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3 years ago

I think i had thw correct answers for thr last two but the keep coming up as incorrect

Mathematics

1 answer:

Oksana_A [137]3 years ago

7 0

Answer:

B. 40

C. 8

Step-by-step explanation:

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Ples help me find slant assemtotes

FrozenT [24]

A polynomial asymptote is a function $p(x)$ such that

$\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0$

$(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}$

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form $p(x)=ax+b$ .

Ignore the negative root (we don't need it). If $y=2x-1+2\sqrt{x^2-x}$ , then we want to find constants $a,b$ such that

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

We have

$\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}$

since $x\to\infty$ forces us to have $x>0$ . And as $x\to\infty$ , the $\dfrac1x$ term is "negligible", so really $\sqrt{x^2-x}\approx x$ . We can then treat the limand like

$2x-1+2x-ax-b=(4-a)x-(b+1)$

which tells us that we would choose $a=4$ . You might be tempted to think $b=-1$ , but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of $b$ , we have to solve for it in the following limit.

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0$

$\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2$

We write

$(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}$

Now as $x\to\infty$ , we see this expression approaching $-\dfrac12$ , so that

$-\dfrac12=\dfrac{b+1}2\implies b=-2$

So one asymptote of the hyperbola is the line $y=4x-2$ .

The other asymptote is obtained similarly by examining the limit as $x\to-\infty$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

$\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0$

Reduce the "negligible" term to get

$\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0$

Now we take $a=0$ , and again we're careful to not pick $b=-1$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0$

$\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2$

$(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}$

This time the limit is $\dfrac12$ , so

$\dfrac12=\dfrac{b+1}2\implies b=0$

which means the other asymptote is the line $y=0$ .

4 0

3 years ago

Question 14 of 20 : Select the best answer for the question.

ddd [48]

The answer is 21/32 that is the answer of 3/4 ×7/8

5 0

3 years ago

Read 2 more answers

A triangle-shaped machine part has sides of 2 1/2 inches, 3 1/4 inches, and 5 inches. The triangle's perimeter is

SOVA2 [1]

Answer:

Step-by-step explanation:

The perimeter of any shape is the distance around the edge of the shape. It is found by adding the side lengths of each side together.

Add each side length listed for the triangle part.

$P = 2\frac{1}{2} + 3\frac{1}{4} + 5 \\P = 2\frac{2}{4} + 3\frac{1}{4} + 5\\P = 10 \frac{3}{4}$

8 0

3 years ago

How to now your timetables by your hands

Ivenika [448]

1
Hold your hands out in front of you with your palms facing up. Each of your ten fingers represent a number. Moving from your left thumb to your right thumb, count out the numbers from one to ten. 2 Point the finger you want to multiply by nine down towards your body. For example, if you want to solve (9x3) you will want to hold down your middle finger on your left hand. The middle finger represents the number three because, if you count your fingers from one to ten beginning with your left thumb, your middle finger is the third finger. 3 Solve the problem by counting fingers to the left and right. First count the fingers to the left of your bent finger - in this case there should be two. Next count the fingers to the right of your bent finger - in this case there should be seven. The first digit of the answer is 2 and the second digit is 7. The answer is 27![1]

7 0

3 years ago

Read 2 more answers

If my diameter is 20.6ft how would i get my radius,area,circumference?

sveta [45]

Step-by-step explanation:

Radius is half of the diameter

Circumference is 2*pi*radius

Area is pi*radius^2

So r (radius)= 10.3

C (circumference)=64.72

and A (area)=333.29

feel free to ask more questions :)

4 0

4 years ago

Read 2 more answers

I think i had thw correct answers for thr last two but the keep coming up as incorrect​

I think i had thw correct answers for thr last two but the keep coming up as incorrect