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4 years ago

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Two cars start to drive around a 2 km track at the same time. car x make one lap every 80 seconds while car y makes one lap ever

y 60 s
(a)how long will it take for the cars to be at their starting point again? give your answer in minutes.
(b)how long will it take to the faster car to be ahead by 15 laps? give your answer in hours.

1 answer:

Volgvan4 years ago

8 0

Answer:

20 minutes

Step-by-step explanation:

Both will meet again at start point after LCM(60,80) seconds.

That is 240 seconds.

in time slower car completes one lap, faster one covers 1 +20/80 lap, that is 1.25 laps. After 20 laps faster by slower car car will be 5 laps ahead, time =20*60 = 1200s = 20 minutes.

hope it help

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PilotLPTM [1.2K]

Answer:

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Step-by-step explanation:

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3 years ago

What is the net price if a purchase would have come to 1500 at the regular price but the 3% discount applied to this purchase

Julli [10]

<u>Answer:</u>

The net price of the product is $1445.

<u>Solution:</u>

Given, regular price of a product is $1500 and it has a discount at the rate of 3%

We have to find the final price of the product.

We know that, <em>final product of price = regular price – discount price </em>

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3 years ago

Find the range of the graphed function.

rusak2 [61]

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Now we don't talk about domain here, we talk about range. See the attachment! You are supposed to focus on y-axis, plane or vertical line. See how the minimum value of function is the negative value while the maximum value is positive.

That means any ranges that don't contain the negative values are cleared out. (Hence A and C choices are wrong.)

Next, range being set of all real numbers mean that graphed functions don't have maximum value or minimum value (We can say that both max and min are infinite.)

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3 years ago

What is 24x128725(7x782)/199+4+23

ryzh [129]

Answer:

$\bold{\frac{8455687800}{113}}$

Step-by-step explanation:

$\frac{24\times \:128725\left(7\times \:782\right)}{199+4+23}$

$\mathrm{Add\:the\:numbers:}\:199+4+23=226$

$=\frac{24\times \:128725\times \:7\times \:782}{226}$

$\mathrm{Factor\:the\:number:\:}\:24=2\times \:12$

$=\frac{2\times \:12\times \:128725\times \:7\times \:782}{226}$

$\mathrm{Factor\:the\:number:\:}\:226=2\times \:113$

$=\frac{2\times \:12\times \:128725\times \:7\times \:782}{2\times \:113}$

$\mathrm{Cancel\:the\:common\:factor:}\:2$

$=\frac{12\times \:128725\times \:7\times \:782}{113}$

$\mathrm{Multiply\:the\:numbers:}\:12\times \:128725\times \:7\times \:782=8455687800$

$\bold{=\frac{8455687800}{113}}$

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3 years ago

: Show that the solution of the differential equation: = − − − − − is of the form: + + ( − ) = + , When = and =

Serhud [2]

Answer:

$y = \tan(x + \frac{x^2}{2})$

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that $y=\tan(x+\frac{x\²}{2})$

When

$\frac{dy}{dx} =1+xy\²+x+y\²$ and $y(0)=0$

We have:

$\frac{dy}{dx} =1+xy\²+x+y\²$

Rewrite as:

$\frac{dy}{dx} =1+x+xy\²+y\²$

Factorize

$\frac{dy}{dx} = (1+x)+y\²(x+1)$

Rewrite as:

$\frac{dy}{dx} = (1+x)+y\²(1+x)$

Factor out 1 + x

$\frac{dy}{dx} = (1+y\²)(1+x)$

Multiply both sides by $\frac{dx}{1 + y^2}$

$\frac{dy}{1+y\²} = (1+x)dx$

Integrate both sides

$\int \frac{dy}{1+y\²} = \int (1+x)dx$

Rewrite as:

$\int \frac{1}{1+y\²} dy = \int (1+x)dx$

Integrate the left-hand side

$\int \frac{1}{1+y\²} dy = \tan^{-1}y$

Integrate the right-hand side

$\tan^{-1}y = x + \frac{x^2}{2} + c$

$y(0)=0$ implies that: $(x,y) = (0,0)$

So:

$\tan^{-1}y = x + \frac{x^2}{2} + c$ becomes

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This gives:

$0 = 0 +0 + c$

$0 =c$

$c = 0$

The equation $\tan^{-1}y = x + \frac{x^2}{2} + c$ becomes

$\tan^{-1}y = x + \frac{x^2}{2} + 0$

$\tan^{-1}y = x + \frac{x^2}{2}$

Take tan of both sides

$y = \tan(x + \frac{x^2}{2})$ --- Proved

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3 years ago