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4 years ago

Which equation has a constant of proportionality equal to 9 y=81/3x y=9x y=3x y==1/9x

Mathematics

1 answer:

aev [14]4 years ago

8 0

Answer:

B) y = 9 x has Proportionality Constant = 9

Step-by-step explanation:

Two quantities P and Q are said to be PROPORTIONAL if and only if:

P ∝ Q ⇔ P = k Q ⇔ $k = \frac{P}{Q}$

Here, k = PROPORTIONALITY CONSTANT

Given : k = 9

Now, let us consider the given expressions in which x ∝y

y = 81/3 x

Here, $\frac{y}{x} = \frac{81}{3} = 27 \ne 9$

So, here Proportionality Constant ≠ 9

y = 9 x

Here, $\frac{y}{x} = 9$

So, here Proportionality Constant = 9

y = 3 x

Here, $\frac{y}{x} = 3 \ne 9$

So, here Proportionality Constant ≠ 9

y = 1/9 x

Here, $\frac{y}{x} = \frac{1}{9} \ne 9$

So, here Proportionality Constant ≠ 9

Hence, only y = 9 x has Proportionality Constant = 9

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3 years ago

Determine the values of the constants B and C so that the function given below is differentiable.

laila [671]

For the function to be differentiable, its derivative has to exist everywhere, which means the derivative itself must be continuous. Differentiating gives

$f'(x)=\begin{cases}24x^2&\text{for }x1\end{cases}$

The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as $x\to1$ from either side.

$\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1}24x^2=24$
$\displaystyle\lim_{x\to1^+}f'(x)=\lim_{x\to1}B=B$

So the derivative will be continuous as long as $B=24$

For the function to be differentiable everywhere, we need to require that $f(x)$ is itself continuous, which means the following limits should be the same:

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}8x^3=8$
$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}Bx+C=24+C$

$24+C=8\implies C=-16$

So, the function should be

$f(x)=\begin{cases}8x^3&\text{for }x\le1\\24x-16&\text{for }x>1\end{cases}$

with derivative

$f'(x)=\begin{cases}24x^2&\text{for }x$

5 0

4 years ago

If the population of a town grew 21% up to 15,049, what was the population last year?

katrin2010 [14]

15,049 x .21 = 3,160
subtract: 15,049 - 3,160 = 11, 888

3 0

3 years ago

Find the savings plan balance after 3 years with an APR of 7% and monthly payments of $150.

Citrus2011 [14]

Answer:

The balance is $5989.5

Step-by-step explanation:

The savings plan balance is given by the following formula:

$A = P*\left[\frac{(1 + \frac{APR}{n})^{n*Y} - 1}{\frac{APR}{n}}\right]$

In which A is the savings plan balance, P is the monthly payment, APR is the annual percentage rate(decimal), n is the number of payments per year and Y is the number of years.

In this problem, we have that

Find the savings plan balance after 3 years with an APR of 7% and monthly payments of $150.

So we have to find A when $P = 150, APR = 0.07, n = 12, Y = 3$ .