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torisob [31]
3 years ago
6

4)

Mathematics
1 answer:
AysviL [449]3 years ago
8 0
B. 200.96 in. The area of the pizza with a 16" diameter (8" radius) is 201.06.
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<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%
Llana [10]

a) The given function is

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

The domain refers to all values of x for which the function is defined.

The function is defined for

x^4+x^3-4x^2-4\ne0

This implies that;

x\ne -2.69,x\ne 1.83

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

x^4+x^3-4x^2-4=0

This implies that;

x= -2.69,x=1.83

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

\frac{x^2-4}{x^4+x^3-4x^2-4}=0

\Rightarrow x^2-4=0

x^2=4

x=\pm \sqrt{4}

x=\pm2

The roots are x=-2,x=2

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

x=0 into the function

f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}

f(0)=\frac{-4}{-4}=1

e) to find the horizontal asypmtote, we take limit to infinity

lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0

The horizontal asymtote is y=0

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is  at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0
3 years ago
D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what
Feliz [49]

Answer:

0.53%

Step-by-step explanation:

hope it is well understood

4 0
3 years ago
Express 60 as the product of its prime factors in ascending order and give your answer in index form
Allisa [31]

Answer:

{2}^{2}, 3, 5 are the prime factors of 60.

Step-by-step explanation:

60 = 2 \times 2 \times 3 \times 5 \\  =  {2}^{2}  \times 3 \times 5 \\

3 0
3 years ago
Please solve the eqution<br> Cos4x + cos2x - 2 =0
horrorfan [7]

cos4x = cos2x

We know that:

cos2x = 1-2cos^2 x

==> cos4x = 1-2cos^2 (2x)

Now substitute:

==> 1-2cos^2 (2x) = cos2x

==> 2cos^2 (2x) + cos2x - 1 = 0

Now factor:

==> (2cos2x -1)(cos2x + 1) = 0

==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3

==> x1= pi/6 , 7pi/6

==> x1= pi/6 + 2npi

==> x2= 7pi/6 + 2npi

==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.

<span>==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}</span>

6 0
3 years ago
Gordan and Harry had 340 marble,altogether.After Gordan gave away 2/5 of his marbles and harry gave away 20 of his marbles, they
BARSIC [14]
109.8
you take 240 and subtract that from 2/5.Then you subtract 20 and that gives you 219.6.Since they have the same amount of marbles left,you have to divide 219.6 by 2 and your answer is 109.8
(I just used a calculator)
6 0
3 years ago
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