Why are 1997 pennies worth almost twenty dollars

Answer:

200 vs 230

$30

Step-by-step explanation:

Answer:

hundredths

Step-by-step explanation:

Numbers after the decimal start with

tenth

hundredth

Answer:

b.

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

(c)

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

Step-by-step explanation:

b. The volume of solid formed is given by the washers formula as follows;

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

Therefore, we have, the integral expression whose solution is the volume formed by rotating 'R', about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is given as follows;

[tex]V = \pi \cdot \int\limits^\pi_0 {\left([2 + cox(x)]^2 - [csc(x)]^2} \right) \, dx[/tex]

(c)  We have;

x = arcos(y - 2), x = arcsin(1/y)

At x = 0, y = 2 + cos(0) = 3

csc(0) = ∞

At x = π, y = 2 + cos(π) = 2 + -1 = 1

csc(π) = ∞

Therefore, we get;

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

B) An equation that involves integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis is;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) An equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x= -1 is;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

B) The volume of solid formed is gotten from applying the washers formula;

[tex]V = \pi \int\limits^a_b ({[f(x)]^{2} - [g(x)]^{2}}) \, dx[/tex]

This means that the integral expression whose solution is the volume formed by rotating R about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is expressed as;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) From answer above, we have;

x = cos⁻¹(y - 2), x = sin⁻¹(1/y)

Now,

At x = 0; y = 2 + cos(0) = 3

csc(0) = 1/0 = ∞

Also,

At x = π; y = 2 + cos(π)

y = 2 + (-1)

y = 1

Also, csc(π) = ∞

Thus, we have;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

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Answer:

x=50, y=20

Step-by-step explanation:

50-20=30, 50+20=70

Answer:

x=1

Step-by-step explanation:

7x-1+2x-1=7

7x+2x-1-1=7

9x-2=7

9x=7+2

9x=9

9x/9=9/9

x=1

Answer:

98 m³

Step-by-step explanation:

For similar shapes

The ratio of the cube of the corresponding length of similar shapes is equal to the ratio of their volume.

Applying,

L³/L'³ = V/V'............... Equation 1

Where, L = Length of the smaller prism, L' = Length of the larger prism, V = Volume of the smaller prism, V' = Volume of the larger prism

From the question,

Given: L = 5 m, L' = 7 m, V = 50 m³

Substitute these values into equation 1

5²/7² = 50/V'

25/49 = 50/V'

V' = (50×49)/25

V' = 98 m³

Answer: 137.2

Step-by-step explanation:

I'm just making the correct answer an actual answer instead of a comment so it's easier to see

The Above triangles are similar, Therefore the corresponding sides would be proportional.

that is : -

[tex]\mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]

Answer:

Part A;

$79

Part B;

The amount Stella would have saved in 'w' weeks = 15 + 8·w

Step-by-step explanation:

Part A

The amount of money Stella already has = $15

The amount she can save per week = $8

The total amount of money, 'A', Stella would have after 8 weeks is given as follows;

A = The amount Stella already has + The amount she can save per week × The number of weeks of savings

Therefore;

A = 15 + 8 × 8 = 79

The amount Stella would have after 8 weeks, A = $79

Part B

The expression that represents the amount of money Stella would have saved in w weeks is given as follows;

A = The initial amount Stella has + The amount she can save per week × w (number of weeks)

∴ A = 15 + 8·w.

Answer:  To find the average rate of change, evaluate the function at the given points.

Evaluate the difference of the function at the given points.

Divide the difference of the function at the given points with the difference of the given points.

Step-by-step explanation:

The Average of rate is -1.

Everytime it goes up by one the y goes down by 1 so it would be -1.

The average rate of change of the function in the table given is: -1.

Average rate of change of a function = change in y / change in x = rise/run.

Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):

Average rate of change of the function = (7 - 5)/(-2 - 0)

Average rate of change of the function = 2/-2

Average rate of change of the function = -1.

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Answer:

option alphabet c is the answer

Answer:

$5.50

Step-by-step explanation:

5+6= 11

11/2

Answer:

33 blooms

Step-by-step explanation:

This can be set up by an equation. x represents the number of days and y represents the number of corresponding blooms. y = 3x + 12 is the equation, as 3 is the rate of change and 12 is the initial amount. One week is 7 days, so 7 can be plugged in for x. 21 + 12 = 33, so after one week, Debbie has 33 blooms.

6,000 + 700 + 30 + 8 is the expanded from.

Answer:

See Below.

Step-by-step explanation:

We want to prove that the expression:

[tex](125^2+25^2)(5^2-1)[/tex]

Is divisible by three.

We can simplify the second factor:

[tex]=(125^2+25^2)(25-1)\\\\ = (125^2+25^2)(24) \\\\ = (125^2+25^2)(8\cdot 3)[/tex]

Since the second factor is being multiplied by three, we can conclude that the entire expression is divisible by three.

Answer:

It is divisible by 3.

Step-by-step explanation:

(125² + 25²)(5² - 1) ÷ 3

(15625 + 625)(25 - 1) ÷ 3

(16250)(24) ÷ 3

390000 ÷ 3

130000

Step-by-step explanation:

the lines on the graph of inequality second option

Answer:yes, base = 9. No, the exponent is not variable. yes, base =9/10.

Step-by-step explanation:

Answer:

The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Step-by-step explanation:

First, we obtain the first and second derivatives of the function by chain rule and derivative for a power function, that is:

First derivative

[tex]f'(x) = -4\cdot (-x+2)^{3}[/tex]

Second derivative

[tex]f''(x) = 12\cdot (-x + 2)^{2}[/tex]

Then, we proceed to do the First and Second Derivative Tests:

First Derivative Test

[tex]-4\cdot (-x+2)^{3} = 0[/tex]

[tex]-x + 2 = 0[/tex]

[tex]x = 2[/tex]

Second Derivative Test

[tex]f''(2) = 12\cdot (-2+2)^{2}[/tex]

[tex]f''(2) = 0[/tex]

The Second Derivative Test is unable to determine the nature of the critical values.

Then, we plot the function with the help of a graphing tool. The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Answer:

9x^2 + 27x + 18

Step-by-step explanation:

(9x + 9)(x + 2)

=9x(x + 2) +9(x + 2)

=9x^2 + 18x + 9x + 18

=9x^2 + 27x + 18

Answer:

A. i think

Step-by-step explanation:

Answer:

4, -16, 64, -256

the common ratio is -4

Step-by-step explanation:

Answer:

84pi

Step-by-step explanation:

Sector Area = (pi x r^2 x *angle*)/ 360

(pi x 12^2 x 210)/ 360

= 84pi

= 263.893

Answer:

6/5

Step-by-step explanation:

2x+3=ky

ky=2x+3

y=(2x+3)/k

y=2x/k + 3/k - > equation 1

y=mx + c - >equation 2

Comparing equation 1 and 2,

2/k=m

2/k=5/3

6/5=k

k=6/5

Option C with h and k

see screenshot for an example

general formula is

r² = (x - x-center)² + (y - y-center)²

The equation of the red graph is g(x) = 6 - [tex]x^4[/tex].

Thus, option (B) is correct.

Given:

Function 1 : f(x) = 3 - [tex]x^4[/tex]

As, the y-intercept is the point where a line or curve intersects the y-axis.

It is the value of y when the corresponding x-coordinate is zero. It is the point(s) where the graph crosses the y-axis.

Now, from the graph of function f(x) has the intercept 6.

Also, the graph of function g(x) is 3 unit up from the function f(x).

So, the equation of g(x) will be

= f(x)  + 3

= 3 - [tex]x^4[/tex] + 6

= 6 - [tex]x^4[/tex]

Thus, option (B) is correct.

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Answer:

∠a=∠b

Step-by-step explanation:

Alternate exterior angles are congruent

Answer:

-2x-11=0

1) Add 11 to both sides

Dividde both sides by - 2

X= _11/2

Drcimal form: - 5.5

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]

7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]

[tex] \huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]

[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]

[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]

[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{\:13}}}}[/tex]

8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]

[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{-14}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

Answer:

The beam should be placed 8 feet from the center.

Step-by-step explanation:

According to the Question,

The struts are y = √(x + 8) and y = √(x − 4).  The struts are 2 feet apart at the location of the beam:

thus, √(x + 8) − √(x − 4) = 2  

on Solving we get,

√(x + 8) = 2 + √(x − 4)

x + 8 = 4 + 4√(x − 4) + x − 4

8 = 4√(x − 4)

2 = √(x − 4)

x − 4 = 4

x = 8

Step-by-step explanation:

The area of a circle = pi r^2

d = 2r Divide by 2 to get the radius

r = d/2

The diameter = 2.8 cm

r = d/2

r = 2.8/2

r = 1.4

The area of the circle = pi * r^1

The area of the circle = 3.14 * 1.4^2

The area of the circle = 6.1544

But you are working with a semic circle

The area of a semicircle is 1/2 that of a circle

Area of semicircle = 1/2 6.1544 = 3.0772 =3.08 when rounded

Answer:

Step-by-step explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

           [tex]= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}[/tex]

Answer:

90 or -270

Step-by-step explanation: