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3 years ago

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Barney and Betty break into a parking meter with $3.90 in dimes and quarters in it (legal disclaimer: don't do this) and agree t

hat Barney will get all the dimes, and Betty will get all the quarters. (Barley isn't terribly bright) Barney ends up with four more coins than Betty. How much money did each get(

1 answer:

Crank3 years ago

7 0

Answer:

Barney got 14 dimes and Betty got 10 quarters.

Step-by-step explanation:

Since there are only dimes and quarters in the parking meter, the total money must be equal to:

$0.1*dimes + 0.25*quarters = 3.9$

Since Barney got all the dimes and he has four more coins than Betty, then the number of dimes is:

$dimes = quarters + 4$

Applying the second expression on the first, we have:

$0.1*(quarters + 4) + 0.25*quarters = 3.9\\0.1*quarters + 0.4 + 0.25*quarters = 3.9\\0.35*quarters = 3.9 - 0.4\\0.35*quarters = 3.5\\quarters = \frac{3.5}{0.35} = 10$

$dimes = quarters + 4 = 10 + 4 = 14$

Barney got 14 dimes and Betty got 10 quarters.

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A circular cake with a radius of 8 inches is cut from the center into 6 equal pieces. How many inches wide, to the nearest tenth

aalyn [17]

Answer: 8.4 inches.

Step-by-step explanation:

We know that the circumference of a circle can be calculated with this formula:

$C=2\pi r$

Where "r" is the radius of the circle.

We know that the circular cake (whose radius is 8 inches) is cut from the center into 6 equal pieces. Then, you need to divide the circumference of this circular cake by 6 to find the width of the outer edge of each piece of cake.

Therefore, this is (to the nearest tenth of an inch):

$C=\frac{2\pi (8in)}{6}\\\\C=8.4in$

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3 years ago

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3. How many 1/8's are in 1 1/4?

Murrr4er [49]

Answer:

10

Step-by-step explanation:

There are two 1/8 in one 1/4. There are eight 1/8 in 1. 8/8 + 1/8 + 1/8 = ten 1/8.

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3 years ago

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graph

diamong [38]

Answer:

a) 8π

b) 8/3 π

c) 32/5 π

d) 176/15 π

Step-by-step explanation:

Given lines : y = √x, y = 2, x = 0.

<u>a) The x-axis </u>

using the shell method

y = √x = , x = y^2

h = y^2 , p = y

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {y.y^2} \, dy$

∴ Vol = 8π

<u>b) The line y = 2 ( using the shell method )</u>

p = 2 - y

h = y^2

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy$

= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀

∴ Vol = 8/3 π

<u>c) The y-axis ( using shell method )</u>

h = 2-y = h = 2 - √x

p = x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

= $(2\pi ) \int\limits^4_0 {x(2-\sqrt{x} ) } \, dx$

= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

<u>d) The line x = -1 (using shell method )</u>

p = 1 + x

h = 2√x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

Hence vol = 176/15 π

attached below is the graphical representation of P and h

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3 years ago

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

Nataliya [291]

Answer:

$f(x)=\frac{1}{2}x^2-4x+5$

Step-by-step explanation:

A parabola is written in the form

$f(x)=a((x-h)^2+k)$ (1)

where:

$h$ is the x-coordinate of the vertex of the parabola

$ak$ is the y-coordinate of the vertex of the parabola

$a$ is a scale factor

For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:

$h=4$ (2)

$ak=-3$

From this last equation, we get that $a=\frac{-3}{k}$ (3)

Substituting (2) and (3) into (1) we get the new expression:

$f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3$ (4)

We also know that the parabola contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

$-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6$

So we also get:

$a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}$

So the equation of the parabola is:

$f(x)=\frac{1}{2}((x-4)^2 -6)$ (5)

Now we want to rewrite it in the standard form, i.e. in the form

$f(x)=ax^2+bx+c$

To do that, we simply rewrite (5) expliciting the various terms, we find:

$f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5$

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3 years ago

5y + 2(11 - 4y) = 82 + y<br> Help Needed Asap

ryzh [129]

Answer:

y=−15

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3 years ago

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