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Tasha has a collection of trading cards. the collection contains 70 cards. she gives 25 of her cards to her friend brad. she gives 10% of her cards to her nephew, she sells 25 cards online. how many cards remain in Tasha's trading card collection

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])

[tex]f(x) = g(x)[/tex] (1)

[tex]4\cdot x - 2 = x^{2}+1[/tex]

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

[tex](x-1)\cdot (x-3) = 0[/tex]

The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:

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

If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:

[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]

[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]

[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]

[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]

[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]

[tex]V = \frac{16\pi}{3}[/tex]

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

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Answer:

  18

Step-by-step explanation:

Maybe you want to fill in the blank so this is true for all x:

  4(4x -14) -14x + ___ = -2(-x +19)

Simplifying, we get ...

  16x -14x -56 + ___ = 2x -38

Adding 56-2x to both sides leaves ...

  ___ = 18

The missing number is 18.

Answer:

A volcano ejected with an initial velocity of 304 feet per second.

The height in feet is given by the equation H=-16t^2+ 304t where t is the time in seconds.

We will use the equation that traces the path of the projectile to determine the following information:

1) The time it takes the projectile to reach its maximum height (using the vertex formula: t=-b/2a)

The equation; H = -16t^2 + 304t, a=-16; b=304

t = -304/2°(-16)

t = 9.5 sec to reach max height

2) The maximum height of the projectile (use the result from part 1 to find the maximum height of the projectile)

t = 9.5

H = -16(9.5^2) + 304(9.5)

h = = -1444 + 2888

h = 1444 ft is the max height

3) Find the time it takes the projectile to return to the ground. Assume that the projectile starts at height H=0.

-16t^2 + 304t = 0

factor out -16t

-16t(t - 19) = 0

t = 19 sec to reach the ground

Step-by-step explanation:

Step-by-step explanation:

standard deviation of $3

Find a 98% confidence interval about the mean (one decimal place).

Is a value of X=48 unusually high or is it normal? Choose correct explanation

Answer:

3/4

Step-by-step explanation:

3/4+x=2x−x+_

2x-x is x

So the equation is now

3/4+x=x+_

So to have infinite solutions, we will have to get both of the sides the same value

Since there is already an x on both sides we don't have to worry about it

Now there isn't a 3/4 on one side so we can just add that to the blank side, thus creating an infinite solution equation

Hope this helps!

Answer:

Makes the lungs able to fill more

Answer:

575

Step-by-step explanation:

23/4 = 5.75 times 100

Answer:

575

Step-by-step explanation:

23×25=575 so 575 would be your answer

Answer:

LETS

GO

BRANDON

Step-by-step explanation:

Answer:

10^3

Step-by-step explanation:

Answer:

10³

Step-by-step explanation:

10 × 10 × 10 = 10³

The expression can be used to determine how much more money Club A will cost than Club B after x months is 7 - 4x

A linear equation is in the form:

y = mx + b;

where y, x are variables,  m is the rate of change and b is the initial value of y.

Let y represent the total cost for x months.

Club A charges a $35 joining fee, plus $19 per month. hence:

y = 19x + 35

Club B charges a $28 joining fee, plus $23 per month. hence:

y = 23x + 28

Club A will cost than Club B:

19x + 35 - (23x + 28)

= 7 - 4x

The expression can be used to determine how much more money Club A will cost than Club B after x months is 7 - 4x

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Answer:

29

hope this helps

Hello there! :-)

The formula for finding the area of a circle is

Notice that only the radius is squared.

We are given the radius of the circle: 21 cm.

We plug the value of r into the formula:

Hope this helps. Use the comment section to clarify your doubts.

Answered by

~A teen whose hobby is helping people with their homework

#LetItSnow

Good luck.

Answer:

A=1.386 cm²

Step-by-step explanation:

[tex]\sf\bf A = \pi \times r \times r[/tex]

[tex]\sf\bf = \frac{22}{7} \times 21 \times 21[/tex]

[tex]\sf\bf = \frac{22}{\cancel{7}} \times \cancel{21} \times 21[/tex]

[tex]\sf\bf = 22 \times 3 \times 21[/tex]

[tex]\sf\bf = 66 \times 21[/tex]

[tex]\sf\bf = 1.386 \: {cm}^{2}[/tex]

Answer:

HOPE THAT HELPS BUT I DO NOT HAVE ANSWER

Step-by-step explanation:

3×2k=????

3×5=??

6×k=??

6×4=??

then put all those together in a 2 step equation and then add 9 to the answer

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

Answer:

x + 2tan X . sec X / X

Step-by-step explanation:

The derivatives of trigonometric functions is as follows

* d/dx (sin x) = cos x

* d/dx (cos x) = - sin X

* d/dx (tan x) = sec ^2 X

* d/dx (Cot x) = -cosec^2 X

* d/dx (sec x) = tan x . sec x

* d/dx (cosec x) = -cot x . cosec x

and so the derivative of sec is tanx . sec x

d/dx x - sec x

the derivative of variables is considered 1.

since we remove 1 from their exponent they'll have 0 as their exponent which can only mean the end value is 1.

so d/dx of X is = 1

d/dx od -sec X is = -tan X . Sec X based on the general derivative properties above.

in conclusion the final answer is = x + 2tan X . sec X / X

The table is an illustration of a proportional relationship. and can be modeled by the function rule y = 12x

The entries of the table is given as:

Hours    Earnings

4               48

6               72

10              120

20             240

Start by calculating the rate (m) of the function

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{72 - 48}{6-4}[/tex]

[tex]m = \frac{24}{2}[/tex]

[tex]m = 12[/tex]

The equation of the table is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = 12(x - 4) + 48[/tex]

[tex]y = 12x - 48 + 48[/tex]

[tex]y = 12x[/tex]

[tex]y = 12x[/tex] means that, the following statements are true:

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Answer:

I think option a k.9

is correct

Check the picture below.

Answer:

aas

Step-by-step explanation:

angle angle and the middle is side

tan (u) = a/b = cot (90° – u)

Let u = 20°

Take it from here.

The equivalent value of the expression is tan20 is a cot(70).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The area of mathematics is concerned with how triangles' sides and angles relate to one another as well as with the pertinent uses of any angle.

Given that the trigonometric expression is tan30. The equivalent expression will be written as,

tan (u) = a/b = cot (90° – u)

tan (20) = cot ( 90 - 20 )

tan 20 = cot 70

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Answer:

C.) 42 cm

Step-by-step explanation:

When you enlarge the rectangle by a scale of 3, you are multiplying its perimeter by 3

2*2+5*2=4+10=14

14*3=42

Answer:

[tex]I(-1,0) \to I \ ' \ (-0.25,0)\\\\J(-1,1) \to J \ ' \ (-0.25,0.25)\\\\K(2,2) \to K \ ' \ (0.5, 0.5)\\\\L(2,-1) \to L \ ' \ (0.5,-0.25)\\\\[/tex]

======================================================

Explanation:

The fraction 1/4 is equivalent to the decimal form 0.25

We multiply 0.25 with each coordinate, of each point.

For example, let's focus on point L which is at (2,-1)

Point L(2,-1) moves to L ' (0.5, -0.25) which will move it closer to the origin, which shrinks the image. Use this idea for the remaining points.

Note: this trick only works if the center of dilation is the origin.

Answer:

Step-by-step explanation:

Answer:

p=5/2   q=3/4

Step-by-step explanation:

-4p+7q=-19/4

-12p+35q=-15/4

get rid of the value p

(-3)(-4p+7q=-19/4)

-12p+35q=-15/4  =

12p-21q=57/4

-12p+35q=-15/4  =

14q=21/2

q=  21/2  /14

q=3/4

substitute q=3/4 into an equation 1 to find p

-4p+7q=-19/4

-4p+7(3/4)=-19/4

-4p+21/4=-19/4

-4p=-19/4-21/4

-4p=-10

p=-10/-4

p=5/2

Answer:

f(-3)= 1

f(1)= -1

If f(x)= -2 then x = 3

If f(x) = 2 then x = -5

Step-by-step explanation:

f(x) can be replaced with any number. It just means y. For example, let's replace the (x,y) with the (-5,2). For this point, this is f(-5) = 2. When they ask for f(x), they are just asking what y is with a given coordinate x. So when they ask what f(-3) is, they are asking what y is with -3 being the x coordinate.

So, f(-3) = 1

f(1) = -1

For these questions:

If f(x) = -2 then x = ?

If f(x) = 2 then x = ?

They are asking what x is when y is -2 or 2. So here:

If f(x) = -2 then x = 3

If f(x) = 2 then x = -5

Answer:

x=4

Step-by-step explanation:

you take both equations, and make them equal to each other. so....

5x-6=3x+2 subtract 3x from both sides

2x-6=2 then add 6 to the other side.

2x=8 then divide 8 by 2.

X=8

is 1.25 because you just add them together

Answer:

1/2

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

We have two points on the line

(-1,3) and ( 1,4)

m = ( 4-3)/(1 - -1)

   = (4-3)/(1+1)

    = 1/2

Answer:

Start where the line meets a point. Then go up and over until it meets another.

The answer is 1/2

So go up one and over two. Then other problems such as this one should be pretty straight forward

Answer:

With what?

Step-by-step explanation:

Ask the question in the comments sections and I'll try to help you if I know the answer :)

Step-by-step explanation:

https://youtu.be/wghLO8hQZrA

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