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3 years ago

Heather has $15 to spend at the carnival

Mathematics

1 answer:

Triss [41]3 years ago

3 0

Answer:

7 rides

Step-by-step explanation:

Entry Fee = $3.60

Cost per ride = $1.50

$15 - $3.60 = $11.40

$11.40 ÷ $1.50 = 7.6 rides

Ans. = 7 rides

Therefore, Heather can only ride 7 rides leaving her with $0.90¢ change.

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A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2.

IRISSAK [1]

Answer:

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Step-by-step explanation:

Given:

Initial speed of the car ( $v_0$ ) = 40 ft/sec

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Negative sign means the velocity is decreasing with time.

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$\frac{dv}{dx}\cdot\frac{dx}{dt}= -10\\\\But\ \frac{dx}{dt}=v.\ So,\\\\v\frac{dv}{dx}=-10\\\\vdv=-10dx$

Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,

$\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft$

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