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Andrej [43]
3 years ago
8

A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 1.5 feet, 30 feet a

way from the player. The height y (in feet) of a second hockey puck is modeled by y=x(0.08−0.002x), where x is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
3 0

Answer:

x₁ > x₂

Step-by-step explanation:

Both actions imply a parable trajectories, since both are projectile shot cases.

Let´s call x₁ maximum distance in the first case

The maximum height is just in the middle of the curve, therefore x₁ the maximum horizontal distance is equal to 60 feet.

In the second case, the parable curve is modeled by:

y = x₂*( 0.08 - 0.002x₂)    or  y = 0.08*x₂ - 0.002*x₂²

A second degree equation, solving for x₂ and dismissing the value x₂ = 0

we get:

y = 0       ⇒    x₂*( 0.08 - 0.002x₂) = 0    x₂ = 0

And 0,08 - 0.002*x₂ = 0

- 0.002*x₂ = - 0.08

x₂ = 0.08/0.002

x₂ = 40 f

Then  x₁ > x₂

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The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.
tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}

so, it passes through the midpoint of AB,

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}

4 0
3 years ago
To make rice, you mix 1.5 cups of water for every 1 cup of dry rice. This will make 2 servings. How many cups of dry rice and ho
dalvyx [7]

Answer:

7.5 cups of water

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Step-by-step explanation:

In total 1.5 water and 1 cup rice will equal 2 servings. If you are serving 10 people, you need to multiply each by 5.

6 0
3 years ago
How do u figure -11/4+1/2
worty [1.4K]

Answer:

-2 1/4 or -9/4, depending if the question says simplified or not.

Step-by-step explanation:

-11/4 + 1/2

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4 0
3 years ago
Vector u has a magnitude of 5sq rt 3 feet and is directed due west. Vector v has a magnitude
Vikki [24]

The magnitude and the direction angle for  the resultant vector are 10N and 120degrees respectively

The formula for calculating the resultant vector is expressed as:

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u = -5√3 feet (west direction)

v = 5 feet

Substitute the given values into the formula above;

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The magnitude of the resultant vector is 10feet

Get the direction:

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Since tan is negative in the second quadrant, hence;

\theta = 180 - 60\\\theta = 120^0

Hence the magnitude and the direction angle for  the resultant vector are 10N and 120degrees respectively.

Learn more here: brainly.com/question/5177683

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Dmitrij [34]
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Sorry if I got that wrong
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3 years ago
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