Mathematics, 03.06.2021 17:30 destinydiamond6887

The height, h metres, of a springboard diver above the surface of the water t seconds after she leaves the board is given by h=-5t-12+7. Find the maximum height reached by the diver? How long does it take for the diver to reach maximum height? Find the height of the diving board?

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Answer from: maya611

$h_{max} = 14.2m$

t = 1.2

The height of the diver is 7m

Step-by-step explanation:

Given

h(t) =-5t^2 + 12t + 7

Solving (a): The maximum height reached

First, we calculate the time to reach the maximum height using:

$t = - \frac{b}{2a}$ --- maximum of a function

Where

a = -5; b = 12; c = 7

So, we have:

$t = -\frac{12}{-2 * 5}$

$t = \frac{12}{10}$

t = 1.2

So, the maximum height is:

h(t) =-5t^2 + 12t + 7

h(1.2)=-5 * 1.2^2 + 12 * 1.2 + 7

h(1.2)=14.2

Hence:

$h_{max} = 14.2m$

Solving (b): Time to reach maximum height

This has been calculated in (a)

t = 1.2

Solving (c): Height of the board.

This can be calculated by setting t =0 --- i.e. the height of the diver before diving

So, we have:

h(t) =-5t^2 + 12t + 7

h(0) = -5 * 0^2 + 12 * 0 + 7

h(0) = 7

Answer from: Quest

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

The graph below shows the value of a $100 deposited into three different accounts over a period of 2

Answer from: Quest

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

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