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1 year ago

I need help and answersWhat is the range of the function ?

Mathematics

1 answer:

Bumek [7]1 year ago

7 0

The range of a function is all the values of the y variable (of a function) that are related to the values of the x variable (in the domain).

In this case, we have that the values that represent the range of the function are in the second set of numbers (see the direction of the arrows).

Therefore, the range is represented by {2, 6, 8}.

In summary, the range of the function is {2, 6, 8} (option D).

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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is...

enot [183]

Answer:

c. $\frac{1}{\pi}$

Step-by-step explanation:

We have been given that the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

We will use derivatives to solve our given problem.

We know that area (A) of a circle is equal to $A=\pi r^2$ .

Let us find derivative of area function with respect to time.

$\frac{dA}{dt}=\frac{d}{dt}(\pi r^2)$

Bring out constant:

$\frac{dA}{dt}=\pi \frac{d}{dt}(r^2)$

Using power rule and chain rule, we will get:

$\frac{dA}{dt}=\pi(2r)* \frac{dr}{dt}$

$\frac{dA}{dt}=2\pi r*\frac{dr}{dt}$ Here $\frac{dr}{dt}$ represents change is radius with respect to time.

We have been given that area of an expanding circle is increasing twice as fast as its radius in linear units. We can represent this information in an equation as:

$\frac{dA}{dt}=2\frac{dr}{dt}$

$2\pi r* \frac{dr}{dt}=2\frac{dr}{dt}$

$2\pi r=2$

$\frac{2\pi r}{2\pi}=\frac{2}{2\pi}$

$r=\frac{1}{\pi}$

Therefore, the radius is $\frac{1}{\pi}$ and option 'c' is the correct choice.

6 0

3 years ago

Jan 258:00:56 AM

horsena [70]

Answer:

The equation of the straight line in point-slope form

$y - 4 = \frac{7}{9} (x-0)$

The equation of the straight line

7x -9y +36 =0

Step-by-step explanation:

Step(i):-

Given that the points (0,4) and (-9,-3)

The slope of the line

$m = \frac{y_{2} - y_{1} }{x_{2}- x_{1} } = \frac{-3-4}{-9-0} = \frac{7}{9}$

Step(ii):-

Equation of the straight line passing through the point (0,4) and having slope m = 7/9

$y - y_{1} = m (x-x_{1} )$

$y - 4 = \frac{7}{9} (x-0)$

9 y - 36 = 7x

9y = 7x + 36

$y = \frac{7x}{9} +\frac{36}{9}$

Slope - intercept form

$y = \frac{7x}{9} +4$

Final answer:-

The equation of the straight line in point-slope form

$y - 4 = \frac{7}{9} (x-0)$

The equation of the straight line

7x -9y +36 =0

8 0

3 years ago

Solving quadratic equations by factoring m(m-3)=0

KatRina [158]

Because it has already been factored, we can solve it straight away. Now, since m is a variable, we yield the same result if m = 0 or m = 3 because we have two components to this equation.

We can either have m = 0 or m - 3 = 0
Hence, m is either 0 or 3

6 0

3 years ago

Find total number of solutions of [x]^2= x + 2 {x}, where (.) and {.} denotes the greatest integer

Art [367]

Answer:

Step-by-step explanation:

There are only 5 solutions:

x=-1

x=-1/3

x=0

x=1

x=8/3

See the graph

In blue: y=[x]²

In red : y=x+2(x-[x])

4 0

3 years ago

Simplify the sum (3x^4 + 2x^2 + 1) + (5x^4 - 9x - 7)

Wittaler [7]

Answer:

8x^4 + 2x^2 - 9x - 6

Hope this helps!

7 0

3 years ago