How do you graph y

A crane is being used to remove a piano from an apartment building. The apartment window is 56 feet directly above the bed of th

gregori [183]

$a^2+b^2=c^2\\(42)^2+(56)^2=c^2\\1764+3136=c^2\\4900=c^2\\70=c$

70 feet.

7 0

3 years ago

Please help!

BaLLatris [955]

a) The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) There is a discontinuity at $x = 2$ with a slant asymptote.

a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form $x-r_{i}$ , where $r_{i}$ is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial $f(x)$ has the following form:

$f(x) = (x-6)\cdot (x+1)\cdot (x+3)$

And the expanded form is obtained by some algebraic handling:

$f(x) = (x-6)\cdot (x^{2}+4\cdot x +3)$

$f(x) = x\cdot (x^{2}+4\cdot x + 3)-6\cdot (x^{2}+4\cdot x +3)$

$f(x) = x^{3}+4\cdot x^{2}+3\cdot x -6\cdot x^{2}-24\cdot x -18$

$f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ (1)

The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) In this question we divide the polynomial found in a) (in factor form) by the polynomial $x^{2}-x -2$ (also in factor form). That is:

$g(x) = \frac{(x-6)\cdot (x+1)\cdot (x+3)}{(x-2)\cdot (x+1)}$

$g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ (2)

The slant asymptote is defined by linear function, whose slope ( $m$ ) and intercept ( $b$ ) are determined by the following expressions:

$m = \lim_{x \to \pm \infty} \frac{g(x)}{x}$ (3)

$b = \lim_{x \to \pm \infty} [g(x)-x]$ (4)

If $g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ , then the equation of the slant asymptote is:

$m = \lim_{x \to 2} \frac{(x-6)\cdot (x+3)}{x\cdot (x-2)}$

$m = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x^{2}-2\cdot x} \right)$

$m = 1$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x-2}-x \right)$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x - 18-x^{2}+2\cdot x}{x-2}\right)$

$b = \lim_{n \to \infty} \left(\frac{-x-18}{x-2} \right)$

$b = -1$

The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at $x = 2$ with a slant asymptote.

We kindly invite to check this question on asymptotes: brainly.com/question/4084552

8 0

2 years ago

What is the surface area of a cube that measures 3 cm

kifflom [539]

Answer: Surface area= 54

Step-by-step explanation:

To find the surface area of a cube you do 6 times s^2

S is the side length. In this case that is 3 cm. S^2 is 9

So now you do 6 times 9, and that is 54.

So, the surface area is 54.

8 0

3 years ago

A sporting goods store sells triangular team pennants in two sizes. The base of one pennant is 18 in. and the length of the side

juin [17]

This is a proportion problem because the problem stated that the two team pennants are similar.

Pennant 1 = base = 18 in ; length = 9 inches
Pennant 2 = base = 6 in ; length = x ?

9/18 = x/6
9*6 = 18x
54 = 18x
54/18 = x
3 = x

The length of the side of the smaller pennant is 3 inches.

6 0

4 years ago

Read 2 more answers

Find the value of k if it is known that the line y=kx+2 goes through point:

MrRissso [65]

Answer:

k = -10/7 and k = -3

Step-by-step explanation:

Given: y = kx + 2

where k is the slope of line and 2 is y-intercept.

∵ line y = kx + 2 is passing through point P (-7, 12), ∴ x = -7 and y = 12

Now substituting the value of x and y in above equation,

y = kx + 2

12 = k(-7) + 2

-7k = 12 - 2

- 7k = 10

$k = \frac{-10}{7}$

In the same way, ∵ line y = kx + 2 is passing through point P (3, -7), ∴ x = 3 and y = -7

y = kx + 2

Now substituting the value of x and y in above equation,

-7 = k(3) + 2

3k = -7 - 2

3k = - 9

k = -3

3 0

4 years ago

How do you graph y < -x