Please help me with math

Oliver hits a baseball at 3 feet above the ground with an initial speed of 135ft/sec at an angle of 20 degrees with the horizont

Serhud [2]

Answer:

Option B) the ball lands in front of the wall

Explanation:

1. Find the vertical and horizontal components of the initial velocity

a) Horizontal component:

$v_{0,x}=v_0\times cos(20\º)=135ft/s\times cos(20\º)=126.86ft/s$

b) Vertical component:

$v_{0,y}=v_0\times sin(20\º)=135ft/s\times sin(20\º)=46.17ft/s$

2. Find the time when the ball runs 380 feet horizontally:

$x=v_{0,x}\times t\\\\380ft=126.86ft/s\times t$

$t= (380ft)/(126.86ft/s)=2.995s\approx 3.0s$

3. Find the height of the ball when the time is 3.0s

$y=y_0+v_{0,y}\times t-gt^2/2$

y₀ = 3 ft
g ≈ 32.174 ft/s²

$y=3ft+46.17ft/s\times 3.0s-32.174ft/s^2\times (3.0s)^2/2$

$y=-3.3ft$

This result means that the ball does not reach the wall because it has fallen to the ground (when y = 0) before 3.0s.

5 0

3 years ago

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2

NeX [460]

Answer:

substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

x = 6y -8

7(6y -8) -y = -2 . . . . . x variable eliminated

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The second equation is easily solved for y, so you could substitute that into the first equation.

y = 7x +2

-x +6(7x +2) = 8 . . . . . y-variable eliminated

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The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

7(-x +6y) +(7x -y) = 7(8) +(-2)

42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

(-x +6y) +6(7x -y) = (8) +6(-2)

-x +42x = -4 . . . . . . . . y-variable eliminated

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It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

3 0

4 years ago

Find the values of x and y that make these triangles congruent by the HL Theorem.

Temka [501]