Answer:
IJ = 68.6 feet
Step-by-step explanation:
In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=84°, and HI = 69 feet. Find the length of IJ to the nearest tenth of a foot.
We solve the above question using the Trigonometric function of Sine
sin x = Opposite/Hypotenuse
x = ∠H=84°
Opposite = IJ
Hypotenuse = HI = 69 feet.
Hence
sin 84 = IJ/69
Cross Multiply
IJ = sin 84 × 69
IJ = 68.62201078 feet
Approximately = 68.6 feet
The mode of this set of data is 12
The equation is s=144t - 16t², s being the distance and V=144 ft/s
a)The maximum (or minimum) is reached when the derivative of s = 0
s' = 144 - 32t = 0 and t= 9/2 or 4.5 second (time needed to reach the max
Now plug t= 4.5 in the original equation and you will find s = 324 ft
(Why it's a max and not a minimum: because 2nd derivative is negative and equals s" = -32)
b) Velocity of the ball: distance (up) s=320 ft, time that means:
320 =144t - 16t² (solve for x) -16t²+144t-320 = 0, t₁ =4 and t₂ =5 (t₂ is not valid since max time to reach summit is 4.5) so t =4s , distance = 320. so the velocity at 320ft is 320/4 = 80 ft/s
c) Due to the symmetry of the parabola, the velocity at 320 ft on its way down = 80 ft/s
a
2
+
10
a
+
25
Rewrite
25
25
as
5
2
5
2
.
a
2
+
10
a
+
5
2
a
2
+
10
a
+
5
2
Check the middle term by multiplying
2
a
b
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
a
⋅
5
(5.4×10^2)(2.5×10^8)
= (5.4 x 2.5) (10^2 × 10^8)
= 13.5 x 10^10
= 1.35 x 10^11
