A linear expression is an algebraic expression that contains a variable to the power of one. 2y is an example. A coefficient is a rational number that is multiplied by a variable. A rational number is a number that can be written as the ratio, or fraction, of two integers. 4 in the expression 4z is an example of a coefficient. Like terms are terms whose variables and their exponents are the same. One example is 4z and -7z.
In the linear expression 2y, the coefficient is the numerical factor 2. The coefficient is the rational number that is multiplied by the variable, which in this expression is y.
The coefficient of a linear expression is usually the first factor, and it is used to determine the rate of change for a variable.
For example, if the coefficient of 2y is 2, then for every increase in y by one, the result of the linear expression will increase by 2.
The coefficient of a linear expression is the numerical (or rational) factor that is multiplied by the variable. In the linear expression 2y, the coefficient is 2, since the expression is equivalent to 2*y. The coefficient is usually the first factor in a linear expression, followed by the variable and, if present, its exponent.
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You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money. A. 3. 99% compounded monthlyb. 4% compounded quarterlyc. 4. 175% compounded annuallyd. 4. 2% simple interest.
Using the formula of compound interest and simple interest, the investment option that is better is at interest rate of 3.99% which is compounded monthly
Which Investment is betterTo compare the investment options, you need to calculate the future value of each investment after 8 years. Here's a breakdown of each option:
A. 3.99% compounded monthly: This option earns interest every month and compounds, meaning the interest is added to the principal, so future interest is earned on the increased principal amount. This type of interest compound is the most advantageous to the investor. The formula for calculating the future value for this option is:
FV = P * (1 + r/n)^(nt)
FV = 12000(1 + 0.0399 / 12) * (12 * 8)
FV = $16,503.58
where P is the principal ($12,000), r is the annual interest rate (3.99%), n is the number of times the interest is compounded in a year (12 times), t is the number of years invested (8 years).
B. 4% compounded quarterly: This option earns interest every quarter and compounds. The formula for calculating the future value is the same as option A, with the only difference being the number of times the interest is compounded in a year (n=4).
Substituting the values into the formula;
FV = $16,499.29
C. 4.175% compounded annually: This option earns interest once a year and compounds. The formula for calculating the future value is the same as options A and B, with the only difference being the number of times the interest is compounded in a year (n=1).
Substituting the values into the formula
FV = $16,645.21
D. 4.2% simple interest: This option earns interest once a year based on the original principal amount and does not compound. The formula for calculating the future value for this option is:
FV = P(1 + rt)
FV = 12000 (1 + 0.042 * 8)
FV = $16032
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Some answer this please.
Answer:
P = 24.997 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 2 radii and the arc
the arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex] ( r is the radius , here r = 7 )
= 2 × 3.142 × 7 × [tex]\frac{1}{4}[/tex]
= 43.988 ÷ 4
= 10.997 cm
Then
P = 10.997 + 7 + 7 = 24.997 cm
What is the amplitude of this function f(x)? f(x)=3cos(2x)+5
Answer:
The Amplitude is 3
Step-by-step explanation:
How that helps
Answer:
The amplitude of this function is 4, which is calculated by subtracting the minimum value (1) from the maximum value (5).
Step-by-step explanation:
Graph the function y=(1/2)^x+1 using the given table of values and following the instructions below.
Answer:
See the attached image.
Explanation:
Given the equation:
[tex]y=\left(\dfrac{1}{2}\right)^x + 1[/tex]
We can graph the top four points in the middle table, as they fit on the shown graph, and their coordinates are all integers:
[tex](-3,9)[/tex] [tex](-2,5)[/tex] [tex](-1,3)[/tex] [tex](0,2)[/tex]
Then, we can draw a curve through the points and along the asymptote of the exponential function at [tex]y=1[/tex].
Note that the asymptote is drawn as a dotted line in purple.
(-3x^2+x^4+x)+(2x^4-7+4x) simplified
Equivalent expression becomes -
(-3x² + x⁴ + x) + (2x⁴- 7 + 4x) = option: D
(x² - 2x) (2x + 3) = option: A
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It is possible to multiply, divide, add, or subtract in math. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, 10m + 5 is an expression including the terms 10m and 5 as well as m, the variable of the supplied expression, all separated by the arithmetic sign "+".
Simplification:
= (-3x² + x⁴ + x) + (2x⁴- 7 + 4x)
= - 3x² + 3x⁴ + 5x - 7
= 3x⁴- 3x² + 5x - 7
option : D
= (x² - 2x) (2x + 3)
= 2x³ + 3x² - 4x² - 6x
= 2x³ - x² - 6x
option: A
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7. use induction to prove the following equation: 1 4 9 ... n2 = n(n 1)(2n 1)/6 where n ≥ 1 (8 points).
By using the induction, the equation 1+ 4 + 9 + ...........+n² = n(n-1)(2n-1)/6 where n ≥ 1 is proved.
The term induction in math is defined as a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n.
In this case, we want to use induction to prove the equation:
=> 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1)/6 for all integers n ≥ 1.
To start the induction proof, we first prove that the statement is true for the base case n = 1.
The left side of the equation is 1, and the right side is
=> 1 * (1 + 1) * (2 * 1 + 1) / 6 = 1 * 2 * 3 / 6 = 1,
so the equation is true for n = 1.
Next, we assume that the equation is true for some integer k, where k ≥ 1. This means that:
=> 1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1)/6.
Now, we use this information to prove that the statement is true for k + 1. The left side of the equation for k + 1 is:
=> 1 + 4 + 9 + ... + k² + (k + 1)².
This is equal to k(k + 1)(2k + 1)/6 + (k + 1)² by the induction hypothesis.
The right side of the equation for k + 1 is:
=> (k + 1)(k + 2)(2k + 3) / 6.
We can simplify this to:
=> (k² + 3k + 3) * (k + 2) / 6 = (k² + 3k + 3)(k + 2) / 6.
Finally, we need to show that these two expressions are equal:
=>k(k + 1)(2k + 1)/6 + (k + 1)² = (k² + 3k + 3)(k + 2) / 6.
Expanding both sides and cancelling common terms, we find that:
=> k³ + 3k² + 2k + k² + 3k + 3 = 2k³ + 9k² + 12k + 6.
This shows that the equation is true for k + 1, and by induction, it is true for all integers n ≥ 1.
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Use the definition of Ax to write the matrix equation as a vector equation. [ 2 7 -5 -1 2 -6 4 8 ] [ 2 -3 ] = [ 17 7 -22 16]
The matrix equation written as a vector equation is .
This is the vector equation equivalent to A = [2 7 -5 -1 2 -6 4 8], x = [2 -3], and b = [17 7 -22 16].
What is matrix equation ?Simultaneous equations can be presented and solved more simply using matrix algebra, a type of mathematical notation. It can be used to generate a mathematical model of the structure and to provide a clear statement of a structural issue.
The vector equation is as follows
r = a(l – t)+ b t
where,
t is some parameter and
for points between A and B then 0≤t ≤ 1.
According to question:
The matrix equation [2 7 -5 -1 2 -6 4 8][2 -3] = [17 7 -22 16] can be written as a vector equation using the definition of the product of a matrix and a vector.
Let's call the matrix [2 7 -5 -1 2 -6 4 8] as matrix A and the vector [2 -3] as vector x. The product of matrix A and vector x is a new vector, which we'll call vector b.
The equation [2 7 -5 -1 2 -6 4 8][2 -3] = [17 7 -22 16] can be written as:
A * x = b
where,
A = [2 7 -5 -1 2 -6 4 8], x = [2 -3], and b = [17 7 -22 16].
This is the vector equation equivalent of the matrix equation, which represents the same linear relationship between the matrix, the vector, and the result vector.
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What is the T symbol in statistics?
T symbol in statistics means Test statistic for t-test ( t-score )
What is t-statistic ?
The t-statistic in statistics measures how far an estimated value of a parameter deviates from its hypothesised value in relation to its standard error.
T symbol in statistics mean Test statistic for t-test ( t-score )
Through the Student's t-test, it is utilised for testing hypotheses. To decide whether to accept or reject the null hypothesis in a t-test, the t-statistic is used.
It is quite comparable to the z-score, but when the sample size is small or the population standard deviation is unknown, the t-statistic is employed instead.
For instance, if the population standard deviation is unknown, the population mean can be estimated using the t-statistic from a sampling distribution of sample means.
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Woolworth’s had a going-out-of-business sale. The price of a telephone before the sale
was $39.98. What was the price of the telephone after a 30% discount? If the sale price of
the same telephone had been $23.99, what would the (percentage) discount have been?
A. The price of the telephone after a 30% discount will be $27.986.
B. The discount in the form of a percentage will be 41.02%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Woolworths had a going-out-of-business sale. The price of a telephone before the sale was $39.98.
A. The price of the telephone after a 30% discount will be given as,
⇒ $39.98 x (1 - 0.30)
⇒ $39.98 x 0.70
⇒ $27.986
B. If the sale price of the same telephone had been $23.99. Then the percentage is given as,
P = [(39.98 - 23.99) / 39.98] x 100
P = (15.99 / 38.98) x 100
P = 0.4102 x 100
P = 41.02%
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find the lateral surface area of the cylinder used to play for for pie and round to the nearest whole number
Answer:
lateral Surface Area(LSA)=2×22/7×4.9(4.9+11.2)
LSA=2×22/7×4.9×16.1
LSA=495.88
The nearest whole number is 496
you read 7 pages in 12 minutes how many pages can you read in 3 hours?
Answer:
105 pages
Step-by-step explanation:
We can solve this using ratios
Changing 3 hours to minutes
3 * 60 = 180 minutes
7 pages x pages
--------------- = ----------------
12 minutes 180 minutes
Using cross products
180 * 7 = 12 x
Divide each side by 12
180*7/12 = x
105 =x
105 pages
Answer:If you can read 7 pages in 12 minutes then you will be able to read 105 pages in 3 hours.
Step-by-step explanation: you multiply 12x15 to get 180 since 180 is 3 hours in minutes then you multiply 7x15= 105. So you will read 105 pages every 3 hours.
100th Answer!!!!
if you have a logical statement in five variables how many rows do you need in the truth table that you would use to evaluate it? answer with an integer.
p → (q → r) is logically equivalent to (p →q) → r
True or False
We need 32 rows in the truth table that would use to evaluate a logical statement in five variables.
It is TRUE.
Now, According to the question:
A truth table provides a method for mapping out the possible truth values in an expression and to determine their outcomes. The table includes a column for each variable in the expression and a row for each possible combination of truth values.
A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q).
The formula to calculate the number of rows is equal to 2ⁿ, where n is the number of basic statement letters involved.
Number of rows = 2ⁿ
If the number of variables in a truth table is 5, then the number of rows = 2⁵
2⁵ = 2×2× 2× 2× 2
= 32
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Bob bought a computer in California the computer cost $600 California has an 8% sale tax how much did bob pay for the computer including sale tax
Answer:
Below
Step-by-step explanation:
600 = cost
.08 * 600 = tax
Add the two together 600 + .08 (600) = 1.08 * 600 = $ 648
find the volume of the solid obtained by rotating the region bounded by the curves y2=x and x=2y about the x-axis.
The volume of the solid is 16π/3 cubic units.
What is the volume of the solid?
The volume of a solid in mathematics is the measure of the space occupied by the solid. It can be calculated using methods such as the disk method or the shell method, depending on the shape of the region being rotated.
To find the volume of the solid obtained by rotating the region bounded by the curves y^2 = x and x = 2y about the x-axis, we would use the disk method. The disk method involves slicing the solid into infinitesimally thin disks, and adding up the volumes of these disks.
First, we need to find the equations for the curves y^2 = x and x = 2y. The first curve is already in the correct form, but the second curve can be rearranged to get y = x/2. Then, we can find the bounds of integration by finding the intersection of the two curves. These bounds are x = 0 and x = 4.
Next, we can set up the integral for the volume:
V = π ∫_0^4 (x/2)^2 dx
Evaluating this integral gives:
V = π/3 (x^3/2) evaluated from 0 to 4
V = π/3 [8/2 - 0/2]
V = π/3 (8) = 16π/3 cubic units
Hence, the volume of the solid is 16π/3 cubic units.
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Zach’s car travels 21 miles on 1 gallon of gas. Write an equation to represent the relationship between the gas Zach’s car uses and the distance he travels. Then solve the equation to see how far Zach travels on a trip if he uses 16 gallons of gas
The function that represents the context is y = 21x and Zach's car can travel 336 miles using 16 gallons of gas.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Zach’s car travels 21 miles on 1 gallon of gas.
Let, x represents the number of gallons of gas and y represents the distance traveled.
Therefore, The function can be formed as,
y = 21x or f(x) = 21x.
The distance covered by Zach's car using 16 gallons of gas would be,
y = 21×16.
y = 336 miles.
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Find the ordered pair that is a member of both y = 18 + x and y = -6x 52 or indicate if it does not exist or there are infinite possibilities.
Please help me with math problem!! Will give brainliest!! :) It's due tonight!! 20 POINTS!!!
The required they could have saved 21.97 feet of cable, as per the given conditions.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
Now, perpendicular p = 30 ft base b = 50 ft hypotenuse h = x ft
According to Pythagoras' theorem h² = p² + b²
x² = 50² + 30²
x = √2500 + 900
x = √3400
x = 58.3 feets
Wire saved = [30 + 50] - 58.3
Wire saved = 21.97
Thus, the required they could have saved 21.97 feet of cable, as per the given conditions.
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tom pays R1250
every month what is his annual rent if his rent increased by 8,5% at the end of the year what will his increased monthly rent be
Tom's increased monthly rent after the 8.5% increase will be R1356.25.
How to determine the increased monthly rentFrom the question, we have the following parameters that can be used in our computation:
Monthly rent = R1250
Yearly rate = 8.5%
If Tom pays R1250 every month, then his annual rent is:
Annual rent = 1250 * 12 = R15000.
If his annual rent increased by 8.5%, his new annual rent will be
New = 15000 * (1 + 0.085) = 16275.
Divide by 12 to get the increased monthly rent
Increased monthly rent = 16275 / 12 = R1356.25.
Hence, the rent is R1356.25.
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Lisa has $580 budgeted for a trip she wants to spend five eights of it at her budget and travel expenses to the nearest cent what is she willing to spend on travel expenses?
Answer:
since it is 5/8ths of 580, multiply 5/8 by 580: 580(5/8) = 362.5 Then it says round to the nearest cent which is 0.5. So she is willing to spend $362.5 of her budget.
What is 200 meters in feet?
To convert 200 meters to feet, you can use the following conversion factor 1 meter = 3.2808 feet
What is 200 meters in feet?Meters and feet are units of length used to measure distances and lengths.
The conversion factor of 1 meter to 3.2808 feet is based on the definition of the foot as being equal to approximately 0.3048 meters.
To convert from meters to feet, simply multiply the number of meters by the conversion factor of 3.2808.
For example, 200 meters is equal to 200 x 3.2808 = 656.1664 feet.
It's important to note that this conversion factor is an approximation and may not be entirely accurate in all situations.
For more precise conversions, it's best to use a conversion calculator or a reference guide that provides exact conversion factors.
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A recipe uses 3 cups of milk to make 9 servings. If the same amount of milk is used for each serving, how many servings can be made from two pints?.
The milk will be served in cups to make it easier for them to consume, we are switching from the larger unit (i.e. quarts) to the smaller unit (i.e. cups).
What is the difference between quart and cups?4 cups or 2 pints are equivalent to one quart (qt). We can switch to utilizing gallons if we still need extra liquid. 16 cups, 8 pints, or 4 quarts make up a gallon (gal). It is a measurement of the largest liquid.
Servings per cup are divided at a rate of 9 servings to 3 cups, or 3 servings per cup. In a quart, there are 4 cups. In 2 quarts, there are 8 cups. In 4 quarts, there are 16 cups.
Servings per cup are divided at a rate of 9 servings to 3 cups, or 3 servings per cup.
1 quart = 4 cups
2 quarts = 2 × 4 quarts = 8 cups
3 servings/cup × 8 cups = 24 servings
The complete question is:
A recipe uses 3 cups of milk to make 9 servings. If the same amount of milk is used for each serving, how many servings can be made from two quarts?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of servings for?
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Please help I can’t find Jonathan’s mistake.
The shortest distance between Tim and Jan is given as follows:
19.2 miles.
(they are 19.2 miles apart).
Jonathan's mistake is that the shortest distance is not obtained passing through the home, but walking diagonally from Tim's position to Jonathan's position or vice versa.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
To obtain the shortest distance between Tim and Jan, we consider a right triangle in which:
The height is of 16 - 4 = 12.The base is of 12 + 3 = 15.Hence the distance is obtained as follows:
d² = 12² + 15²
d = square root(12² + 15²)
d = 19.2 miles.
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Pls awnser
I have to have more words to ask this question
The end behavior of the function f(x) is defined as follows:
As x -> - ∞, f(x) -> ∞. As x -> ∞, f(x) -> 0.
How to obtain the end behavior of the function?The function for this problem is defined as follows:
y = 1.5(0.8)^x.
(converting the fractions to decimals).
The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
When x -> -∞, (0.8)^(-∞) = (5/4)^∞ -> ∞, hence:
As x -> - ∞, f(x) -> ∞.
When x -> -∞, (0.8)^(∞) -> 0, as it has a base value with absolute value less than 1, hence:
As x -> ∞, f(x) -> 0.
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3x + y = -5, 6x + 2y = 10 with substitution
Answer:
no solution is the answer
Can anybody help me with s/-31=25
The solution of the expression is,
⇒ s = - 775
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The expression is,
⇒ s / - 31 = 25
Now, We can simplify as;
⇒ s / - 31 = 25
Multiply by - 31 both side,
⇒ s = - 31 × 25
⇒ s = - 775
Thus, The solution of the expression is,
⇒ s = - 775
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When u and v are nonzero vectors, Spanlu,v) contains only the line through u and the line through v and the origin. OA. False. Span(u,v) includes linear combinations of both u and v. 0 B. False. Span(u,v) will not contain the origin. ° C. True. Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v
False. Span(u,v) includes linear combinations of both u and v.
The correct option is A
Now, According to the question:
When u and v are nonzero vectors, Span {u, v} contains only the line through u and the origin, and the line through v and the origin. b. Any list of five real numbers is a vector in ℝ5 .
Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.
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Brody calculated the area of a square to be 16 36 square foot. Which shows the side length of the square? A. 2 9 ft B. 1 3 ft C. 4 9 ft D. 2 3 ft
The side length of the square be 4/6 foot.
What is meant by square?A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.
Having four sides, a square is a quadrilateral. Each side measures the same length. A square has 360 degrees of angles total. In a square, every angle is a right angle.
Let the equation be
Area of a square = length²
If the area of a square is known, find the square root of the area to get the length.
√16 / 36 = 4/6 foot
Therefore, the side length of the square be 4/6 foot.
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which type of unit cell has a coordination number of 12?
A cubic close-packed (ccp) unit cell has a coordination number of 12.
A cubic close-packed (ccp) unit cell has an arrangement of atoms where each atom is surrounded by 12 other atoms, resulting in a coordination number of 12.
A cubic close-packed (ccp) unit cell is a type of unit cell that has an arrangement of atoms where each atom is surrounded by 12 other atoms. This arrangement forms a structure with a coordination number of 12, meaning that each atom has 12 other atoms in contact with it. This type of arrangement is very common in many materials, and is often used to describe the structure of metals and other crystalline materials. The atoms in a ccp unit cell are arranged in a regular pattern, with three atoms in each of the eight corners and four atoms in the center of each face of the unit cell.
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What is the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x2 about the x-axis? Use the Shell method.
The volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2 about the x-axis is approximately 2.667 cubic units.
What is the shell method for finding the volume of the solid?
The shell method for finding the volume of a solid formed by revolving a region about an axis is a method used to find the volume of the resulting solid by adding up the volumes of an infinite number of thin cylindrical shells.
In this case, the region bounded by the graphs y = √x and y = x^2 is revolved about the x-axis. To use the shell method, we first need to determine the height and radius of each cylindrical shell. The height of each shell is equal to the difference between the upper and lower bounds of the region, which is x^2 - √x. The radius of each shell is equal to the value of y at that point, which is either √x or x^2.
The volume of each shell can then be calculated as V = 2πr * h, where r is the radius and h is the height. To find the total volume, we need to integrate the volume of each shell over the interval of x.
The definite integral for the volume is given by:
∫_{0}^{1} 2π x * (x^2 - √x) dx
Evaluating this definite integral gives a volume of approximately 2.667.
Hence, the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2 about the x-axis is approximately 2.667 cubic units.
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A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 3:5?
33 cm
20 cm
14 cm
12 cm
The answer is 12 or option (d)
I took the test~ good luck!