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3 years ago

Consider the line y=5x-4.

Mathematics

1 answer:

Bezzdna [24]3 years ago

3 0

Answer:

Parallel= y-5x-3

perpendicular=y=5x

Step-by-step explanation:

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Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis

Lesechka [4]

Answer:

The limit of the function does not exists.

Step-by-step explanation:

From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.

For x<2

$f(x)=6$

The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.

For x>2

$f(x)=-3$

The value of y is 1 at x=2, because of he close circles on (2,1).

For x=2

$f(x)=1$

Therefore the graph represents a piecewise function, which is defined as

$f(x)=\begin{cases}6& \text{ if } x2 \end{cases}$

The limit of a function exist at a point a if the left hand limit and right hand limit are equal.

$lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)$

The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.

$lim_{x\rightarrow 2^-}f(x)=6$

$lim_{x\rightarrow 2^+}f(x)=-3$

$6\neq-3$

Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.

6 0

3 years ago

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Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

3 years ago

9 Questions/45 points

Finger [1]

You have a lot of questions here, try breaking them up into multiple posts and you may get more responses.

I will help with some.

(x+3)=0

The solution is just -3.
-----------------------------------------------------------------
3m(m-4)=0

The two solutions are 0 and 4.
-----------------------------------------------------------------
(r-3)(r+2)=0

The two solutions are and 3 and -2.

I hope this gets you started in the right direction.

3 0

3 years ago

Please help me solve this step by step please :(

Ratling [72]

Answer:

B) 60.21 ft²

Step-by-step explanation:

Area of a triangle = 1/2bh

You can‘t used mixed measurements (feet and inches), so you have to convert each length to inches

8’6”=102’

14’2”=170’

Now find the area

1/2 x 102 x 170 = 8670 in²

This is one of the answers, but the quetion asks how many quart feet you need.

So, convert it back to feet.

8670 x 0.06944444444 = 60.2083333

(You could also have converted the two lengths to feet. 8’6” = 8.5 ft. 14’2” = 14.16666666. This way would probably have been faster.

1/2 x 8.5 x 14.166666 = 60.20833333)

3 0

3 years ago

What's 9-2x=35 please need help and explain it

Degger [83]

Answer:

x = -13

Step-by-step explanation:

9 - 2x = 35

-9 -9

-2x = 26

divide by -2

x = -13

6 0

3 years ago

Read 2 more answers