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2 years ago

8

the singh and robinson families planned a trip to busch gardens. they needed to buy one ticket per person and then pay for parki

ng. the singh's spent $335 for 5 people and the robinsons spent $ 465 for 7 people. how much did each ticket cost? How much was parking

1 answer:

hjlf2 years ago

5 0

Let x represent cost of each ticket and y represent cost of parking.

We have been given that the Singh's spent $335 for 5 people and parking. We can represent this information in an equation as:

$5x+y=335...(1)$

We are also told that the Robinson spent $465 for 7 people and parking. We can represent this information in an equation as:

$7x+y=465...(2)$

Now we will use elimination method to solve our given system of equations.

Upon subtracting equation (1) from equation (2), we will get:

$7x-5x+y-y=465-335$

$2x=130$

$\frac{2x}{2}=\frac{130}{2}$

$x=65$

Therefore, the each ticket costs $65.

Upon substituting $x=65$ in equation (1), we will get:

$5(65)+y=335$

$325+y=335$

$325-325+y=335-325$

$y=10$

Therefore, the parking costs $10.

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3 years ago

A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

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Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

a.

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

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3 years ago

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3 years ago

If three quarters of a number decreased by twenty is equal to eighty two, what is that number?

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A number is :

$x$

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Three quarters of it means :

$\frac{3}{4}x \\$

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Decrease by 20 means :

$\frac{3}{4}x - 20 \\$

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Equals to 82 means :

$\frac{3}{4}x - 20 = 82 \\$

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What is that number ?

x asked so we must solve the above equation for x.

Let's do it....

$\frac{3}{4}x - 20 = 82 \\$

Plus sides 20

$\frac{3}{4}x = 82 + 20 \\$

$\frac{3}{4}x = 102 \\$

Multiply sides by 4

$3x = 102 \times 4$

Divided sides by 3

$x = \frac{102 \times 4}{3} \\$

$x = \frac{102}{3} \times 4 \\$

Simplify

$x = 34 \times 4$

$x = 136$

So that number is 136 .

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And we're done.

Thanks for watching buddy good luck.

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3 years ago