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Agata [3.3K]
2 years ago
11

A truck leaves point A traveling 60 mph. After two hours, a car leaves point A traveling 90 mph and follows the truck's route. A

t what distance from point A will the car catch up with the truck?
Mathematics
1 answer:
aliina [53]2 years ago
7 0

The car catches up with the truck after a distance of 360 miles from point A.

Speed is the ratio of distance travelled to total time taken. It is given by:

Speed = distance / time

For truck:

60 = d / t

d = 60t

Since the car leaves the truck after 2 hours, hence:

For the car:

90 = d/ (t - 2)

d = 90t - 180

For the truck and car to catch up:

60t = 90t - 180

30t = 180

t = 6 hours

d = 60t = 60(6) = 360 miles

The car catches up with the truck after a distance of 360 miles from point A.

Find out more at: brainly.com/question/22610586

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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
melamori03 [73]

Answer:

6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs AB=3, BC=4, and AC=5. The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base b and height h is given by A=\frac{1}{2}bh. Therefore, the area of this right triangle is:

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The other triangle is a bit trickier. Triangle \triangle ADC is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

A=\sqrt{s(s-a)(s-b)(s-c)}, where a, b, and c are three sides of the triangle and s is the semi-perimeter (s=\frac{a+b+c}{2}).

The semi-perimeter, s, is:

s=\frac{5+5+4}{2}=\frac{14}{2}=7

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A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}

Thus, the area of the quadrilateral is:

6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}

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3 years ago
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Answer:

The answer is 5 people

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