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4 years ago

Which of the following is the horizontal asymptote for the graph below?

Mathematics

2 answers:

Lena [83]4 years ago

7 0

Answer: Y=-4

Step-by-step explanation:

umka2103 [35]4 years ago

6 0

Answer:

B. y=-4

Step-by-step explanation:

The horizontal asymptote is the horizontal line that the graph behaves as if it is going to touch as the x-values approaches positive and negative infinity.

From the graph the horizontal asymptote is

$y = - 4$

As we move towards negative infinity the graph approaches y=-4.

As we move towards positive infinity the graph approaches y=-4.

The correct answer is option B.

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Please help to answer with working.

dusya [7]

Answer:

When r=0.2, m=0.016g

When m=0.25, r=0.5cm

When r=0.7, m=0.686g

When m=11.664, r=1.8cm

Step-by-step explanation:

General outline of steps for proportionality problems:

Identify the type or proportionality.
Find the proportionality constant using a known input/output pair.
Use the proportionality equation to find other unknowns.

<h3><u>Background on proportionality relationships</u></h3>

There are two main types of proportionality, "direct" and "inverse", and then there are modifications that can be made to them. Several examples are listed below:

<u>Direct proportionality examples</u>

y is directly proportional to x: $y=kx$
y is directly proportional to the square of x: $y=kx^2$
y is directly proportional to the cube of x: $y=kx^3$

<u>Inverse proportionality examples</u>

y is inversely proportional to x: $y=\dfrac{k}{x}$
y is inversely proportional to the square of x: $y=\dfrac{k}{x^2}$

In each case, irregardless of which type, the two quantities are related with some extra letter "k", called the proportionality constant. Either way, the proportionality constant "k" is always in the numerator, and the quantity is either multiplied to or divided from the proportionality constant "k".

Notice that for direct proportionality, in each case, the equation always ends up as "k times" the quantity.

On the other hand, notice that for inverse proportionality, in each case, the equation always ends up as "k divided by" the quantity.

<h3><u>Step 1. Identify the type or proportionality </u><u>(Setting up our proportionality equation)</u></h3>

The problem says "... the mass, <em>m</em> g, of a sphere is directly proportional to the cube of its radius, <em>r</em> cm...", so our equation will look like $m=kr^3$ .

<h3><u>Step 2. Finding the proportionality constant</u></h3>

To find the proportionality constant for our situation, one must know a full input/output pair. Notice that in the 4th column, $r=1.5$ and $m=6.75$ .

Substituting these values into our equation, we can find "k".

$(6.75)=k(1.5)^3$

$6.75=k*3.375$

$\dfrac{6.75}{3.375}= \dfrac{k*3.375}{3.375}$

$2=k$

So, the proportionality constant for this situation is 2, and our equation for this situation becomes: $m=2r^3$

<h3><u>Step 3. Finding the other inputs/outputs</u></h3>

Now that we know the proportionality constant for this situation, if we have either the input OR the output, we can solve for the other unknown.

$m=2r^3$

$m=2(0.2)^3$

$m=2(0.008)$

$m=0.016$

Recall the the question said that the mass, m, was measured in grams, and the radius, r, was measured in centimeters. So, if the radius is 0.2cm, then the mass of the sphere would be 0.016g.

$m=2r^3$

$(0.25)=2r^3$

$\dfrac{0.25}{2}=\dfrac{2r^3}{2}$

$0.125=r^3$

$\sqrt[3]{0.125} = \sqrt[3]{r^3}$

$0.5=r$

So, if the mass of the sphere were 0.25g, the radius of the sphere would be 0.5cm.

$m=2r^3$

$m=2(0.7)^3$

$m=2(0.343)$

$m=0.686$

So, if the radius is 0.7cm, then the mass of the sphere would be 0.686g.

$m=2r^3$

$(11.664)=2r^3$

$\dfrac{11.664}{2}=\dfrac{2r^3}{2}$

$5.832=r^3$

$\sqrt[3]{5.832} = \sqrt[3]{r^3}$

$1.8=r$

So, if the mass of the sphere were 11.664g, the radius of the sphere would be 1.8cm.

7 0

2 years ago

What is the equation of a line that is perpendicular to a line with a slope of 2 and passes

geniusboy [140]

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b So now we know the y-intercept and slope. We just put them together now

y=3x-7

6 0

3 years ago

Read 2 more answers

Translate the following statement into an equation and solve for x

Tamiku [17]

Answer:

104 = -13 x -8

Step-by-step explanation:

The reason you got it wrong is, I'm assuming, because of the way you formatted it. Try this and see if it works.

3 0

3 years ago

What is the fraction twelve twentieths in it's simplest form

tatyana61 [14]

We start with 12/20. Half both numbers = 6/10. Half again = 3/5.
Because 3/5 are both odd numbers and can't be made smaller without using decimals (which you don't want to use within a fraction), 3/5 is the simplest form for this fraction.

7 0

3 years ago

Read 2 more answers

Geometry Homework: Find m<Q

White raven [17]

Answer: angle Q = 75 degrees

--------------------------------------------

The tickmarks on segments PR and PQ indicate they are congruent, ie PR = PQ. Because of this, the base angles R and Q (opposite the segments mentioned) are congruent

Angle R = Angle Q
Since angle R is (2x+15) degrees, so is angle Q

Now use the idea that adding three angles of a triangle leads to 180 degrees
P+Q+R = 180
x+(2x+15)+(2x+15) = 180
5x+30 = 180
5x = 180-30
5x = 150
x = 150/5
x = 30

If x = 30, then angle Q is
angle Q = (2x+15) degrees
angle Q = (2*x+15) degrees
angle Q = (2*30+15) degrees
angle Q = (60+15) degrees
angle Q = 75 degrees

5 0

3 years ago