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The value in the part (c) is 1/(b-a) if the graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L, the volume obtained depends on L.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L.

For part(c)

[tex]\rm V(L) = \int\limits^b_a {\pi(f(x) -L)^2} \, dx\\\\\rm V(L) = \int\limits^b_a {\pi((f(x))^2 -2f(x)+L^2)} \, dx\\\\\rm V(L) = \pi \int\limits^b_a {(f(x))^2} \, dx-2\pi L \int\limits^b_a {f(x)} \, dx +L^2\pi\int\limits^b_a {} \, dx[/tex]

Now finding V'(L)

[tex]\rm V'(L) = -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L \int\limits^b_a {} \, dx[/tex]

[tex]\rm V'(L) = -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L (b-a)[/tex]

Now equation V'(L) to zero; V'(L) = 0

[tex]\rm -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L (b-a)=0[/tex]

[tex]\rm \int\limits^b_a {f(x)} \, dx= L (b-a)[/tex]

[tex]\rm L = \frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex]

The above expression is representing the critical point.

Now finding V''(L)

V''(L) = 2π(b-a) >0 at L

[tex]\rm L = \frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex]   (minimizines the volume)

Thus, the value in the part (c) is 1/(b-a) if the graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L, the volume obtained depends on L.

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Answer:

c)20 1/4

Step-by-step explanation:

[tex]9x^{2}y^{-2}[/tex]

If We replace x by -3 and y by 2 we get  :

[tex]9\left( -3\right)^{2} \left( 2\right)^{-2}[/tex]

Or we have :

[tex]\left( -3\right)^{2} =9\ \text{and} \ \left( 2\right)^{-2} =\frac{1}{2^{2}} =\frac{1}{4}[/tex]

then

[tex]9\left( -3\right)^{2} \left( 2\right)^{-2}=9\times9\times\frac{1}{4} = \frac{81}{4}[/tex]

on the other hand :

[tex]\frac{81}{4} =\frac{80+1}{4} =\frac{80}{4} +\frac{1}{4} =20+\frac{1}{4}=20\frac{1}{4}[/tex]

Answer:

x = -3/2

Step-by-step explanation:

note: 1/125 can be written as 5 exponent -3 thus, 5^-3

Expressing it in this form, we can rewrite the above equation as

5^2x = 5^-3

As part of the laws of indices and logarithms, when the bases are the same and they are equating, You equate only the exponents

therefore, we have;

2x = -3

divide through by 2

x = -3/2

Answer:

1 trapezoid

2 triangle

3 rectangle

Answer:

-6x-10

Step-by-step explanation:

you multiply 3x by -2

and 5 by -2

never forget the negative

Answer:

2/3

Step-by-step explanation:

They rolled an even number 40/60 times which simplifies to 2/3

Answer:

C

Step-by-step explanation:

Table

Dice Roll             Number of times

1                               4

2                              11

3                               6

4                              17

5                              10

6                              12

Total                        60

Total of the even numbers

11

17

12

40  

P(even) = even / total

P(even)  = 40/60

AnswerP(even) = 2/3

Answer:

14.9 %

Step-by-step explanation:

2  = double

2 = ( 1+ i)^5       i  = interest in decimal   5 = years

i = .149   = 14.9 %  

The line of best fit is an illustration of a linear regression

Using the assumed parameters, the value of x when x = 24 is 30.75

The equation of the line of best fit is not given, and the parameters to calculate the line of best fit are missing.

So, I will assume the following parameter values.

Assume that the line of best fit passes through the points

(x,y) = (1,2) and (5,7)

The slope of the line would be:

m = (7 - 2)/(5- 1)

m = 1.25

The equation is then calculated as:

y =m(x - x1) + y1

This gives

y = 1.25(x - 1) + 2

Expand

y = 1.25x - 1.25 + 2

Evaluate

y = 1.25x + 0.75

When x = 24, we have:

y = 1.25 * 24 + 0.75

Evaluate

y = 30.75

Using the assumed values, the value of x when x = 24 is 30.75

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Answer:

346in

Step-by-step explanation:

[tex]\hookrightarrow Here,\\\\\hookrightarrow a=56 in, b = 22 in, c = 73 in, and d = 25 in\\\\Now,\\\\\hookrightarrow Perimeter=Sum\:of\:all\:sides\\\\\hookrightarrow Perimeter=a+b+b+d+(c-2d)+b+d+b+a+c\\\\\hookrightarrow Perimeter=56+25+22+22+(73-25-25)+22+25+22+56+73\\\\\hookrightarrow Perimeter=346in[/tex]

Answer:

x = 4  or x = -3

-1

Step-by-step explanation:

26.

x² = x + 12

x² - x - 12 = 0

(x - 4)(x + 3) = 0

x - 4 = 0  or  x + 3 = 0

x = 4  or x = -3

27.

(-6 + 4)/2 = -2/2 = -1

Answer:

  6076π ≈ 19088.3 cubic units

Step-by-step explanation:

The volume of a cylinder is found using the formula ...

  V = πr²h

__

For the given dimensions, the volume is ...

  V = π(14²)(31) = 6076π ≈ 19088.3 . . . cubic units

Answer:

y= .45x + 11/3

Step-by-step explanation:

Those points are not on the same line but you can get pretty close with

y= .45x + 11/3

We need theta first (angle

[tex]\\ \rm\rightarrowtail sin\theta=\dfrac{P}{H}[/tex]

[tex]\\ \rm\rightarrowtail sin\theta=\dfrac{11.8}{12}[/tex]

[tex]\\ \rm\rightarrowtail sin\theta=0.9834[/tex]

[tex]\\ \rm\rightarrowtail \theta=sin^{-1}(0.9834)[/tex]

[tex]\\ \rm\rightarrowtail \theta=79.54°[/tex]

On rounding it will go till 80°

Answer:

C. lifestyle

Step-by-step explanation:

Hope this helps!

circumference= 3.14m

the radius of the circle

Circumference of a circle = 2πr

Given, circumference = 3.14 meters

Therefore:

2πr = Circumference of a circle

2πr = 3.14

2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14]

6.28r = 3.14

r = 3.14/6.28

r = 0.5

[tex]( 7 . 3^{6} ) ^{4}[/tex]Answer:

= [tex](7^{-3--2}[/tex] x [tex]3^{-8--2} ) ^{-4}[/tex]

= [tex](7^{-1}[/tex] x [tex]3^{-6}) ^{-4}[/tex]

= [tex]( 7^{1}[/tex] x [tex]3^{6}) ^{4}[/tex]

= [tex]7^{4}[/tex] x [tex]3^{24}[/tex]

OR

= [tex](\frac{3^{-8} }{7 . 3^{-2} }) ^{-4}[/tex]

= [tex](\frac{1}{7 . 3^{6} } ) ^{-4}[/tex]

= [tex]( 7 . 3^{6} ) ^{4}[/tex]

= [tex]7^{4}[/tex] x [tex]3^{24}[/tex]

Step-by-step explanation:

y = 2

To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.

[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Substitute the coordinates of the given points:

[tex]\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10 }[/tex]

Simplify the equation to determine the slope:

[tex]\implies \text{Slope} = \dfrac{0}{-3 - 10 }[/tex]

∴ 0 divided by ANY number is ALWAYS 0.

[tex]\implies \text{Slope} =0[/tex]

Point slope form formula: y - y₁ = m(x - x₁)

Substitute the values in the point slope form:

[tex]\implies \text{Equation of line:} \ y - y_{1} = m(x - x_{1} )[/tex]

[tex]\implies \text{Equation of line:} \ y - 2 = 0(x - 10)[/tex]

Simplify the equation to determine the equation of the line:

∴ Any number multiplied by 0 is 0.

[tex]\implies \text{Equation of line:} \ y - 2 = 0[/tex]

[tex]\implies \text{Equation of line:} \ y = 0 + 2[/tex]

[tex]\implies \text{Equation of line:} \ y = 2[/tex]

Thus, the equation of the line is y = 2.

Answer:

Each pencil costs 50 cents

Step-by-step explanation:

Step 1:  Determine the price per unit

(Price of Items) / (Amount of items)

($3) / (6)

$0.5

Answer:  Each pencil costs 50 cents

The house will cost approximately $246,359.85 seven years from now.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

In this problem,

P = $140,000

r = 0.07

n = 1 (compounded annually)

t = 7.

Plugging in these values.

A = $140,000 (1 + 0.07/1)^(1 x 7)

A = $140,000 (1.07)^7

A = $246,359.85

Therefore,

The house will cost approximately $246,359.85 seven years from now.

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Step-by-step explanation:

p(p-q) - q(q-p)

p²-pq - q² +pq

p² - q²

Choice 1

Answer:

D

Step-by-step explanation:

to find the value in grams, we just multiply by a 1000

so, 31.8 × 1000 = 31,800 grams

Answer:

it's 460 I think, because the last number is a five so if it's over a five you round up

Answer:

Option B, [tex]49m^2 - 81n^4[/tex]

Step-by-step explanation:

Step 1:  Determine the difference of two squares

According to online, "In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra."  a^2 - b^2 gives us (a + b)(a - b)

The only one that would work is Option B so lets factor it out.

[tex]49m^2 - 81n^4[/tex]

[tex](7m + 9n^2)(7m - 9n^2)[/tex]

Answer:  Option B, [tex]49m^2 - 81n^4[/tex]

Answer:

The anwer is B 1200 in

Step-by-step explanation:

And in numerical form, 20

Answer:

20

Step-by-step explanation:

first yo get the number 19 then after that you can add 1 and your answer is 20 and aafter 20 (just incase you want to know) is 21

Answer:

3. -1/3  ± 2i√5 / 3

Step-by-step explanation:

3x^2 + 2x = -7

Divide through by 3:

x^2 + 2/3 x = -7/3

Completing the square:

x^2 + 2/3 x + (1/3)^2 = -7/3 + (1/3)^2

(x + 1/3)^2 = -7/3 + 1/9

(x + 1/3)^2 = -20/9

x + 1/3 =  ±√(-20) / 3

x + 1/3 = ± 2√-5/3

x  = -1/3  ± 2i√5 / 3

Answer:

  see attached

Step-by-step explanation:

The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.

__

This sum is shown in the attachment.

Answer:

Step-by-step explanation:

f(-6) is the corresponding number of -6 and you can spot it on the y-axis