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andreev551 [17]
3 years ago
12

What is the horizontal asymptote of (3x-2)/(x+6)

Mathematics
2 answers:
Margarita [4]3 years ago
7 0

f(x)=\dfrac{3x-2}{x+6}\\\\\lim\limits_{x\to\pm\infty}\dfrac{3x-2}{x+6}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(3-\frac{2}{x}\right)}{x\left(1+\frac{6}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{3-\boxed{\frac{2}{x}}^{\to0}}{1+\boxed{\frac{6}{x}}_{\to0}}=\dfrac{3}{1}=3\\\\Answer:\boxed{y=3}

melomori [17]3 years ago
7 0

The horizontal asymptote is y=3

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Greg is covering a wall with equal-sized tiles that cannot be cut
Kitty [74]

Answer:

C. 36 in.

Step-by-step explanation:

The wall is 66 inches high by 72 inches wide.

The tiles are

a) 9 inch square = 3 by 3

b) 16 inch square = 4 by 4

c) 36 inch square = 6 by 6

d) 64 inch square = 8 by 8

Factors of 66 = 2 x 3 x 11

Factors of 72 = 2 x 2 x 2 x 3 x 3

Now, we can see that in both 66 and 72 , we have 2 x 3 common that is 6.

And square of 6 is 36.

So, the answer is option C.

4 0
4 years ago
Zack watered his garden with 1 3/8
victus00 [196]

Answer:

<u>The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.</u>

Step-by-step explanation:

Let's find out the pattern Zack is using to water his garden, this way:

First week =  1 3/8  gallons of water

Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4

Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8

The constant of adding every week is 3/8 gallons, therefore,

Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water

Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water

<u>The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.</u>

3 0
3 years ago
Jamarius buys T-shirts for $6 each and marks up the price by 45%. How much profit does Jamarius make from each T-shirt sold?
3241004551 [841]

Answer:

$2.70

Step-by-step explanation:

To add 45 percent to the original price you do 100%+45%=145%=1.45

times 1.45  by the original price.

Then take away the original price from the answer you just got.

$1.45×$6=$8.70

$8.70-$6=$2.70

6 0
3 years ago
"Suppose an object falling in the atmosphere has mass m=15kg and the drag coefficient is γ=9kg/s. Recall that the differential e
Art [367]

Answer:

a. v(t)= -6.78e^{-16.33t} + 16.33 b. 16.33 m/s

Step-by-step explanation:

The differential equation for the motion is given by mv' = mg - γv. We re-write as mv' + γv = mg ⇒ v' + γv/m = g. ⇒ v' + kv = g. where k = γ/m.Since this is a linear first order differential equation, We find the integrating factor μ(t)=e^{\int\limits^  {}k \, dt } =e^{kt}. We now multiply both sides of the equation by the integrating factor.

μv' + μkv = μg ⇒ e^{kt}v' + ke^{kt}v = ge^{kt} ⇒ [ve^{kt}]' = ge^{kt}. Integrating, we have

∫ [ve^{kt}]' = ∫ge^{kt}

    ve^{kt} = \frac{g}{k}e^{kt} + c

    v(t)=   \frac{g}{k} + ce^{-kt}.

From our initial conditions, v(0) = 9.55 m/s, t = 0 , g = 9.8 m/s², γ = 9 kg/s , m = 15 kg. k = y/m. Substituting these values, we have

9.55 = 9.8 × 15/9 + ce^{-16.33 * 0} = 16.33 + c

       c = 9.55 -16.33 = -6.78.

So, v(t)=   16.33 - 6.78e^{-16.33t}. m/s = - 6.78e^{-16.33t} + 16.33 m/s

b. Velocity of object at time t = 0.5

At t = 0.5, v = - 6.78e^{-16.33 x 0.5} + 16.33 m/s = 16.328 m/s ≅ 16.33 m/s

6 0
3 years ago
How many minutes are there in 12.5 hours?
neonofarm [45]

Answer:

750 minutes

Step-by-step explanation:

7 0
3 years ago
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