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gtnhenbr [62]
3 years ago
14

Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the dis

tance in 4 h. Car A traveled 22 mph faster than Car B. How fast did Car A travel? (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
Mathematics
2 answers:
MArishka [77]3 years ago
3 0
If Car A's speed is x, then Car B's speed is x-22. Using the formula, we get that the distance is the same in both, so 4*(x-22)=D and 2.4*x=D due to that we plug 2.4 and 4 in for T and x-22 and x for R. Since they both equal D, we can write it as 2.4*x=4*(x-22). Using the distributive property, we get 4*(x-22)=4x-88=2.4*x. Subtracting 2.4*x from both sides as well as adding 88, we get 1.6*x=88. Dividing both sides by 1.6, we get 88/1.6=55= x=Car A's speed
amm18123 years ago
3 0

wait so what is the answer then

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Answer:

\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: }  \frac{3\pi}{2}\text{ mi}

Step-by-step explanation:

The circumference of a circle with radius r is given by C=2\pi r. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle \theta^{\circ} is equal to 2\pi r\cdot \frac{\theta}{360}.

Formulas at a glance:

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<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}

<u>Question 2:</u>

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C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}

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\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}

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