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4 years ago

Jenny is 34 years old. Two years ago she was twice as old as her cousin. How old is her cousin now?

2 answers:

8 0

The answer is 18. she was 32 2 years ago so 32 divided by 2 beacause shes twice as old which is 16 then add 2 for 2 years so the answer is 18

Tanya [424]4 years ago

5 0

Hello there!

I hope you are having a wonderful day!

I would be happy to help!

Your question states: Jenny is 34 years old. Two years ago she was twice as old as her cousin. How old is her cousin now?

Two years ago, she was 32.

One half of 32 is 16

Her cousin was 16 two years ago

16 plus 2 = 18

Her cousin is now 18

34 - 2 = 32

32/2 = 16

16 + 2 = 18

Answer = 18

Hope I helped!

Let me know if you need anything else!

~ Zoe

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Which is an x-intercept of the graph of the function y=cot(3x)

AveGali [126]

Answer:

x-intercept of the graph of the function $y = \cot(3x)$ is, $(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$

Step-by-step explanation:

Given the function: $y = \cot(3x)$ ......[1]

x-intercept defined as the graph crosses the x-axis.

Substitute value of y = 0 in [1] and solve for x;

$0 = \cot(3x)$ or

$\cot(3x) = 0$

Take the inverse cotangent of both sides of the equation and solve for x;

3x = arccot (0)

We know the exact value of $arc\cot(0) = \frac{\pi}{2}$

then;

$3x = \frac{\pi}{2}$

Divide both sides by 3 we get;

$x = \frac{\pi}{6}$

Since, the cotangent function is positive in the first and third quadrants.

The period of the function $\cot(3x)$ is $\frac{\pi}{3}$ so values will repeat every $\frac{\pi}{3}$ radians in both directions.

we have;

$x =\frac{\pi}{6} \pm \frac{n\pi}{3}$

Therefore, the x-intercept of the graph of the function $y = \cot(3x)$ is ;

$(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$ for every integer n;

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3 years ago

POSSIBLE POINTS: 4 The length of a rectangle is 4 inches more than the width. The area of the rectangle is 45 in2 Find the lengt

EleoNora [17]

Answer:

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(x + 9)(x - 5) = 0

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Step-by-step explanation:

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PSYCHO15rus [73]

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PtichkaEL [24]

Answer:

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Step-by-step explanation:

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3 years ago

A certain country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The

mash [69]

Answer:

$\bf x(t)=10(1-e^{-0.005*t})$

Step-by-step explanation:

The differential equation

$\bf \displaystyle\frac{dx}{dt}=0.005(10-x)$

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$\bf \displaystyle\frac{dx}{10-x}=0.005dt$

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$\bf \int\displaystyle\frac{dx}{10-x}=\int0.005dt\Rightarrow -ln(10-x)=0.005t+C\Rightarrow\\\\\Rightarrow ln(10-x)^{-1}=0.005t+C\Rightarrow (10-x)^{-1}=e^{0.005t}e^C$

where C is a constant.

$\bf e^C$ is also a constant and we will keep calling it C, (there is no reason to change the letter). We have then

$\bf (10-x)^{-1}=Ce^{0.005t}\Rightarrow \displaystyle\frac{1}{10-x}=Ce^{0.005t}\Rightarrow 10-x=\displaystyle\frac{1}{Ce^{0.005t}}\Rightarrow\\\\\Rightarrow x(t)=10-(1/C)e{-0.005t}$

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$\bf x(t)=10-Ce^{-0.005t}$

Now, we use the initial condition x(0)=0

$\bf x(0)=10-Ce^{-0.005*0}=0\Rightarrow C=10$

and the particular solution is

$\bf x(t)=10-10e^{-0.005*t}=10(1-e^{-0.005*t})\\\\\boxed{x(t)=10(1-e^{-0.005*t})}$

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3 years ago