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Gala2k [10]
3 years ago
14

I NEED ANSWER ASAP!!! PLEASE HELP!!! A shot put is thrown upward with a velocity of 35 ft./sec. at a height of 4 ft. and an angl

e of 40°. How long will it take for the shot put to be a horizontal distance of 40 ft. from the person throwing it? Acceleration due to gravity is 32 ft/s^2. Round your answer to the nearest hundredth.
Mathematics
1 answer:
krek1111 [17]3 years ago
4 0
The horizontal component of the velocity of the shot is 35 cos 40 ft/sec which is constant
Therefore:-
Velocity = distance / time
35 cos 40  = 40 / t

t = = 40 / 35cos40  =  1.49 seconds to nearest hundredth

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Maths functions <br> please help!
Vlad [161]

Answer:

\textsf{1)} \quad f(x)=-x+3

2)   A = (3, 0)  and C = (-3, 0)

\textsf{3)} \quad g(x)=x^2-9

4)  AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}

<h3><u>Part (1)</u></h3>

Given points:

  • H = (-1, 4)
  • T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4

\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1

Subtract the first equation from the second to eliminate c:

\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

\implies f(4)=-1(4)+c=-1

\implies c=-1-(-4)=3

Therefore the equation for function f(x) is:

f(x)=-x+3

<h3><u>Part (2)</u></h3>

Function f(x) crosses the x-axis at point A.  Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

\implies f(x)=0

\implies -x+3=0

\implies x=3

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

<h3><u>Part (3)</u></h3>

Points on function g(x):

  • A = (3, 0)
  • G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0

\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8

Subtract the second equation from the first to eliminate b:

\begin{array}{r l} 9a+b & =  \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& =  \phantom{))}8}\end{aligned}

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

\implies g(3)=1(3^2)+b=0

\implies 9+b=0\implies b=-9

Therefore the equation for function g(x) is:

g(x)=x^2-9

<h3><u>Part 4</u></h3>

The length AC is the difference between the x-values of points A and C.

\implies x_A-x_C=3-(-3)=6

Point B is the y-intercept of g(x), so when x = 0:

\implies g(0)=(0)^2-9=-9

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

\implies y_O-y_B=0-(-9)=9

Therefore, AC = 6 units and OB = 9 units

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I believe you have to get all the like terms on the same side. So since 7m+n is being divided by Q in order to move it to the other side of the equal sign you must multiply each side by Q. Then you would end up with 7m+n=2m(q). 7m and 2m are alike so you then take the 2m and subtract it from each side. So your equation should look like 7m-2m+n=Q. Then combine your like terms and you end up with 5m+n=q 
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(2y + 9)(3y - 1) = 5y2 + 25y - 9
Vikki [24]

Answer:

y1= 0, y2= 5/3

Step-by-step explanation:

Remove the parentheses and multiply

then cancel the equal terms

collect the lie terms

move the variables to one side

divide both sides by two

split into possible cases

then solve the equation to get

y= 0 and

y= 5/3

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timama [110]

Hello!

\large\boxed{z = 75^{\circ}}

In an isosceles trapezoid, both angles on each side of the base are congruent.

∠z ≅ 75°

∠y ≅ ∠x

Because of this, we can get the angle measure for z easily:

m∠z = 75°

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3 years ago
One and seven tenths in decimal form
Dima020 [189]
1/7 is .14285714 I hope this helps!
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3 years ago
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