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2 years ago

Arithmetic of functions

Mathematics

1 answer:

Rzqust [24]2 years ago

5 0

Its B.

If $f(x)=4x+1$ and $g(x)=x^2-5$ then, $(\frac{g}{f})(x)=\frac{x^2-5}{4x+1}$ and $x\neq-\frac{1}{4}$ because if x were $-\frac{1}{4}$ then you would have division by 0.

Hope this helps.

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What is an equation of the line that passes through the point (−5,−1) and is parallel to the line 4x+5y=45?

frozen [14]

This gives you, 4x + 5y = -25 as your final answer.

8 0

2 years ago

Read 2 more answers

a factory could produce 84 toy robots in one day. They purchased some new equipment. Now they can produce 105 robots in one day.

kompoz [17]

Answer:

The answer to the question is

25 % increase in production rate

Step-by-step explanation:

To solve the question, we note that

Initial number of products = 84 toy robots per day

Present production rate = 105 robots per day

The percentage increase is given by the increase in production rate divided by the original production rate multiplied by 100

Where increase in production rate = 105 - 84 = 21

Percentage increase = 21/84 ×100 = 25 % increase

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2 years ago

The deck of a bridge is suspended 275 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of

Ivenika [448]

Answer:

Our equation for the height is:

y(t) = 275 - 16*t^2.

a) To find the average velocity between two times, t1 and t2, (where t2 > t1) the equation is:

$AV = \frac{y(t2) - y(t1)}{t2 - t1}$

Then:

i) t1 = 4s, t2 = 4s + 0.1s = 4.1s

The average velocity is:

$AV = \frac{(275 - 16*4.1^2) - (275 - 16*4^2)}{4.1 - 4} = \frac{16(4^2 - 4.1^2)}{0.1} = -129.6$

And the units will be ft/s, so the average speed is:

-129.6 ft/s

The minus sign is because te pebble is falling down.

ii) t1 = 4s, t2 = 4s + 0.05s = 4.05s

The average velocity is:

$AV = \frac{(275 - 16*4.05^2) - (275 - 16*4^2)}{4.05 - 4} = \frac{16(4^2 - 4.05^2)}{0.05} = -128.8$

So the average speed is -128.9 ft/s

iii) t1 = 4s, t2 = 4s + 0.01s = 4.01s

The average speed is:

$AV = \frac{(275 - 16*4.01^2) - (275 - 16*4^2)}{4.01 - 4} = \frac{16(4^2 - 4.01^2)}{0.01} = -128.16$

The average speed is -128.16 ft/s.

b) The instantaneous velocity of the pebble after 4 seconds can be obtained by looking at the velocity equation, that is the derivative of the height equation.

v(t) = dy(t)/dt.

v(t) = -2*16*t + 0

Then the velocity at t = 4s is:

v(4s) = -32*4 = -128

The instantaneous velocity at t = 4s is -128 ft/s.

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2 years ago

What is the volume (in terms of pi) for a cylinder with a radius of 3 inches

Likurg_2 [28]

Answer:

254.469

Step-by-step explanation:

Formula for Volume of Cylinder: V=πr²h

8 0

2 years ago

Please explain and/or show your work!! :)

PolarNik [594]

$\left[ \begin{matrix} 2 & a \\ -1 & -2 \end{matrix} \right] + \left[ \begin{matrix} b & 4 \\ -2 & 1 \end{matrix} \right]$

This addition of matrices can be combined into one matrix.
To add matrices, add the corresponding components of each matrix.

After adding, we'll have the following

$\left[ \begin{matrix} 2+b & a+4 \\ -3 & -1 \end{matrix} \right]$

This matrix should be equal to the matrix on the right-hand side of the equation. This means that each corresponding component of this matrix and the other matrix should be equivalent.

This means that

$2+b=1$
AND
$a+4=0$

Solving these one-step equations will give the values of a = -4 and b = -1. That's answer choice D.

3 0

3 years ago