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3 years ago

H(x)= (x^2 -36)/x +6 explain why the following function is not continuous at x=-6

Mathematics

1 answer:

sergeinik [125]3 years ago

8 0

You can solve this problem through factoring.

First, you have the equation,

$h(x) = \frac{x^2-36}{x-6}$

Then, you can factor the numerator.

$h(x) = \frac{(x+6)(x-6)}{x-6}$

You can cancel out the x-6 in both the numerator and the denominator because they would equal to just 1.

You are left with $h(x) = x+6$

The function is removable noncontinuous at x=6 because if you plug in 6 in x-6, your denominator would be undefined.

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The function has three factors. Two of these factors

borishaifa [10]

The values of a and b will be -2 and 22 while the other factor in the function is x - 3/2.

<h3>How to illustrate the function?</h3>

The function is given as:

f(x) = ax³ - x² + bx - 24.

Since (x - 2) and (x - 4) are the factors, they will give functions of 8a + 2b = 28 and -16a - b = 10.

This will be solved by elimination method and the values of a and b will be -2 and 22.

Therefore, f(x) = -2x³ - x² + 22x - 24

Learn more about functions on:

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6 0

1 year ago

wariber [46]

Answer:

Step-by-step explanation:

5 0

2 years ago

Solve for x please thanks

N76 [4]

Answer:

Step-by-step explanation:

So, lets go over what we know:

The equation to find x is the same on both sides.

Now, lets find this equation:

So, the total area of the two lines on the left side of the triangle are 24.

Lets first subtract the first line from the total of the two lines to find the value of the second line:

24-3

21.

Now that we know the value of the 2nd line is 21. lets divide it by the first line(3) to find the scale factor:

21/3

So the scale factor is 7!

Lets plug this in for x.

We know that the first line is 4.

The second line is 7x bigger than 4.

So we can calculate this as:

7x4

So x is 28!

This is your answer!

Hope it helps! :)

6 0

2 years ago

the function y=-2(x-3)^2+4 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog

Roman55 [17]

X intercept would mean plug in 0 for Y.
Then finding the y intercept would mean X is 0. Your answer will be 69420

8 0

3 years ago

3. In a single growing season at the Smith Family Orchard, the average yield per apple tree is 150 apples when the number of tre

g100num [7]

Answer:

A.10000

B.25 more trees must be planted

Step-by-step explanation:

⇒Given:

The intial average yield per acre $y_{i}$ = 150

The initial number of trees per acre $t_{i}$ = 100

For each additional tree over 100, the average yield per tree decreases by 1 i.e , if the number trees become 101 , the avg yield becomes 149.
Total yield = (number of trees per acre) $*$ (average yield per acre)

A.

⇒If the total trees per acre is doubled , which means :

total number of trees per acre $t_{f}$ = $2*t_{i}$ = 200

the yield will decrease by : $t_{f}$ - $y_{i}$

$y_{f}= 150-100= 50$

⇒total yield = $50*200=10000$

B.

⇒to maximize the yield ,

let's take the number of trees per acre to be 100+y ;

and thus the average yield per acre = 150 - y;

total yield = $(100+y)*(150-y)\\=15000+50y-y^{2} \\$

this is a quadratic equation. this can be rewritten as ,

⇒ $=15000+50y-y^{2}\\=15000+625 - (625 - 50y +y^{2})\\=15625 - (y-25)^{2}$

In this equation , the total yield becomes maximum when y=25;

⇒Thus the total number of trees per acre = 100+25 =125;

3 0

2 years ago