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3 years ago

What is the range of the function y=x+8?

Mathematics

2 answers:

Kruka [31]3 years ago

8 0

I think it is

(-infinity, infinity)

MArishka [77]3 years ago

6 0

There are no restrictions on x. If x can be any value, then the same goes for y.

Answer: Range = ALL REAL NUMBERS.

We can also express the answer as

(-infinity, infinity).

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

If an hour is 45 years how long is a minute

Ainat [17]

Since one hour = 45 years, one minute should be 1/60th of 45 years because 60 minutes = an hour.

45/60 = 3/4

So one minute would be 3/4 of an hour, or 45 minutes.

Hope this helps!

8 0

3 years ago

You have a six-sided die that you roll once. Let Ri denote the event that the roll is i. Let G j denote the event that the roll

Misha Larkins [42]

Answer:

a. $P (R3 | G1)=\frac{1}{5}$

b. $P (R6| G3)= \frac{1}{3}$

c. $P(G3|E)=\frac{2}{3}$

d. $P (E|G3)=\frac{2}{3}$

Step-by-step explanation:

The sample space associated with the random experiment of throwing a dice is is the equiprobable space {R1, R2, R3, R4, R5, R6}. Then,

a. The conditional probability that 3 is rolled given that the roll is greater than 1? $P (R3 | G1) = \frac{P (R3\bigcap G1)}{P(G1)} = \frac{1/6}{5/6} = \frac{1}{5}$

b. What is the conditional probability that 6 is rolled given that the roll is greater than 3? $P (R6| G3) = \frac{P (R6\bigcap G3)}{P(G3)} = \frac{1/6}{3/6} = \frac{1}{3}$

c. What is P [GIE], the conditional probability that the roll is greater than 3 given that the roll is even? $P(G3|E) = \frac{P (G3\bigcap E)}{P(E)} = \frac{2/6}{3/6} = \frac{2}{3}$

d. Given that the roll is greater than 3, what is the conditional probability that the roll is even? $P (E|G3) = \frac{P (E\bigcap G3)}{P(G3)} = \frac{2/6}{3/6} = \frac{2}{3}$

6 0

3 years ago

Rob laid three sticks end to end. The lengths of the sticks were 45 millimeters, 32 centimeters, and 4 decimeters. How long, in

Oksanka [162]

Answer:

<u>0.765 meters</u> long were the sticks when laid end to end.

Step-by-step explanation:

Given:

Rob laid three sticks end to end. The lengths of the sticks were 45 millimeters, 32 centimeters, and 4 decimeters.

Now, to find the length in meters of the sticks when laid end to end.

The lengths of the sticks are:

1st stick - 45 millimeters.

2nd stick - 32 centimeters.

3rd stick - 4 decimeters.

So, we convert the units of sticks into meters by using conversion factor:

1st stick:

1 millimeter = 0.001 meter.

45 millimeters = 0.001 × 45

45 millimeters = 0.045 meter.

2nd stick:

1 centimeter = 0.01 meter.

32 centimeters = 0.01 × 32

32 centimeters = 0.32 meter.

3rd stick:

1 decimeter = 0.1 meter.

4 decimeters = 0.1 × 4

4 decimeters = 0.4 meter.

Now, adding all the three sticks length to get the the length in meters of the sticks when laid end to end:

$0.045+0.32+0.4\\\\=0.765\ meters.$

Therefore, 0.765 meters long were the sticks when laid end to end.

5 0

4 years ago

What's the next answer in BADEHGJK

alina1380 [7]

BADEHGJK NM because it's going backwards and then it skips a letter

3 0

4 years ago

What is the range of the function y=x+8?​

What is the range of the function y=x+8?