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]
George wanted to measure the angle of a water slide at the lake. He used a sheet of folded paper that formed a 20° angle. He measured and found that three of the folded paper angles would fit in the angle made by the slide and the ground.
Which of the following was the angle of the water slide?
The angle of the water slide is 60 degrees.
The equation that models his work is 3 × 20 = 60 degrees.
How to find the sum of angles of a figure/object?
He wants to measure the angle of a water slide at the lake.
He used a sheet of folded paper that formed 20 degrees to measure the angle of the the water slide at the lake.
He noticed three folded paper angle fits in the angle made by the slide and the ground.
Since each angle is equals to 20 degrees, and the three fits into the angle made by the slide and the ground, the angle of the water slide is as follows:
20 × 3 = 60 degrees
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Help help help help
1350 + 238
After 2 years, a certain car is worth $16600. When it is 9 years old, the same car is then worth
$9950.
Find the equation of the line in this situation.
Identify the slope for this situation and interpret it.
Identify the y - intercept for this situation and interpret it.
Identify the x - intercept for this situation and interpret it.
The linear function that describes the situation is:
y = -950x + 18500.
The slope of -950 means that the price of the car decays $950 per year.The y-intercept of 18500 means that the initial value of the car is of $18,500.The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, in 7 years, the price of the car decays by $6,650, hence the slope is given by:
m = -6650/7 = -950.
The slope of -950 means that the price of the car decays $950 per year.
Then, the equation is:
y = -950x + b.
After 2 years, a certain car is worth $16600, hence when x = 2, y = 16600, and:
16600 = -950(2) + b
b = 18500.
The equation is:
y = -950x + 18500.
The y-intercept of 18500 means that the initial value of the car is of $18,500.
The x-intercept is found when y = 0, hence:
-950x + 18500 = 0.
x = 18500/950
x = 19.47.
The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.
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f(x)=x-5 is the function linear quadratic exponential or neither
Answer:
Linear
Step-by-step explanation:
It is a first-degree function, the variable "x" has power 1
when graphed, a straight line results in
Hope this helps
A painter bought 14 gallons of paint just enough to cover 2 room
7
Step-by-step explanation:
[tex]Based\ on\ the\ given\ conditions,\ formulate:[/tex]
[tex]14\div 2[/tex]
[tex]\frac{14}{2}[/tex]
Creoss out the common factor
[tex]7[/tex]
I hope this helps you
:)
What number (X) comes next in the series (17, 9, 18, 7, 19, 5, 20, X)
3
4
16
21
23
Answer:
17, 9, 18, 7, 19, 5, 20, X
Bold: 17, 18, 19, 20, .....
Other: 9, 7, 5, 3, 1 ....
I think the answer is 3
By finding the pattern, we conclude that the next number in the sequence is 3.
What number comes next in the series?
We have the sequence:
17, 9, 18, 7, 19, 5, 20, x.
Here the pattern is kinda simple.
First, we have a two-digit number which increases by one unit (on the odd positions). Then we have a single-digit number that decreases by two (on the even positions).
Then we will have:
x = 5 - 2 = 3
We conclude that the next number in the sequence is 3, we get:
17, 9, 18, 7, 19, 5, 20, 3.
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simplify the following 42÷7+14-4×5
Answer:
1
Step-by-step explanation:
42/7 + 14 - 4 × 5
7 + 14 - 4 × 5
7 +14 - 20
20 - 20
0
Answer:0
because 42 divided by 7 is 6 and 6 + 14 is 20 and 4 times 5 is 20 som then 20 -20 = 0
In the diagram, ABCD is a parallelogram. Write an argument to support the claim that
M x = M y
The angles m∠x = m∠y because alternate interior angles are equal.
What is a parallelogram?A parallelogramis a quadrilateral in which opposite sides are equal and parallel to each other.
The opposite angles are also congruent, whereas consecutive interior angles are supplementary.
In the quadrilateral ABCD:
m∠x = m∠y (alternate interior angles are equal)
The angles m∠x = m∠y because alternate interior angles are equal.
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hello help me with this question thanks in advance
Answer:
B. 98 ft
Step-by-step explanation:
x^2 + y^2 = z^2
z = sqrt(84^2 + 50^2) = 97.7 ft ~ 98 ft
B. 98 feet
Step by-step explanation:[tex]Solution:\ From\ question\\ 84\ feet\ long\ and\ 50\ feet\ wide\\ so\ he\ will\ run\ \sqrt{{84}^2+{50}^2}\ \approx98\ feet[/tex]
25 am
15 cm
15 om
E9 cm
-
9 cm
What is the area of the trapezold?
O
354 cm
o
408 cm2
0 510 cm2
0 O
595
cm2
The answer is 408 cm2 after applying the formula of right angled triangle,adding 25 and both 9 and applying the formula 1/2(p1+p2)h
Please give me brainliest
The round temperature dial on a thermostat has a diameter of 26 millimeters. What is the dial's circumference?
C = 2 x pi x r = pi x d
so
C = 3,14 x 26 = 81,64 mm
For context, question 6 is:
What inverse operation will be used to undo the volume of Julie's jewelry box to find its edge lengths?
Volume formula for a cube is: volume = edge^3
//I have already answered This, I need help with #7, which is:
"If V = 216, what is the edge length of Julie's jewelry box?"
Answer:
6
Step-by-step explanation:
The inverse of cubed is cubed root. The cubed root of 216 is 6.
What is the factorization of the trinomial below?
-x^2 - 2x + 48
A. -1(x - 8)(x + 6)
B. -1(x + 8)(x - 6)
C. (x + 6)(x - 8)
D. (x - 6)(x + 8)
Answer:
The answer to this question is A
A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 360 square yards. Find the length and the width.
Answer: The width is 15 yards and the length is 24 yards
Step-by-step explanation:
Let x represent the width of the parking lot in yards
Let the length of the parking lost be (x + 9) as the length is 9 yards greater than the width
So, area = width * length
i.e. 360 = x(x + 9)
360 = x2 + 9x
x2 + 9x - 360 = 0
x2 + 24x - 15x - 360 = 0
x(x + 24) - 15(x + 24) = 0
(x + 24)(x - 15) = 0
Either x = -24 or, x = 15
But as width can not be negative, so we can not have, x = -24
So, we have, x = 15
Therefore, (x + 9) = (15 + 9) = 24
So, we have the following answers.
Width : 15 yards
Length : 24 yards
This figure is the pre-image of a prism that has undergone a dilation with a scale factor of 2/5.
What is the surface area of the image after the dilation?
206225 m²
26845 m²
51512 m²
58225 m²
Answer:
Step-by-step explanation:
Answer:
Yeah. The answer is [tex]206\frac{2}{25}[/tex].
Step-by-step explanation:
I really need help with the answers
Answer:
Part A: 512 ft²
Part B: 3 cans
Step-by-step explanation:
Part A:
We can divide the shape into 2 areas or rectangles.
The top rectangle's area: 20 x 12 =240
The bottom: 34 x 8 = 272
add these 2 up, 240 +272, and you get 512, the area of this figure.
Part B:
We have to divide the number of feet covered by the area:
512/200 = 2.56
However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.
So, we get 3 cans.
Please help
I don’t know what to do with this
Answer:
The prediction should be 5 via interpolation.
Step-by-step explanation:
Based on the values you have, the linear equation is f(x)=x-1. So replace x with the number you're looking for (6).
In a general sense, to extrapolate is to infer something that is not explicitly stated from existing information. Interpolation is an estimation of a value within two known values in a sequence of values.
You roll two number cubes
Let event A = You roll an even number on the first cube.
Let event B = You roll a 2 on the second cube.
Are the events independent or dependent? Why?
O A. Dependent, because both cubes have six sides.
O B. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
O C. Independent, because they have no outcomes in common.
D. Dependent, because 2 is an even number.
Answer: B: Independent, because the outcome of the first roll doesn't affect the outcome of the second roll.
Step-by-step explanation:
Events are independent when the outcome of one does not effect the other. Rolling dice for example: If you roll an even number on your first cube, there is no way that it will effect the roll on the second cube, hence the two events are independent.
Help picture below please
Answer:
B. NRS
Step-by-step explanation:
You have to put the letters left to right.
Below is the graph of a polynomial function with real coet
of the function are shown in the graph.
m
27
Use the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
o(-00,-5) o (-5, -2) 0 (-2,2) 0 (2,6) o(-2,6) o (6,00)
(b) At which x-values does the function have local maxima? If there is more than
one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all
that apply.
5
06
08 09
04
07
This question is about Polynomial Functions. The reading below is done using the attached graph.
a) Over which intervals is the function increasing?The function is increasing over the following intervals:
(2,6) Option D; and (-2,6) Option E.b) Yes, the points on the x-axis that has local maxima are:
Point -2, and Point 6.
c) The leading coefficient is negative. The sign is given as:
f(x) → -∞
as x → + ∞
d) The possible degree of the function is:
06- (Option B).
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helpppppppppppppppppppppppppp walk me thru
Answer:
i think its a trapazoid
Step-by-step explanation:
The number 1 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
Answer:
The number 1 is a factor of C)all whole numbers.
1 is a factor of all whole numbers.
Every single number, including odd numbers and even numbers, is divisible by 1 (evenly, without any remainders)
Remember, whole numbers include odd numbers, even numbers, and 0.
note:-Hope everything is clear; if you need any more explanation and/or clarification, kindly let me know, and I will comment and/or edit my answer.
What common donminator of 1/3 and 3/4
Answer:
12
Step-by-step explanation:
The least common denominator (LCD) of 1/3 and 3/4 is 12, because if you multiply the denominators of both fractions, 3 * 4 = 12.
This would change the fractions to-
1/3 * 4/4 = 4/12
3/4 * 3/3 = 9/12
I hope this was helpful! Have a lovely day!! :)
F(4g2-9)=n i need to solve for f
Answer:
Step-by-step explanation:
Whats 5-5-5-5-5-5x5757575
Answer:
-28787890
Step-by-step explanation:
A case of glue weighs 24 pounds. A pallet loader can lift 3 tons. How many cases can a pallet loader lift?
Answer:
250 cases
Step-by-step explanation:
3 tons is 6000 pounds
you divide 6000 by 24 and get 250
that is your answer
It takes 7 hours and 12 minutes to fly
from Singapore to Tokyo, Japan. You have
to arrive at the airport 45 minutes before
departure. It is a 17 minute taxi ride from
your hotel. By what time would you need
to leave the hotel if the flight lands
at 3:23 p.m.?
The time I would need to leave the hotel if the flight lands at 3:23 p.m is 7 : 09 am
What time should I leave the hotel?The first step is to add the total hours of the flight to the time of the tax ride and the time you need to get to the airport.
7h + 12 min + 45 + 17 = 8 hours 14 minutes
Now subtact 8 hours 14 minutes form 3: 23
(12 + 3:23) - 8 hours 14 minutes =7 : 09 am
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7 is less than y by 5.Find y.
Answer:
12
Step-by-step explanation:
If 7 is less then y by 5, you add 5 to 7
7 + 5 = 12
resulting in y equaling 12
12 - 5 = 7
I NEED HELP IMMEDIATLY! 100 POINTS AND BRAINLY!!!!!!!
Solve for ccc.
Give an exact answer.
0.2(10-5c)=5c-160.2(10−5c)=5c−160, point, 2, left parenthesis, 10, minus, 5, c, right parenthesis, equals, 5, c, minus, 16
c =c=c, equals
C = 2.7
First, simplify both sides of the equation.
0.2(1 − 5c) = 5c − 16
(0.2)(1) + (0.2)(−5c)= 5c + −16
0.2 + −c = 5c + −16
−c + 0.2 = 5c − 16
Now subtract 5c from both sides of the equation, then subtract 0.2 from both sides.
−c + 0.2 − 5c = 5c − 16 − 5c
−6c + 0.2 = −16
−6c + 0.2 −0.2 = −16 - 0.2
−6c = −16.2
Lastly, divide both sides by -6.
-6c/-6 = -16.2/6
2.7
Please mark this as brainliest, cheers.
The average daily rainfall in Seattle for the month of June has a mean absolute deviation of 1.3 inches. What conclusion can you make about the average daily rainfall in Seattle for the month of June?
Using the mean absolute deviation, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.In this problem, the mean absolute deviation is of 1.3 inches, hence, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
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Answer:
Step-by-step explanation: