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2 years ago

Help with my homework Evaluate the exponent expression for a = 1 and b = –2.

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

7 0

Answer:

-1/16

Step-by-step explanation:

Put the values where the variables are and do the arithmetic.

1 to any power is 1, so you can ignore all of the 'a' factors. That leaves ...

1/(2b^3) = 1/(2(-2)^3) = 1/(2(-8)) = -1/16

___

A calculator can help you figure this out.

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Greg buys a home for $328,500. His home is predicted to increase in value 4% each year. What is the predicted value of his home

GaryK [48]

The initial value of the Greg`s home: $328,500. If his home is predicted to increase in value 4% each year, that means that the value will rise 1.04 times every year.
The predicted value after 30 years:
$328,500 * ( 1 + 0.04 ) ^30 =
= $328,500 * 1.04^30 =
= $328,500 * 3.2434 =
= $1,065,456.
Answer: The predicted value of his home in 30 years is $1,065,456.

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3 years ago

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miskamm [114]

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2 years ago

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The function f(x) = −x2 + 28x − 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number

Rudik [331]

9514 1404 393

Answer:

C- (14, 4); The vertex represents the maximum profit.

Step-by-step explanation:

The leading coefficient of the quadratic function is negative, so the graph opens downward, and the vertex represents a maximum.

The maximum value is at ...

x = -b/(2a) = -28/(2(-1)) = 14

f(14) = -14^2 +28(14) -192 = 4

The vertex is (14, 4). It represents the maximum profit.

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2 years ago

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t in measured in seconds.

natima [27]

Answer:

-16t² + 13.4t + 120

= ( t-3.189)(t+2.352)

t = 3.189s or t = -2.352s (ignore)

ignore -2.352s because time cannot be in negative form

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3 years ago

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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