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3 years ago

Please Help!............................

Mathematics

1 answer:

ryzh [129]3 years ago

6 0

Ok. a function is something that if you draw a vertical line, it should only touch one point on the line.the ones on the left both touch twice. the bottom right has infinite points touching. the top right has only one point touching a vertical line at any time, so it's a function. hope this helps

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What is the total number of common tangents that can be drawn to the circles?

erastovalidia [21]

Answer:

B. 0

Step-by-step explanation:

The circles do not intersect, tangents require intersection

6 0

3 years ago

Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2+4x−8y+20=0 has horizontal and vertical t

Komok [63]

Answer:

The parabola has a horizontal tangent line at the point (2,4)

The parabola has a vertical tangent line at the point (1,5)

Step-by-step explanation:

Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.

-To obtain horizontal tangent lines, the condition is:

$\frac{dy}{dx}=0$ (The slope is zero)

--To obtain vertical tangent lines, the condition is:

$\frac{dy}{dx}=\frac{1}{0}$ (The slope is undefined, therefore the denominator is set to zero)

Derivating respect to x:

$\frac{d(x^{2}-2xy+y^{2}+4x-8y+20)}{dx} = \frac{d(x^{2})}{dx}-2\frac{d(xy)}{dx}+\frac{d(y^{2})}{dx}+4\frac{dx}{dx}-8\frac{dy}{dx}+\frac{d(20)}{dx}$ = $2x -2(y+x\frac{dy}{dx})+2y\frac{dy}{dx}+4-8\frac{dy}{dx}= 0$

Solving for dy/dx:

$\frac{dy}{dx}(-2x+2y-8)=-2x+2y-4\\\frac{dy}{dx}=\frac{2y-2x-4}{2y-2x-8}$

Applying the first conditon (slope is zero)

$\frac{2y-2x-4}{2y-2x-8}=0\\2y-2x-4=0$

Solving for y (Adding 2x+4, dividing by 2)

y=x+2 (I)

Replacing (I) in the given equation:

$x^{2}-2x(x+2)+(x+2)^{2}+4x-8(x+2)+20=0\\x^{2}-2x^{2}-4x+x^{2} +4x+4+4x-8x-16+20=0\\-4x+8=0\\x=2$

Replacing it in (I)

y=(2)+2

y=4

Therefore, the parabola has a horizontal tangent line at the point (2,4)

Applying the second condition (slope is undefined where denominator is zero)

2y-2x-8=0

Adding 2x+8 both sides and dividing by 2:

y=x+4(II)

Replacing (II) in the given equation:

$x^{2}-2x(x+4)+(x+4)^{2}+4x-8(x+4)+20=0\\x^{2}-2x^{2}-8x+x^{2}+8x+16+4x-8x-32+20=0\\-4x+4=0\\x=1$

Replacing it in (II)

y=1+4

y=5

The parabola has vertical tangent lines at the point (1,5)

4 0

3 years ago

NEED HELP WITH

Fed [463]

Let the average profit or loss in year 2006 be x millions,

The average profit for the 8-year period, is the total sum of the profits (or losses) of each year, divided by 8:

so we have:

$\displaystyle{ \frac{3.40+2.10+x+0.60+2.10+0.20+1.30+0.75}{8}=1$

$\displaystyle{\frac{10.45+x}{8}=1$

$10.45+x=8$

x=8-10.45=-2.45

Answer: the loss in 2006, was 2.45 million dollars

3 0

3 years ago

What do variables and functions have in common

klemol [59]

Answer:

A function is a mathematical relationship in which the values of a single dependent variable are determined by the values of one or more independent variables. Function means the dependent variable is determined by the independent variable(s).

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Suppose you play a coin toss game in which you win $1 if a head appears and lose $1 if a tail appears. In the first 100 coin

NARA [144]

Answer:

Percentage of heads = 42 %

Net loss = $16

Step-by-step explanation:

Given:

Total number of tosses = 100

Number of heads come = 42

Number of tails come = 58

Find:

Percentage of heads

Net loss

Computation:

Percentage of heads = Number of heads come / Total number of tosses

Percentage of heads = 42 / 100

Percentage of heads = 42 %

Net loss = 58(1) - 42(1)

Net loss = $16

6 0

2 years ago