The height h in feet of a projectile launched vertically upward from the top of a 96 foot tall bridge is givem by h=90+16t-16t^2 where t is time in seconds. what is the maximum height an how long will it tale the projectile to strike the ground?

Hi!

h(t)= -16t^2+16t+90 
h(t) = -16(t^2 - t) + 90 
h(t) = -16(t^2 - t + (1/2)^2) + 90 + 4 
h(t) = -16(t - 1/2)^2 + 94 
vertex at(1/2 , 94) , since a = -16 < 0 , the parabola opens down, which makes the vertex. the global maximum, so: 
Max at(1/2 , 94) 
object hits the ground at h = 0, then: 
-16(t - 1/2)^2 + 94 = 0 
(t - 1/2)^2 = 94/16 = 47/8 
t - 1/2 = ± √(47/8) 
t = 1/2 ± √(47/8) 
t = -1.9 , 2.9 => reject t = -1.9 
t = 2.9 sec => time it takes for the projectile to hit the ground

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.