Find the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares

Answers

Answer 1

The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

for given question,

We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.

Now we rewrite given curve y = x³ in terms of x.

[tex]x=\sqrt[3]{y}[/tex]

Since the length of the side of each cross sectional square is [tex]2\sqrt[3]{y}[/tex], the cross sectional area A(y) can be given by

A(y) = [tex](2\sqrt[3]{y})^2[/tex]

A(y) = [tex]4y^{\frac{2}{3} }[/tex]

The region is bounded from y = 0 to y = 1

so, the volume V can be found by,

[tex]V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4[/tex]

Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

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Related Questions

What is -33.44/-1.9 in division?

Answers

The division of the number -33.44/-1.9 is 17.6.

What is referred as division?

Division is one of four fundamental mathematical operations, along with addition, subtraction, as well as multiplication.

Division is defined as the separating of a large group in to other smaller groups so that each group has an equal amount of items.Division is a process of repeated subtraction. It is the inverse operation of multiplication.It is characterized by the creation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of the those smaller numbers equals the larger number taken.

For the given expression;

=  -33.44/-1.9

as, both numerator and denominator is negative values, both negative signs will be cancelled.

Now, divide numerator 33.44 by denominator by 1.9, we get 17.6.

Thus, the division of the number -33.44/-1.9 gives quotient 17.6.

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Devante will buy 3 packs of gum and four candy bars.gum is 21 cents a pack and candy bars are 45 cents each.how much will devante spend in dollars and cents?

Answers

Devante spent 2 dollars 43 cents

In this question,

A gum is 21 cents a pack and candy bars are 45 cents each.

Devante buy 3 packs of gum.

So for 3 packs of gum total amount would be,

3 × 21 = 63 cents

Devante buy 4 candy bars.

So for the four candy bars the total amount would be,

4 × 45 = 180 cents

Total purchase would be,

63 cents of packs of gum + 180 cents of candy bas

= 243 cents

We know that 1 dollar = 100 cents

S0, 243 cents = 2.43 dollars

Therefore, Devante spent 2 dollars 43 cents

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Which graph models function

Answers

The function g(x) models a downward facing parabola shape which is option A

The function g(x) have the solutions which are given in the form of coordinates

This can be solved on a sheet of graph using coordinate geometry  

(-3,0), (-2,-4) , (-1, -6) , (0, -6 ), (1,-4),(2,0)  and (3,6)

If we will plot all the given seven points given on the graph and join the points we would get a downward sloping parabola model which looks like reverse 'U' shaped  whose highest point is between -1 and 0 that is -0.5

lies in second quadrant of the graph sheet.

Hence the given function g(x) models a parabola shape which is option A

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A speculative statement about the relationship between two or more variables is known as a? a-correlation b- hypothesis c- sample d- research design

Answers

A speculative statement about the relationship between two or more variables is known as a b - hypothesis.

Variables:

A variable is a measurable trait or characteristic that is subject to change under different conditions.

Given,

Here we need to find what is meant by a speculative statement about the relationship between two or more variables.

The definition of Hypothesis is,

It is basically a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

So, a speculative statement about the relationship between two or more variables is known as a b - hypothesis.

So, the option (b) - Hypothesis is correct.

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What is the standard notation for the following expression?
4.62 × 10⁻³

Answers

Answer:

Step-by-step explanation:

Calculate 10 to the power of −3 and get  1 over 1000

4.62(1/1000)

the answer is 231 over 50000 or 0.00462

Taylor makes $13 per hour at the grocery store. she always works between 10-15 hours per week to leave time for her homework and band practice. her gross wages can be modeled as w(h) = 13h, where h is the number of hours worked per week.
1. how much will her gross wages be if she works 12 hours this week?
2. what is the domain of this function?
3. what is the range of this function?

Answers

a) Her gross pay will be $156

b) The domain is D: [10, 15]

c) The range is R: [$130, $195]

What will be her gross wage if she works 12 hours this week?

We know that Taylor earns 13 dollars per hour on her job at the grocery store.

Then, if she works x hours in the week, her gross wage will be given by the linear equation:

g(x) = $13*x

So,  if she works 12 hours, her gross pay will be:

g(12) = $13*12 = $156

what is the domain of this function?

we know that she works between 10 and 15 hours peer week, so the domain (set of the possible inputs of the function) is:

10 ≤ x ≤ 15 or [10, 15] in interval notation.

what is the range of this function?

The range is the set of the outputs, the minimum of the rane is:

g(10) = $13*10 = $130

The maximum of the range is:

g(15) = $13*15 = $195

The range of the linear function is: [$130, $195]

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A salesclerk is creating a display of 12 polo shirts and 48 team shirts. Only one type of shirt can be in each row. What is the maximum number of shirts in each row so that all the rows are equal in length? 12 4 3 2

Answers

The maximum number of shirts in each row so that all the rows are equal in length is 12.

How to illustrate the information?

From the information, the salesclerk is creating a display of 12 polo shirts and 48 team shirts and only one type of shirt can be in each row.

It should be noted that the value van be found by knowing the highest common factor for the numbers.

The highest common factor for 12 and 48 is 12.

Therefore, the correct option is A.

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the store has a speaker equipment listed for a price of $100 per set of speakers there is a sale, the current selling price is 89.99 how much money does the customer save ?

Answers

The amount of money saved by the customer is $10.01

If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit or the money saved.

If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss or the money loss.

Profit/ Loss= Cost Price(CP)- Selling Price(SP)

When CP> SP, then we can say there is a profit.

When CP<SP, then we can say there is a loss.

When CP=SP, then we can say neither there is a loss nor profit.

Given data, CP= $100

SP= $89.99

Profit/Loss= CP- SP

= $100- $89.99

= $10.01

As we can see our result is positive, so there is a profit.

Final answer: The amount of money saved by the customer is $10.01

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Oliver and his friends like to collect and trade cards from a certain combat card game. Oliver used his allowance to purchase 5 booster packs and 4 premade decks, which included a total of 178 cards. For his birthday, he received 4 booster packs and 7 premade decks, which included a total of 264 cards. How many cards come in every booster pack and every premade deck?

Answers

Solving system of equations in two variable gives that the number of cards in every booster pack are 10  and number of cards in every premade deck are 32

What is system of equations in two variables and how to find its solution by substitution?

Let x and y be two variables and

a₁x+b₁y =c₁              

a₂x+b₂y =c₂        

Where a₁, a₂, b₁, b₂, c₁, c₂ are  constants   then  we can solve these simultaneous equations by substitution take value of x from equation (1) and then put it in (2) to get an equation for y only and then solve for y. put value of y in equation (1) to get value of x.

Let the number of cards in every booster pack are  x and the number of cards in every premade deck  be y

Number of cards in 5 booster packs will be 5x  and Number of cards in 4  premade deck will be 4y

As Oliver purchases 5 booster packs and 4 premade decks, which included a total of 178 cards.

Thus we get       5x + 4y = 178    .....(1)

Number of cards in 4 booster packs will be 4x  and Number of cards in 7  premade deck will be 7y

As Oliver received 4 booster packs and 7 premade decks, which included a total of 178 cards.

Thus we get     4x +7y = 264       ...(2)

System of equations to be solved is

5x + 4y = 178    .....(1)

4x +7y = 264       ...(2)

From (1) , we get x = [tex]\frac{178-4y}{5}[/tex]

Put this value in (2)

[tex]4(\frac{178-4y}{5}) +7y= 264\\\frac{712}{5} -\frac{16y}{5} +7y = 264\\\frac{712}{5}-264=\frac{16y}{5} -7y\\ y= 32\\x= \frac{178-4(32)}{5 }\\ x=50/5\\x=10[/tex]

Therefore x=10 and y= 32

The number of cards in every booster pack are 10   and number of cards in every premade deck are 32

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6. Select all the expressions that result in the same value as
40 + 120.
A. 4 (10
+30)
B. 2 (20 + 120)
C. 40 (1 + 3)
D. 40 (1 +30)
E. 10 (4+12)

Answers

Answer:

A, C, E

Step-by-step explanation:

40 + 120 = 160

Remember the correct order of operations, and do the operation inside parentheses first.

A. 4(10 + 30) = 4(40) = 160

B. 2(20 + 120) = 2(140) = 280

C. 40(1 + 3) = 40(4) = 160

D. 40(1 + 30) = 40(31) = 1240

E. 10(4 + 12) = 10(16) = 160

Answer: A, C, E

imagine the biology department needs to decide which lab curriculum yields better student outcomes. five sections are assigned to curriculum a, and five sections are assigned to curriculum b. all sections are administered a pre- and post-test that measures students’ attitudes toward science and knowledge of biology. the department wants to see if students’ gains are greater in one curriculum or the other. what statistical test should be done to determine if there is a significant difference? explain why you chose this test.

Answers

The statistical test that should be done to determine if there is a significant difference is the independent t-test.

What're is an independent t-test?

It should be noted the independent t-test or students t-test for two samples should be used.

The Independent Samples T-Test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different.

In this case, the biology department needs to decide which lab curriculum yields better student outcomes, the.t text can be applicable.

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Which venn diagram represents x

Answers

Answer:

Step-by-step explanation:

A

What does the symbol bc represent

Answers

Answer:

ray BC

Step-by-step explanation:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle.

P = 2L + 2W

Answers

Answer is P - 2L / 2

Step by step

- Subtract 2L from both sides of the equation to isolate W

P = 2L -2L + 2W

P -2L = 2W

- Divide both sides of the equation by 2 to solve for W

P-2L/2 = 2/2 W

P - 2L /2 = W

So W = P - 2L/2 is your answer

A rectangular field is 15m longer than it is wide.
The area of the field is 800m²
Work out the length of the field.
Give your answer to 1 decimal place.

Answers

The length of rectangular field is 36.76 m.

What is a length?

Distance is quantified by length. A quantity with the dimension of distance is called length in the International System of Quantities. Most measurement systems choose a length base unit from which all other units are derived. The fundamental unit for length in the International System of Units is the metre.

The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.

Area of rectangle is L × W = 800

given L = 15 + W

W × ( 15+ W) = 800

15W + [tex]W^{2}[/tex] = 800

[tex]W^{2}[/tex] + 15W - 800 = 0

by solving the above quadratic equation W= 21.76 m.

L = 15 + W

L = 36.76 m

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State the property that justifies the statement.
If m∠ 1=25 and m∠2=25 , then m∠1=m∠2.

Answers

The equality property that justifies the statement "If m∠ 1=25 and m∠2=25 , then m∠1=m∠2" is; Substitution Property

What is the property of equality used?

The substitution property of equality states that 'If a variable C is equal to another variable D, then C can be substituted in place of D in any equation/expression and D can be substituted in place of C in any equation/expression.

Now, we are given the expressions;

If m∠ 1  = 25 and m∠2 = 25 , then m∠1 = m∠2.

Thus, we can also say that the property used here is called substitution property because the parameters were interchanged and still equal.

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Round 45.8 to the nearest whole number

Answers

Answer: 46

Step-by-step explanation: 8 is closer to 10, so 45.8 would round to 46

What is the quotient of 81/(-9)/(-3)

Answers

Answer:

3

Step-by-step explanation:

81/(-9)/(-3)=3

The number 3 is prime number.

Solve negative four and one third ÷ two and one fifth.

Answers

Answer: -2/15 according to the calculator.

Answer:

-1.9681

the 81 is repeating

Step-by-step explanation:

what is the answer for this it’s pre algebra pls answer quickly it’s due in 10 mins

Answers

The answer is k⁴n⁶/3 after solving the expression.

Given, the expression is kn/3k⁻³n⁻⁵

now we must simplify the expression with the help of the negative exponent rule.

A base that is on the fraction line's denominator side can be indicated by a negative exponent. In other words, according to the negative exponent rule, a number with a negative exponent should be added to the numerator and vice versa.

that is, a⁻ⁿ = 1/aⁿ

therefore,  kn/3k⁻³n⁻⁵ = knk³n⁵/3

Multiply the monomials.

Monomials should be multiplied by adding the exponents to the coefficients before moving on to the variables. You can sum the exponents of monomials while multiplying them by the same base. The Product of Powers Property is used to describe this.

k⁴n⁶/3

Hence we get the answer after simplification as k⁴n⁶/3

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HELP I WILL GIVE BRAINLIEST!!!! M14. Select all the situations that could be represented by the expression 40. (-18).
A hot air balloon descends 18 inches per a second for 40 seconds.
A hot air balloon ascends 40 inches per a second for 18 seconds.
Trey withdraws $18 from his checking account once a week for 40 weeks.
Suzanne deposits $18 into her savings account once a week for 40 weeks.
Morty withdraws $40 from his checking account once a month for 18 months.

Answers

The statements that could be represents the expression 40×(-18) is

A hot air balloon descends 18 inches per a second for 40 secondsTrey withdraws $18 from his checking account once a week for 40 weeks.Morty withdraws $40 from his checking account once a month for 18 months.

The expression= 40×(-18)

A hot air balloon descends 18 inches per a second for 40 seconds=40×(-18)

A hot air balloon ascends 40 inches per a second for 18 seconds=40×18

Trey withdraws $18 from his checking account once a week for 40 weeks=40×(-18)

Suzanne deposits $18 into her savings account once a week for 40 weeks=40×18

Morty withdraws $40 from his checking account once a month for 18 months=40×(-18)

Hence, The statements that could be represents the expression 40×(-18) is

A hot air balloon descends 18 inches per a second for 40 secondsTrey withdraws $18 from his checking account once a week for 40 weeks.Morty withdraws $40 from his checking account once a month for 18 months.

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NEED HELP IMMEDIATELY!

Simplify 10√2y + 5√2y + 3√2y.
A. 18√6y
B. 18√2y
C. 12√2y
D. 18√6y^3

(ANSWER IS NOT A)

Answers

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

10 + 5 + 3 = 18 therefore it is B

q equals 4 l plus 2 k with l on the horizontal axis and k on the vertical axis, draw an isoquant. the slope of this isoquant equals

Answers

The slope of this isoquant equals -2.

What is an isoquant?

A contour line formed across a set of locations where the same quantity of output is produced while changing the quantities of two or more inputs is called an isoquant (derived from quantity and the Greek word iso, meaning equal). A factor of production, like as labor, money, land, or organization, is typically represented by the x and y axes on an isoquant. Another name for an isoquant is a "Iso-Product Curve" or a "Equal Product Curve."

The isoquant mapping deals with the cost-minimization, profit, and output maximization problems of producers, whereas an indifference curve mapping helps consumers address the utility-maximizing problem. Indifference curves and isoquants diverge much more.

Calculations:

q=4L+2K

So, MPL=dq/dL =4

MPK=dq/dK =2

So,Slope=-MPL/MPK

=-4/2=-2

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9. What is the slope of the graph of y= 12 x - 19?

Answers

12

Explanation:

Slope Intercept form is: y=mx+b
m would be the slope

So in y=12x-19, 12 would be the slope in this case.

Write √-45 in simplest radical form.

Answers

Answer:  3[tex]\sqrt4[/tex]

Step-by-step explanation:

Simplified radical form of the square root of 45

Square root of 45 can be expressed as, √45 = √(9 × 5) = 3√5. 45 is not a perfect square, so, it remains within roots. The simplified radical form of the square root of -45 is 3√5.

Answer:

3√5i

Step-by-step explanation:

[tex]\sqrt{-45}=\sqrt{-1}\sqrt{45}\\\sqrt{-1}\sqrt{45}\\i\sqrt{45}\\**Prime\:Factorization*\\3 \times 3 \times 5 = 45\\=3\sqrt{5}i[/tex]

➲ Hope this helps.

A(n) ____ turns a figure a certain number of degrees around a point.

Answers

A “rotation” turns a figure a certain number of degrees around a point.

In geometry, shapes are changed through three forms of variance: transformations, dilations, and rotations. In transformation, a point is moved around a fixed amount of space. In a dilation, a scale factor is used to either enlarge or shrink a figure. In a rotation, a shape rotates a certain number of degrees around a point.

Answer Recap: A rotation turns a figure a certain number of degrees around a point.

Rashon needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.

Answers

Answer:

Step-by-step explanation:

The cost of labor per hour is $45.

The total cost of the parts is $141.The total time for which the technician worked is 4.25 hours.The total cost of repair is $332.25.Let the cost of labor per hour be "x".The total cost of labor is the product of the total time for which the technician worked and the cost of labor per hour.The cost of labor is 4.25*x.The total cost of repairing the computer is the sum of the cost of the parts and the cost of labor.The total cost of repairing the computer is $141 + 4.25*x.The equation is as follows:332.25 = 141 + 4.25*x191.25 = 4.25xx = 191.25/4.25x = 45Thus, the cost of labor per hour is $45.

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A​ town's population is 42,975. About 125 people move out of the town each month. Each​ month, 150 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be​ equal? Write an equation to model the situation. Then solve the equation and answer the question.

Answers

It would take 10 months to equate the population of both the towns

Let the number of months required to equate the population of both the town( Town A and Town B) be x

This question can be solved using linear equations

So, town A's population would be current population adjusted with migration of people  which is 42975-125x+150x

And town B's population would be current population adjusted with migration of people  which is 45225 -200x

As at the end of x months the population of the two towns is equal, so equating both the linear equations

 42975 -125x +150x = 45225-200x

Now solving the equation for x

150x-125x+200x= 45225-42975

225x=2250

Therefore x= 2250/225= 10

Hence it would take 10 months to equate the population of both the towns

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3 is subtracted from three times a number

“a number” is x

Answers

Answer:

3x - 3

The answer above matches with the statement:

"Three is subtracted from three times a number."

Hope this helps :)

are the ratios 1:4 and 3:5 equivalent

Answers

Answer:no

Step-by-step explanation:1:4 is not equivalent to 3:5

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