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sleet_krkn [62]
3 years ago
15

Two cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the e

nd of 4 hours, the two cars are 520 miles apart. Find the average speed in mph of the other car. (Enter an exact number.
Mathematics
1 answer:
Alinara [238K]3 years ago
6 0

Answer:

50 mph

Step-by-step explanation:

80 mph x 4 = 320 miles. so the first car went 320 miles

520 miles apart- 320 = 200 I subtracted the 320 miles so i can figure out how far the other car went.

200 / 4 hours = 50 mph

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check the picture below.

now, we're assuming the trapezoid is an isosceles trapezoid, namely AD = BC, and therefore the triangles are twins.

incidentally, b is the height of the trapezoid and likewise is also the altitude or height of the concrete triangle.

so we can simply get the area o the trapezoid, notice the bottom base is a+185+a, and then get the area of the concrete triangle and subtract the triangle from the trapezoid, what's leftover is just the vegetation area.

\bf \begin{cases} a=283\cdot cos(80^o)\\ a\approx 49.14\\ --------\\ b=283\cdot sin(80^o)\\ b\approx 278.70 \end{cases}\\\\ -------------------------------\\\\ \textit{area of a trapezoid}\\\\ A=\cfrac{h(x+y)}{2}~~ \begin{cases} x,y=\stackrel{bases}{parallel~sides}\\ h=height\\ ----------\\ x=185\\ y\approx \stackrel{a+185+a}{283.28}\\ h\approx\stackrel{b}{278.70} \end{cases} \\\\\\ A=\cfrac{278.70(185+283.28)}{2}\implies A\approx 65254.818

so that's the area of the trapezoid, now let's get the area of the triangle.

\bf \stackrel{triangle}{\cfrac{1}{2}(185)(b)}\implies \cfrac{1}{2}(185)(278.70)\qquad \approx 25779.80\\\\ -------------------------------\\\\ \stackrel{\textit{area for vegetation}}{\stackrel{\textit{area of trapezoid}}{65254.818}~~-~~\stackrel{\textit{area of triangle}}{25779.80}}\implies 39475.018

since we know 36 yd² cost 12 bucks, then how much will it be for 39475.018 yd²?

\bf \begin{array}{ccll} yd^2&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 36&12\\ 39475.018&x \end{array}\implies \cfrac{36}{39475.018}=\cfrac{12}{x}\implies x=\cfrac{39475.018\cdot 12}{36} \\\\\\ x\approx 13158.339\overline{3}

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