To solve you need to set the equation equal to 6 (the height at which the player caught the ball.

6 = -16t^2 + 70t + 4

Next put the equation in standard form by subtracting 6 from both sides

-16t^2 + 70t - 2 = 0

This equation can be simplified by dividing by 2

-8t^2 + 35t - 1 = 0

This equation cannot be factored, but we can use the quadratic formula to find a value for x. Using the equation above we can find the values for a=-8, b = 35 and c = -1.

using the quadratic formula we can solve for x

-b +/- sqrt(b^2 - 4ac)
-------------------------------
2a

The solutions are

0.03 and 4.35. as 0.03 seems an unrealistic time to hit and catch a baseball we would expect the time to be 4.35 seconds.

8 0

3 years ago

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping c

g100num [7]

Answer:

a) 0.4567

b) 6 hours

Step-by-step explanation:

We are given the following information the question:

The battery life follows a normal distribution with

$\mu = 9.75\\\sigma = 2.3$

Formula:

$z = \displaystyle\frac{x-\mu}{\sigma}$

a) We have to find probability such that battery life exceeds 10 hours, that is,

P(X>10)

$P(z > \displaystyle\frac{10 - 9.75}{2.3}) = P(z>0.1086)\\\\= 1 - P(z \leq 0.1086)\\= 1- 0.5433\\=0.4567$

b) We have to find battery life such that

$P(X \leq x) = 0.05\\\\P(z \leq \displaystyle\frac{x-9.75}{2.3}) = 0.05\\\\\displaystyle\frac{x-9.75}{2.3} = -1.64 \\\\x = (-1.64)(2.3) + 9.75\\x = 5.978$

Here, we calculated the value of z from the normal distribution table.

So, after approximately 6 hours one should plan to recharge the phone.

7 0

3 years ago

5. mc035-1.jpg What is the area of the kite? 135 m2 216 m2 90 m2 108 m2

Ahat [919]

Pls. see attachment.

9√2 → 12.73

sin θ = opposite / hypotenuse
sin 45° = opposite / 12.73
0.707 * 12.73 = opposite
9 = opposite

cos θ = adjacent / hypotenuse
cos 45° = adjacent / 12.73
0.707 * 12.73 = adjacent
9 = adjacent

Area of a kite = pq/2
p = 9 + 9 = 18
q = 9 + 6 = 15

Area = (18m*15m) / 2
Area = 270m² / 2
Area = 135 m²

The area of the kite is 135 m².

5 0

3 years ago