<span>Highest point = 1406.25
Number of seconds = 9.375
We've been given the quadratic equation y = -16t^2 + 300t which describes a parabola. Since a parabola is a symmetric curve, the highest value will have a t value midway between its roots. So using the quadratic formula with A = -16, B = 300, C = 0. We get the roots of t = 0, and t = 18.75. The midpoint will be (0 + 18.75)/2 = 9.375
So let's calculate the height at t = 9.375.
y = -16t^2 + 300t
y = -16(9.375)^2 + 300(9.375)
y = -16(87.890625) + 300(9.375)
y = -1406.25 + 2812.5
y = 1406.25
So the highest point will be 1406.25 after 9.375 seconds.
Let's verify that. I'll use the value of (9.375 + e) for the time and substitute that into the height equation and see what I get.'
y = -16t^2 + 300t
y = -16(9.375 + e)^2 + 300(9.375 + e)
y = -16(87.890625 + 18.75e + e^2) + 300(9.375 + e)
y = -1406.25 - 300e - 16e^2 + 2812.5 + 300e
y = 1406.25 - 16e^2
Notice that the only term with e is -16e^2. Any non-zero value for e will cause that term to be negative and reduce the total value of the equation. Therefore any time value other than 9.375 will result in a lower height of the cannon ball. So 9.375 is the correct time and 1406.25 is the correct height.</span>
1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
N-2.5 represents the cost for each shirt being subtracted by $2.50 due to the coupon
The area is just the dimensions multiplied, so multiply 7 by 18 and you get 126.
It is B Because you are finding the intrest rate which means find the rate first hen subtract the actual rate to the interest rate<span />
