set up the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.y=x2/3+3,y=3,x=6
About the line y=16.

Answer:

Second option:

[tex]\mbox{\large \dfrac{a}{\sin(35^\circ)} = \dfrac{30}{\sin(60^\circ)}}[/tex]

Step-by-step explanation:

The law of sines states that the ratio of the sides of a triangle to the sine of the angle opposite the sides is the same for both sides

So we get

[tex]\dfrac{AB}{\sin 85} = \dfrac{BC}{\sin 35} = \dfrac{AC}{\sin B}}[/tex]

We are not given ∠B but we know the three angles of a triangle must add up to 180°

Therefore m∠B + 35 + 85 = 180

m∠B  + 120 = 180

m∠B = 180 - 120 = 60°

and we also have AB = c. BC = a and AC = 30

Hence

[tex]\dfrac{c}{\sin 85} = \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\\\\textrm{from which}\\\\ \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\[/tex]

The equation which will yield the value of a will be : a/sin35 = 30/sin60

Given,

Triangle.

Here,

According to sine law,

30/sinB = c / sin85 = a/ sin35

Firstly calculate angle B .

Therefore m∠B + 35 + 85 = 180

m∠B  + 120 = 180

m∠B = 180 - 120 = 60°

Here,

AB = c.

BC = a

AC = 30

Hence to calculate a ,

Use the proportion,

a/sin35 = 30/sin60

Thus equation 2 is correct .

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Answer:

D

Step-by-step explanation:

Raising a nonzero real number to the power of zero always gives you one.

Answer:

x = ± √20

or if you want an approximate solution correct to the nearest hundredth:

x = -4.47, 4.47.

Step-by-step explanation:

4x^2-80=0

This a quadratic equation and will have 2 solutions.

Add 80 to both sides of the equation:

4x^2 = 80

Divide both sides by 4:

x^2 = 20

Take the square root of both sides:

x = ± √20.

The sample mean is the average of selected observations taken from population, whereas the population mean averages of whole population Sample mean: [tex]\bar{x}[/tex] = ∑x / n

Population mean: μ =  ∑x / N

Therefore, the sample mean is average of a sample selected from population whereas population mean is average of whole population.

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The number of floors can this elevator travel directly up in 80 seconds is, 26 2/3 floors

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

We are given that the elevator travels 36 floors in 108 seconds, so the rate can be calculated as follows:

rate = 36 floors / 108 seconds

      = 1 floor / 3 seconds

To determine how many floors the elevator can travel in 80 seconds, we can use the rate and the formula: distance = rate x time:

distance = rate x time

distance = (1 floor / 3 seconds) x 80 seconds

distance = 80 / 3 floors

distance = 26 2/3 floors

So, the elevator can travel directly up 26 2/3 floors in 80 seconds.

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Answer:5kg

Step-by-step explanation:

Step 1.

Write in y=mx+c format

m= $/kg

c=flat fee

x=additional kilograms

FedEx:

y=2x+15

USPS:

y=5x

Step 2.

Keep Changing the x value (the no. of kilograms) in both equations until y is the same number

y=5×5

=25

y=2×5+15

=25

∴It would cost the same for both options at 5kg

The product of (x - 3)² is a perfect square trinomial.

What is a perfect square?

An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax² + bx + c. Real numbers a, b, and c are present here, and a ≠ 0.

By multiplying a binomial by another binomial, perfect square trinomials—algebraic expressions with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of just two terms, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions. When a binomial made up of a constant and a variable is multiplied by itself, a perfect square trinomial with three terms is produced. A positive or a negative sign separates each term in a perfect square trinomial.

Given expression is

(x - 3)²

Apply the formula (a - b)² = a² - 2ab - b²:

= x² - 2×x×3 + 3²

= x² - 6x + 9

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Answer:9

Step-by-step explanation:

3/8=x/24

3/8=x/3*8

[tex]\frac{3}{8} =\frac{\frac{x}{3} }{8}[/tex]

3=x/3

x=9

Answer:

First, we evaluate the amount that the portion has been multiplied by. We want to determine how many number 8's fit in to the number 24 because the bottom of the portion is 24.

The solution would be 3, because eight multiplied by 3 equals 24. Also because the bottom of the fraction has been multiplied by three, the top, known as the numerator, also needs to be multiplied by three. As a result, the top becomes 3 multiplied by 3, which equals 9. As a result, the portion is 9/24.

Step-by-step explanation:

3/8=?/24

3/8*3/3=9/24

9/24

____     =/8

3/3

The correct statement regarding the quadratic function is given as follows:

C. The ball hit the ground after 3.5s.

For this problem, the intervals are given as follows:

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It is an observation that significantly differs from the other observations in a dataset is referred to as an outlier in statistics.

An observation that significantly differs from the other observations in a dataset is referred to as an outlier in statistics. A true abnormality in the data may be the cause of an outlier, but they can also happen by chance as a result of random variation in the data, or they might be a sign of a measurement or data entry error.By modifying the dataset's mean, variance, or correlation, outliers can alter the outcomes of statistical studies. In order to properly handle outliers, it is crucial to recognise them.

There are several techniques to identify outliers in a dataset, including graphical techniques like scatter plots or box plots, as well as numerical techniques like computing z-scores or utilising the interquartile range (IQR). Consider any observation more than once is a general rule of thumb.

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Answer: 28282

Step-by-step explanation:

I think

Answer:

below

Step-by-step explanation:

He needs 6 times as many as 1/6 th  to have a complete report

  6 * 2 5/6 =   6  * 17/6 = 102/6 = 17 pages total

Answer:

$2.90---1 day

$29.85----x days

x=29.85×1/2.90

x=10.29 days

Answer:

-5/8

Step-by-step explanation:

-7/8 = -0.875

-5/8 = -0.625

The closer the negative number is to 0, the bigger that number.

-0.625 is closer to 0 than -0.875

So, -5/8 is bigger.

Answer: E

Step-by-step explanation: This is from my mathematical knowledge however there is an asymptote at y=1. All values for y must be higher than one for it to be viable. So E is the only one that works.

If equation y = x/x-1 and x > 1,  then 1.9 is the possible value of y.Option E is correct.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given equation is y=x/x-1

Where value of x should be greater than one.

x>1

We have to find the possible value of y from the given options.

We have to check the options by considering the value is greater than one or not.

-1.9 is less than one so it is not possible value of y.

-0.9  is less than one so it is not possible value of y.

0.0  is less than one so it is not possible value of y.

0.9  is less than one so it is not possible value of y.

1.9 is greater than one so it is possible value of y.

Hence, if equation y = x/x-1 and x > 1,  then 1.9 is the possible value of y.

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Absolute error and relative error are two measures of the difference between an estimated or calculated value and the true or exact value of a quantity.

The main difference between absolute and relative error is that absolute error gives the magnitude of the difference between the estimated value and the true value, while relative error gives a measure of this difference relative to the size of the true value.

Absolute error is the magnitude of the difference between the estimated or calculated value and the true value.

It is calculated as the absolute value of the difference between the estimated value and the true value. Absolute error is expressed in the same units as the quantity being measured.

Relative error, on the other hand, is the absolute error expressed as a fraction or percentage of the true value. It is calculated as the absolute error divided by the true value, and is usually expressed as a percentage.

Relative error is a useful measure when the scale of the quantity being measured varies over a wide range, or when comparing the accuracy of measurements of different quantities.

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its a x, x, x√2 special triangle

so x and y are 19 <--- answer

2 angles are 90 & 45 so the third angle must be 45

that means x and y are equal

Answer:

4/3

Step-by-step explanation:

This is the worse piecewise function I have ever seen in my life.

4/3. Just plug in an infinitely close number to -1 in a calculator and you get 1.3

Answer:Iterative

Step-by-step explanation:

Answer:

-70

Step-by-step explanation:

-2, -6, -10, -14, ...

-6 - (-2) = -4

The common difference in -4.

The nth term of an arithmetic sequence with common difference d is

a_n = a_1 + d(n - 1)

For n = 18,

a_18 = -2 + (-4)(18 - 1)

a_18 = -2 + (-4)(17)

a_18 = -2 - 68

a_18 = -70

Answer: -70

Step-by-step explanation:

{[tex]a_{n}[/tex]=[tex]a_{1}[/tex]+(n-1)d}

a_{1}= -2

d= -4

[tex]a_{18} =-2+(18-1)*(-4)=-2-68 = -70[/tex]

Answer:

2(x + y)

Step-by-step explanation:

2x + 2y ← factor out the common factor of 2 from both terms

= 2(x + y)

Answer:

Step-by-step explanation:

Here's how you can find the length of the longer diagonal of a rhombus with sides of length 8 m and a shorter diagonal of length 10 m:

Step 1: Draw a diagram of the rhombus with the shorter diagonal labeled as 10 m.

Step 2: Draw a perpendicular bisector from one corner of the rhombus to the opposite corner, dividing the rhombus into two congruent right triangles.

Step 3: Label the longer diagonal as "d".

Step 4: Since the two congruent right triangles have sides that are half the length of the sides of the rhombus, the hypotenuse of each triangle must have length 4 m.

Step 5: Using the Pythagorean theorem, we can find the length of the other side of each triangle:

a^2 + b^2 = c^2

4^2 + b^2 = 10^2

16 + b^2 = 100

b^2 = 84

b = √84 = 2√21

Step 6: Now that we know the length of one side of each triangle, we can use it to find the length of the longer diagonal:

d^2 = 4^2 + (2√21)^2

d^2 = 16 + 168

d^2 = 184

d = √184 = 2√23

So, the length of the longer diagonal of the rhombus is 2√23 m.

The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' and 'y' be the number of students at Jefferson School and non-Jefferson school, respectively. Then the equations are given as,

x + y = 500                    ...1

5x + 10y = 3135             ...2

From equations 1 and 2, then we have

5(500 - y) + 10y = 3135

2500 - 5y + 10y = 3135

5y = 635

y = 127

Then the value of 'x' is given as,

x + 127 = 500

x = 373

The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively

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The simplest form of the fraction 7/2 is 7/2.

3.5 is the decimal number form of 7/2.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

Given:

A fraction number is 7/2.

And 2 and 7 are the prime numbers.

The factors of 7 are 7 and  1.

The factors of 2 are 2 and 1.

There is no other than 1 common factor between 7 and 2.

So, the simplest form of the fraction 7/2 is 7/2.

Now, fraction as a decimal,

= 7/2

= 3.5

Therefore, 3.5 is the required decimal number.

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The complete question;

Write 7/2 as a fraction in simplest form and as a decimal.

when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

[tex]\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}[/tex]

Hope this helps : -)

- Jeron

The surface area of the right rectangular pyramid is 96 sq. ft.

A net pattern is produced when the surface of a three-dimensional figure or solid is spread out flat and each aspect of the shape is visible. The net may then be used to calculate the solid's surface area.

The surface area of the net is calculated by adding the areas of all of its faces. The net's surface area is calculated by summing the surface areas of all its forms.

The surface area of the given net is calculated by adding the area of all the individual shapes in the net.

For the given net the area of the triangle with h= 5 ft and b = 8 ft is:

A1 = 1/2(8)(5)

A1 = 20 sq. ft.

There are two such triangles thus:

A1 = 2(20) = 40 sq. ft

For the triangle with h = 6 ft and b = 4 ft:

A2 = 1/2)(4)(6)

A2 = 12

There are two such triangles thus:

A2 = 2(12) = 24 sq. ft

The area of the rectangle in the center is:

A3 = (8)(4)

A3 = 32 sq. ft

The total surface area of the net is:

A = A1 + A2 + A3

A = 40 + 24 + 32

A = 96 sq. ft.

Hence, the surface area of the right rectangular pyramid is 96 sq. ft.

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If Adrian has 75 baseball cards. He wants the same number of cards in each pile. He can have 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.

Adrian wants to divide his 75 baseball cards into piles such that each pile has the same number of cards. This means the number of cards in each pile must be a factor of 75. To find all the possible numbers of cards in each pile, we can find all the factors of 75.

The factors of 75 are:

1, 3, 5, 15, 25, and 75.

So, Adrian can have the same number of cards in each pile as:

1, 3, 5, 15, 25, or 75.

Therefore, Adrian can have his 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.

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Answer:

30 degrees.

Angles must add up to 180 so,

180 - 150 = 30.

Step-by-step explanation:

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System of equations can be used to find each digit is option A.

An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

Let's represent the hundreds, tens, and units digits as h, t, and u, respectively. Then we can use the given information to set up a system of equations:

A three-digit number has a digit sum of 13:

h + t + u = 13

One more than the hundreds digit (h) is the tens digit (t):

t = h + 1

The digit in the units, u, is 3 greater than the total of the digits in the tens and hundreds:

u = t + h + 3

Therefore, the correct system of equations is:

h + t + u = 13

t = h + 1

u = t + h + 3

Therefore, the answer is (A).

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Answer:

y= -3x+4

Step-by-step explanation:

You need to simplify down to y=mx+b by dividing -2 from both sides:

-2/-2= cancels out making y

6/-2= -3

-8/-2= 4

New equation:

y= -3x+4

Hope this helped!