A javelin is thrown in the air. Its height is given by ( ) 1 2 8 6 20 h x x x = − + + , where x is the horizontal distance in feet from the point at which the javelin is thrown. a. How high is the javelin when it was thrown? b. What is the maximum height of the javelin? c. How far from the thrower does the javelin strike the ground?'

This question is incomplete, the complete question is;

A javelin is thrown in the air. Its height is given by h(x) = -1/20x² + 8x + 6

where x is the horizontal distance in feet from the point at which the javelin is thrown.

a. How high is the javelin when it was thrown?

b. What is the maximum height of the javelin?

c. How far from the thrower does the javelin strike the ground?'

a. height of the javelin when it was thrown is 6 ft

b. the maximum height of the javelin is 326 ft

c. distance from the thrower is 160.75 ft

Explanation:

a)

Given h(x) = -1/20x² + 8x + 6

we determine the height when x = 0

h(0) = -1/20(0)² + 8(0) + 6 = 6 ft

therefore height of the javelin when it was thrown is 6 ft

b)

to determine the maximum height of the javelin;

we find the vertex of the quadratic

so

h = - [ 8 / ( 2(-1/20) ) ] = 80

therefore

h(80) = -1/20(80)² + 8(80) + 6

= -320 + 640 + 6 = 326 ft

therefore the maximum height of the javelin is 326 ft

c)

Now the thrower is at the point ( 0,0 ) and the javelin comes down at another point ( x,0 )

this is possible by calculating h(x) = 0

⇒ -1/20x² + 8x + 6 = 0

⇒ x² - 160x - 120 = 0

⇒ x = [ -(-160) ± √( (-160)² - 4(1)(-120) ) ] /  [ 2(1) ]

x = [ 160 ± √(25600 + 480) ] / 2

so

[x = 160.75 ; x = -0.75 ]

distance cannot be Negative

therefore distance from the thrower is 160.75 ft

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards