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Otrada [13]
4 years ago
8

3. Melissa knows that 30 miles per hour is equivalent to

Mathematics
1 answer:
VashaNatasha [74]4 years ago
3 0

Answer:

7 0 miles/hour = 103 feet/second

Step-by-step explanation:

Given

30 miles/hour = 44 feet/second

Required

Determine the equivalent of 70 miles per hour

30 miles/hour = 44 feet/second

Multiply both sides by 7/3

\frac{7}{3} * 30 miles/hour = \frac{7}{3} * 44 feet/second

7 * 10 miles/hour = \frac{7}{3} * 44 feet/second

7 0 miles/hour = \frac{7}{3} * 44 feet/second

7 0 miles/hour = \frac{308}{3} feet/second

7 0 miles/hour = 102.67 feet/second

7 0 miles/hour = 103 feet/second <em>(Approximated)</em>

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Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground
Scorpion4ik [409]

Answer:

125.4\ \text{m/s}

Step-by-step explanation:

u = Initial velocity of baseball

\theta = Angle of hit = 30^{\circ}

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

y_0 = Height of hit = 2.5 ft

a_y = g = Acceleration due to gravity = 32.2\ \text{ft/s}^2

t = Time taken

Displacement in x direction

x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}

Displacement in y direction

y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}

The minimum initial velocity needed for the ball to clear the fence is 125.4\ \text{m/s}

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3 years ago
Solve for x &amp; y. 30x−42y=−6 and 5x−7y=−1
vladimir1956 [14]
Um.. Both of those equations are the exact same. Divide both sides of the first equation by 6. You get:

\frac{30x  - 42y}{6} = \frac{-6}{6} \\ 5x - 7y = -1

That is the exact same as the second equation. This system has an infinite number of solutions. 5x - 7y = -1 is a line, so basically every point on that line is a solution to the system.

For example, x = 0 and y = \frac{1}{7} would work, but so would x = 1 and y = \frac{6}{7}
4 0
3 years ago
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
aliya0001 [1]

Answer: Use 1.75 cups of blue and 1 cup of yellow

Step-by-step explanation:

The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

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