Region R is bounded by the curves y = √x, y = 1, and x = 4. A solid has base R, and cross sections perpendicular to the x-axis are squares. The volume of this solid is
A. 4/3
B. 8
C. 7/6
D. 15/2
Answers
The cross sections have side length equal to the vertical distance between y = √x and y = 1, or |√x - 1|. The two curves meet at the point (1, 1), and y = √x meets x = 4 at (4, 2), so we'll be integrating with respect to x on the interval [1, 4]. Over this interval, √x ≥ 1, so |√x - 1| = √x - 1.
A cross section of thickness ∆x has volume
(√x - 1)² ∆x = (x - 2√x + 1) ∆x
Then the volume of the solid is
[tex]\displaystyle \int_1^4 (x - 2\sqrt x + 1) \, dx = \boxed{\frac76}[/tex]
Related Questions
need help with this question
Answers
Answer:
f'(0)= -2/5
Step-by-step explanation:
What are prime numbers used for?
Answers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
Here is a prism drawn on an isometric grid how many vertices
Answers
Answer:
C-12
Step-by-step explanation:
The definition of a Vertex of a 3D shape is 'Where 3 lines meet to form an angle' which in this case would be 12.
Answer:
it's c12 first do the edge face vertical nameing polygon and then you can get your answers
What is gain 3 pounds as a integer
Answers
Answer:
it would be +3
Step-by-step explanation:
This is he answer because +3 is equal to p+3 if pounds=p
Over a year, Andy placed 836 phone calls. When he looked at his yearly call log, he noticed that all the calls went to 11 phone numbers.
If he made the same number of calls to each of the numbers, how many times did he call each number?
87
76
847
912
Answers
By taking the quotient between the number of calls and the number of phone numbers, we see that each number was called 76 times.
How many times did he call each number?
We need to find the quotient between the total number of calls and the total number of phone numbers called.
We know that the total number of calls is 836, while it is equally distributed between 11 phone numbers.
The number of times that each of these numbers was called is given by:
N = 836/11 = 76
This means that he calls each number 76 times.
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The surface area of a rectangular-prism-shaped skyscraper is 1,115,000 m2. What is the surface area of a similar model that has a scale factor of 1/800? Round your answer to the nearest tenth.
Answers
The surface area of a similar rectangular-prism-shaped skyscraper that has a scale factor of 1/800 would be equal to 1.7 meter.
The surface area of a rectangular prism.Mathematically, the surface area of a rectangular-prism is given by this formula:
A = 2(wl + hl + hw)
Where:
A is the surface area.l is the length.w is the width.h is the height.Given the following data:
Surface area of rectangular prism = 1,115,000 m²
Scale factor = 1/800
The length, height and width of the similar model would be 1/800 the original rectangular-prism-shaped skyscraper.
Substituting the given parameters into the formula, we have;
Surface area = 1,115,000 × 1/800 × 1/800
Surface area = 1.7 meter.
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The two triangles are similar.
What is the value of x?
Enter your answer in the box.
X=
Answers
Answer:
Step-by-step explanation:
In similar triangles, the corresponding sides are in same proportion.
[tex]\sf \dfrac{4x}{3x+1}=\dfrac{15}{12}[/tex]
Cross multiply,
4x*12 = 15*(3x + 1)
48x = 15*3x + 15*1
48x = 45x + 15
48x -45x = 15
3x = 15
x = 15/3
x = 5
The rate of change is ____.
-4
-1
1
4
Answers
Answer:
-4
Step-by-step explanation:
Rate of Changes:
[tex]\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Pick two values of x and y from the given table:
I pick (1,5) and (-1,13).I define (1,5) be (x2,y2) and (-1,13) be (x1,y1)Therefore:
[tex]\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{5-13}{1-(-1)}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{1+1}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{2}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=-4}[/tex]
Therefore, rate of change is -4
In ΔABC, AB=24.9, AC=15.8, and BC=24.4. What is m∠A?
Answers
Answer:
approximately 71.50215
Step-by-step explanation:
Which equation illustrates the identity property of multiplication? (a bi) × c = (ac bci) (a bi) × 0 = 0 (a bi) × (c di) = (c di) × (a bi) (a bi) × 1 = (a bi)
Answers
The equation that illustrates the identity property of multiplication is (a+bi) × 1 = (a+bi).
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The identity property of multiplication states that when a factor is multiplied by 1 the result is the factor itself. Therefore, the equation that illustrates the identity property of multiplication is (a+bi) × 1 = (a+bi).
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Answer:
D
Step-by-step explanation:
duh
Without buying points, a monthly mortgage payment will be $1,250. buying 1 point at closing would reduce the payment to $1,236. to the nearest year, how long would it take to break even by buying 1 point, with a $100,000 mortgage? a. 5 years b. 6 years c. 7 years d. 8 years
Answers
Without buying points, the time that will be taken to break even will be 6 years.
How to calculate break-even?The monthly mortgage payment will be $1,250. Buying 1 point at closing would reduce the payment to $1,236.
1 point= $1000
The time taken will be:
Monthly savings = 4250/1236 = 14
Time taken = 7
1000/14 = 71.4 months
71.4/12=5.95 years = ~6 years
Thus, The time that will be taken to break even will be 6 years.
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Answer: 6
Step-by-step explanation:
Factor out and show the step by step explanation of the answer for x^2+24x+5
Answers
Answer:
x =(24-√596)/2=12-√ 149 = -0.207
x =(24+√596)/2=12+√ 149 = 24.207
Step-by-step explanation:
Factoring x2-24x-5
The first term is, x2 its coefficient is 1 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is -5
Multiply the coefficient of the first term by the constant 1 • -5 = -5
Find two factors of -5 whose sum equals the coefficient of the middle term, which is -24 .
-5 + 1 = -4
-1 + 5 = 4
Two solutions were found :
x =(24-√596)/2=12-√ 149 = -0.207
x =(24+√596)/2=12+√ 149 = 24.207
Please help first correct answer gets brainleist and 100 points please I'll answer your questions
Answers
Answer:
a) AE and BC are parallel (as shown by the markings)
b) ED and CD are equal in length (as shown by the markings)
c) 3: AE is perpendicular AB, AB is perpendicular to AE/AC, AC is perpendicular to AB
Use the information provided to answer Part A and Part B for question 11.
Three congruent figures are shown in the coordinate plane.
8
-7
-5
9-3-7 65
A
N
-4
-5
-6
-7
-8
3
11. Part A
Which statement describes a possible sequence of transformations that
transforms figure 1 into figure 2?
A. a reflection across the x-axis, followed by a translation 2 units to the left
B. a reflection across the x-axis, followed by a translation 3 units to the right
C. a rotation 180° clockwise about the origin, followed by a translation
2 units to the left
D. a rotation 180° clockwise about the origin, followed by a translation
3 units to the right
Answers
B. A reflection across the x-axis followed by a translation 3 units to the right.
The correct statement about the congruent figures is,
⇒ a reflection across the x-axis, followed by a translation 3 units to the right.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Three congruent figures are shown in the coordinate plane.
Now, From figure A and figure B,
Figure B is reflection across the x-axis, followed by a translation 3 units to the right across the figure A.
Thus, The correct statement about the congruent figures is,
⇒ a reflection across the x-axis, followed by a translation 3 units to the right.
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How many hours will it take them to mow their lawn?
Answers
Answer:
C. 2
Step-by-step explanation:
h/6 + h/3 = 1
h/6 + 2h/6 = 1
3h/6 = 1
3h = 6
h = 2
Because 2/3 turns to 4/6 and 4/6+2/6 equals 1
A rectangle’s length is 5 inches more than twice its width. its area is 50 square inches. which equation can be used to find its width, w? 2w(2w 5) = 50 2w(w 5) = 50 w(2w 5) = 50 w(w 5) = 50
Answers
The equation of the area of the rectangle is w(2w + 5) = 50. Then the correct option is C.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
A rectangle’s length is 5 inches more than twice its width. its area is 50 square inches.
Let the width of the rectangle be w, then the length of the rectangle will be (2w + 5).
Then the area of the rectangle is given as
Area = l × w
Then we have
w(2w + 5) = 50
More about the rectangle link is given below.
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What is the area of a circle whose radius is 4 ft?
Question 2 options:
16πft2
64πft2
8πft2
4πft2
Answers
Answer:
16pi ft^2
(the first answer)
Step-by-step explanation:
Please help me , answer steps . Thanks..
Answers
Answer:
I think the answer is 3150 miles
I multiplied 1.50 by 21 and the answer I converted to miles
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JUST CLICK THE ATTACHMENT PHOTO Ans: ➝ The taxi travel 13 miles⊱─━━━━━━━⊱༺●༺⊰━━━━─⊰
#CARRY ON LEARNINGPLEASE HELP 20 POINTS
Answers
cos(a) = 45/60
a = cos^-1(45/60)
a = 41.41 to the nearest hundredth.
what is the distance between (4,7) and (-3,9)
Answers
Answer:
7 to the left, and up 2.
Step-by-step explanation:
how do I find the volume of an upright rectangle?
Answers
Answer:
v=l×h×w
Step-by-step explanation:
that the furmula
please teach me how to do this
Answers
Answer:
7.2
Step-by-step explanation:
We know that the radius is always the same throughout the entire circle. That is, any line going from the center of the circle to the edges = radius. In this problem, radius = 20.9 and so does the other 4 lines going from the center of the circle to the edge.
Since there is a right angle, we know that both triangles are right triangles where hypotenuse, c = 20.9 and b = 19.6. To solve for x, use pythagorean theorem:
a² + b² = c²
x² + 19.6² = 20.9²
x² + 384.16 = 436.81
x = √(436.81 - 384.16)
x = √52.65
x ≈ 7.256
Hope this helps!
x-3 and 2x-1 are factors of 2x^3-px^2-2qx+q. Find the values of p and q.
Answers
Answer:
p =1
q = 9
Step-by-step explanation:
f(x) = 2x³ - px² + 2qx + q
(x - 3) is a factor of f(x)
⇒f(3) = 0
2(3)³ - p*3² - 2q*3 +q = 0
2*27 - 9p - 6q + q = 0
54 - 9p - 5q = 0
-9p - 5q = -54 -------------------(I)
(2x - 1) is a factor of f(x)
2x - 1 = 0
2x = 1
[tex]\st x = \dfrac{1}{2}[/tex]
f(1/2) = 0
[tex]2*(\dfrac{1}{2})^{3}-p*(\dfrac{1}{2})^{2}-2q*\dfrac{1}{2}+q=0\\\\2*\dfrac{1}{8}-p*\dfrac{1}{4}-q+q = 0\\\\\dfrac{1}{4}-\dfrac{1}{4}p =0\\\\[Multiply the entire equation by 4]\\\\4*\dfrac{1}{4}-4*\dfrac{1}{4}p=0\\\\[/tex]
1 - p = 0
-p = -1
p = 1
Substitute p =1 in equation (I)
-9*1 - 5q = -54
-9 - 5q = -54
-5q = -54 + 9
-5q = -45
q = -45/(-5)
q = 9
When dealing with an equation containing two variables, we can put the graph of the equation on the coordinate plane because the number of variables is equal to the number of dimensions that are needed to properly graph the solution. Each axis on a graph represents one variable in the equation being graphed. What would you use to graph the solution to an equation with one variable? What would you use to graph the solution to an equation with three variables? Could you graph an equation containing more than four variables? Explain.
If you were given the graph of an equation with two variables on a coordinate plane, what would happen to the graph if all the y-values were increased by 1? What would happen to the graph if all the x-values were increased by 1? What would happen to the graph if all the y-values were multiplied by 2 or by 1/2? Explain
ill mark the brainliest if the answer isnt a copy and paste from the other answers
Answers
Answer:
Step-by-step explanation:
See attached image.
1. What would you use to graph the solution to an equation with one variable?
I picked an example equation, y=2x+3, to demonstrate the impacts of changing condions. It is the blue line. I'm not sure how to answer the quesion "What would you use . . .", but my response would be "I would use DESMOS to graph the solution." It is free, efficient, and very flexible. It can handle multiple equations and a variety of functions.
2. What would happen to the graph if all the y-values were increased by 1?
I added 1 to the right side of the equation to increase all the y values by 1. It is the black line. All points are raised by 1.
3. What would happen to the graph if all the x-values were increased by 1?
I added +1 to each x value, shown as the red line. All points are increased by 2 over the original line.
4. What would happen to the graph if all the y-values were multiplied by 2 or by 1/2?
See Increeases2, attached. The slopes of the lines are doubled when the y values are doubled, and decreased by (1/2) when they are multiplied by (1/2). The y intercepts are also doubled or halved, respectively.
Solve with picture PLEASE show all work
Answers
Answer:
40 in.^2
Step-by-step explanation:
Let's name the 2 shaded triangles: The left one is T1 and the right one is T2.
The area of a right triangle can be found using the equation (a*b)/2.
The 2 legs of T1 are 8 in. and 6 in. (from 10 - 4)
Area of T1 = [tex]\frac{8 * 6}{2}[/tex] = 24 in.^2
The 2 legs of T2 are 8 in. and 4 in.
Area of T2 = [tex]\frac{8 * 4}{2}[/tex] = 16 in.^2
Area of shaded region = 16 + 24 = 40 in.^2
What is the area of parallelogram ABCD?
Will mark brainlyest!!!
Answers
A=Bh
4x3 = 12cm^2
An onion soup recipe calls for 3 2/3 cups of chopped onions Katrina has already chopped 1 1/3 cups of onions. She wants to know how many more cups she needs to chop. PLLLLS HELP ILL BE UR BESTIE!!
Answers
Answer:
2 1/3 cups of onions
Step-by-step explanation:
3 2/3-1 1/3= 2 1/3 cups
Your homeowners policy has a premium of $150, a deductible of $5000, and a limit of $300,000. Your home suffers $500,000 in damages. How much will you pay? How much will your insurance pay?
Answers
this question was already asked and somebody answered!!
He will pay $200,000.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Your homeowners policy has a premium of $150, a deductible of $5000, and a limit of $300,000.
And, Your home suffers $500,000 in damages.
Now,
Since, Homeowners policy has a premium of $150, So we can pay the amount = 12 x 150
= $1,800
And, Homeowners policy has a deductible of $5000.
Then, The remain amount = $500,000 - $5,000
= $495,000
Since, The limit of the policy = $300,000
Hence, The remain amount = $495,000 - $300,000
= $195,000
After including the deductible amount we get;
Deductible amount = $195,000 + $5,000
= $200,000
Thus, He will pay $200,000.
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Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a? -9 -3 3 9
Answers
The value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
What is the solution of equation?The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.
Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,
[tex](x +2)^2=a[/tex]
For this equation, one solution is x=1. Put this value in the above equation to get the value of a,
[tex](1 +2)^2=a\\(3)^2=a\\9=a\\a=9[/tex]
Thus, the value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
Learn more about the solution of the equation here;
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Answer:
D. 9
Step-by-step explanation:
Write the polynomial in standard form.
( look at photo )
Answers
Answer:
[tex]b^{2} -2b+5[/tex]
Step-by-step explanation: