by-step explanation:
Slope m=4
Y intercept b=(-5)
formula f(x)=4x-5
If u need how to solve do let me know
which of the following is true about the sequence graphed below?
Answer:
The sequence is arithmetic because the terms have a common difference
Step-by-step explanation:
The difference between each term in the sequence is constant. The sequence shown below, considering the y values of the coordinates, are 9, 7.5, 6, 4.5, 3, 1.5. Each term has a difference of 1.5, thus making all terms have a common difference, and making the sequence arithmetic.
Paul leaves £4000 in the bank for two years. It earns compound interest of 5% per year. Calculate the total amount Paul's has in the bank at the end of the two year.
Pls give me working out and explanation !!!!
Answer:
£4400
Step-by-step explanation:
5% of 4000 is 200
200*2=400
4000+400=4400
£4400
A flashlight is projecting a triangle onto a wall
Answer:
24
Step-by-step explanation:
The the triangles are similar, the lengths of corresponding sides are in proportion.
15/20 = 18/n
3/4 = 18/n
1/4 = 6/n
n = 4 × 6
n = 24
Answer:
n = 24
Step-by-step explanation:
In similar triangles, corresponding sides are in same ratio.
[tex]\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24[/tex]
There should be 2 answers
[tex]|6m-2|=0\\\\\implies 6m-2 =0~~~~~~~~~~~~~;[\text{If}~ |x| = 0 ~\text{then}~ x = 0]\\\\\implies m = \dfrac 26 = \dfrac 13[/tex]
A=
B=
C=
? ? ? ? ? ? ? ? ? ? ? ? ? ?
Answer:
a=5 b=7 c=9
hope I helped :)
Probability Practice: Cass is interested in figuring out how many customers have applied for a home mortgage recently.
Review the data and calicut are the probability that if Cass runs into one of the financial institutions customers at random, that person has applied for a home mortgage this year.
What is the total number of customers?
How many customers applied for a home mortgage?
The data given relating to the probability shows that the total number of customers will be 27300.
How to calculate probability?The total number of customers will be:
= 24300 + 3000
= 27300
The number of customers that applied for a home mortgage will be:
= 2430 + 150
= 2580
In conclusion, the total number of customers will be 27300.
Learn more about probability on:
https://brainly.com/question/24756209
-1/4 (24ab + 8c) please help
the sum of three consecutive natural numbers is 1146, find the numbers.
the three numbers in increasing order are ______ , _____, and ________
[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]
Adam is purchasing a new television that costs $2,187.96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3.5%. What is the interest he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
Using simple interest, considering the parameters stated in the exercise, it is found that he will pay an interest of $153.16.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of interest after t years in is modeled by:
I = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.In this problem, the parameters are given as follows:
P = 2187.96, r = 0.035, t = 2.
Hence, the interest paid will be of:
I = Prt = 2187.96 x 0.035 x 2 = $153.16.
More can be learned about simple interest at https://brainly.com/question/25296782
use multiplication to show how many twelfths equal 2/3.
you can get 74 points
[tex]\\ \rm\rightarrowtail \dfrac{2}{3}[/tex]
We need. the denominator as 12
So
[tex]\\ \rm\rightarrowtail \dfrac{2(4)}{3(4)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{8}{12}[/tex]
Answer is 4Answer:
[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]
Step-by-step explanation:
To get from 3 to 12, we must multiply 3 by 4 since 3 x 4 = 12
Therefore, multiply both the numerator and denominator by 4:
[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]
The sum or difference of p and q is the of the x-term in the trinomial.
a. ss. www.
coefficients
Answer:
coefficient..........
Pablo had $319 in his savings account. He got $28 for helping a neighbor, and he saved all but $11 of it.
How much is in Pablo's savings account now?
A.
$330
B.
$336
C.
$347
D.
$358
Answer:
the correct answer is B. $336
Step-by-step explanation:
you first add 319 and 28. Then, you subtract the product with 11.
To be honest I think the answer is B
How do I do this question folks?
Answer:
Correct answer: B
Step-by-step explanation:
Syntax: in piecewise functions such as the one attached, the "if:" section shows the domain, or x-axis values which that function pertains to.
In the graph, you can see that the graph is defined for [tex]-3\leq x < 1[/tex] (not-including 1 because there is an open hole there, indicating it is not part of the domain), and [tex]2\leq x\leq 4[/tex].
Now that we know the domain, we can attach it to the graphs that lie on those domains.
We see that the leftmost line appears to have a positive slope and a negative y-intercept, and that the second line should have a positive y-intercept and a negative slope.
At this point, you can just start crossing off answers that don't meet this criteria.
Cheers!!
Which CANNOT be the third side of a triangle if the two sides measure 10 cm and 32 cm ?
A.
32 cm
B.
33 cm
C.
44 cm
D.
40 cm
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
The Length of the third side of a triangle shouldn't be greater than the some of other two sides,
So, let the side be x
[tex]\qquad \sf \dashrightarrow \: x < 32 + 10[/tex]
[tex]\qquad \sf \dashrightarrow \: x < 42[/tex]
And hence, the third side should be less than 42 cm, therefore the only option that doesn't satisfy the condition is option D
Therefore, 44 cm can't be a side of that Triangle.
Does anyone know all of these? (11th Grade Algebra)
Answer:
Step-by-step explanation:
17) In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠A + ∠D = 180
5x + 30 + x = 180
5x +x + 30 = 180 {Combine like terms}
6x + 30 = 180 {Now, subtract 30 from both sides}
6x + 30 - 30 = 180 - 30
6x = 150
Now divide both sides by 6
x = 150/6
x = 25
∠A = 5x + 30
= 5*25 + 30
= 125 + 30
= 155
In parallelogram, opposite angles are congruent.
∠C = ∠A
∠C = 155°
18)In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠A + ∠D = 180
3x + 4 + x = 180
3x +x + 4 = 180 {Combine like terms}
4x + 4 = 180 {Now, subtract 4 from both sides}
4x + 4 - 4 = 180 - 4
4x = 176
Now divide both sides by 4
x = 176/4
x =44
19) In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠GAC + ∠ACF = 180
125 + ∠ACF = 180
Now, subtract 125 from both sides
∠ACF = 180 - 125
∠ACF = 55
21) In parallelogram, adjacent angles are supplementary (add up to 180)
∠CFG + ∠ACF = 180
2w +30 + w + 15 = 180
2w +w + 30+ 15 = 180
3w + 45 = 180
3w = 180 - 45
3w = 135
w = 135/3
w = 45
∠ACF = w + 15
= 45 + 15
∠ACF = 60
21) In parallelogram, opposite sides are congruent.
GF = AC
4x - 14 = 2x + 2
4x = 2x + 2 + 14
4x = 2x + 16
4x - 2x = 16
2x = 16
x = 16/2
x = 8
22) In parallelogram, the diagonals bisect each other.
XC = GX
3y - 3 =2y + 2
3y = 2y + 2 + 3
3y = 2y + 5
3y - 2y= 5
y = 5
23) The length of the middle segment of trapezium is half the sum of the two parallel sides.
[tex]\dfrac{b_{1}+b_{2}}{2}=110\\\\\\b_{1}+b_{2}=110*2\\[/tex]
Help help ASAP math math
Answer:
-9
Step-by-step explanation:
225 ÷ -25 = -9