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3 years ago

How do I solve this?

Mathematics

1 answer:

Iteru [2.4K]3 years ago

8 0

Using the formula 64(0.5)^r ,
64(0.5)^0=64
64(0.5)^1=32
64(0.5)^3=16
64(0.5)^=8

answer:(1)

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Amy ran 2/3 of a marathon. Beth ran 5/6 of a marathon. Who ran farther ? How much farther?

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2/3 is equal to 4/6.

So, Beth ran further by 1/6 of the marathon

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3 years ago

A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

Darina [25.2K]

Answer:

$100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy$ ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving $y=x^2$ about y axis in the interval $0\leq x\leq 3$ .

Density of the fluid in the tank, $D=100\ lbs/ft^3$

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, $y(0)=0^2=0$

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in $x=3$ in the parabolic equation . This gives,

$H=3^2=9\ ft$

So, the height of top of tank is, $y(3)=H=9\ ft$

Now, 5 ft above 'H' means $H+5=9+5=14$

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

$\Delta y=(14-y)$ ft

Now, area of cross section of the tank is given as:

$A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section$

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, $y=x^2$

So, $x=\sqrt y$

Therefore, radius, $r=\sqrt y$

Now, area of cross section is, $A(y)=\pi (\sqrt y)^2$

Work done in pumping the contents to 5 feet above is given as:

$W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy$

Plug in all the values. This gives,

$W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}$

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3 years ago

Find the area of a rectangle that is 12 cm long and 10 cm wide.

gregori [183]

Answer:

area is length * width

12* 10 = 120cm

the answer is 120cm

Step-by-step explanation:

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3 years ago

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Length of the cylinder = 84.5 cm
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The line is passing through the y-axis at 3. The slope of the line is 3.
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C. y - 6 = 3(x - 3)
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D. y - 6 = 3(x - 1)
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y = 3x + 3

E. y = 3x + 2

F. y = 3x + 3

Which letters equaled y = 3x +3?
A, D, and F.

The equations that describe the line are A, D, and F.

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3 years ago