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1 year ago

Solve: let f(x)=2x-1 and g(x)=x^2-4. find g(f(x))

Mathematics

1 answer:

Stella [2.4K]1 year ago

3 0

<h3>Answer: g(f(x)) = 4x^2 - 4x - 3</h3>

Work Shown:

g(x) = x^2 - 4

g(f(x)) = ( f(x) )^2 - 4

g(f(x)) = ( 2x-1 )^2 - 4

g(f(x)) = (2x-1)(2x-1) - 4

g(f(x)) = 4x^2-2x-2x+1 - 4

g(f(x)) = 4x^2 - 4x - 3

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The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

BartSMP [9]

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

5 0

3 years ago

Divide, <br><br> 24x^6 - 12x^3 divided by 4x^3<br><br> Simplify as much as possible

LekaFEV [45]

24x6=24-(12x3)-12 divided 4x3is 12
The awnser:0

Hope it help

3 0

2 years ago

Which of the following represents the factorization of the trinomial below?

saw5 [17]

Answer: (x-8)(x+6)

Step-by-step explanation: For this equation, you need to figure out what two numbers add up to add -2, and multiply to get -48.

These numbers are +6 and -8. So the factored pair will be (x+6)(x-8)

Hope this helps:)

3 0

3 years ago

Read 2 more answers

Which shows a function that is decreasing<br>over its entire graph? Working on it now need ASAP

PtichkaEL [24]

One thing everyone always forgets is we don't usually see the <em>entire</em> graph. Once out of the frame, these functions can do anything they want.

From what we can see, only the bottom right one is always decreasing.

Answer: bottom right

By the way, the top right graph (a vertical line) isn't a function.

7 0

2 years ago

PLSSS HELPPPPPPP ASAPPPP I NEED THIS

krek1111 [17]

True because u could divide the number of cubes on the top, front, and left to get how many are in the structure

4 0

2 years ago