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guapka [62]
2 years ago
8

A car initially traveling at 20 kilometers per hour takes 10 seconds to speed up to 70 km/hour. At what rate is it changing spee

d?
Mathematics
1 answer:
Snezhnost [94]2 years ago
7 0
  • Initial velocity=u=20km/h
  • Final velocity=v=70km/h
  • Time=10s=t

Convert speeds to m/s

\\ \rm\longmapsto u=20\times\dfrac{5}{18}=5.05m/s

\\ \rm\longmapsto v=70\times \dfrac{5}{18}=19.4m/s

\boxed{\sf Acceleration=\dfrac{v-u}{t}}

\\ \rm\longmapsto Acceleration=\dfrac{19.4-5.05}{10}

\\ \rm\longmapsto Acceleration=\dfrac{14.3}{10}

\\ \rm\longmapsto Acceleration=143m/s^2

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What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?
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The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

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The area of a triangle =

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Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

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