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3 years ago

What are the solutions of the compound inequality 2d + 3 ≤ –11 or 3d – 9 > 15?

Mathematics

1 answer:

pentagon [3]3 years ago

3 0

Step-by-step explanation:

$2d + 3 \leqslant - 11 \\ 2d \leqslant - 11 - 3 \\ 2d \leqslant - 14 \\ \frac{2d}{2} \leqslant \frac{ - 14}{2} \\ d \leqslant - 7$

$3d - 9 > 15 \\ 3d > 15 + 9 \\ 3d > 24 \\ \frac{3d}{3} > \frac{24}{3} \\ d = 8$

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the radious of each wheel of a car is 16 inches at how many revolutions per minute should a spin balancer be set to balance the

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Answer:

revolutions per minute for 16 inches is 946 / minute

revolutions per minute for 14 inches is 1081 / minute

Step-by-step explanation:

Given data

radius = 16 inch

speed = 90 mph = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute

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to find out

revolutions per minute

solution

first we calculate the circumference of the wheel i.e. 2× $\pi$ ×radius

circumference = 2× $\pi$ ×16

circumference = 32 $\pi$

we know that revolution is speed / circumference

revolution = 95040/32 $\pi$

revolution = 945.38 / minute

we have given radius 14 inches than revolution will be i.e.

revolution = speed / circumference

circumference = 2× $\pi$ ×14

circumference = 28 $\pi$

revolution = 95040/ 28 $\pi$

revolution = 1080.43 / minute

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