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ad-work [718]
2 years ago
5

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function

h = –16t2 + 48t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Mathematics
1 answer:
Masja [62]2 years ago
3 0
The equation modeling the height of the ball at time,t is given by h=-16t²+48t+6
<span>a. In how many seconds does the ball reach its maximum height?
Time taken for the ball to reach the maximum height will be given by:
h'(t)=-32t+48=0
finding the value of t we get:
32t=48
t=48/32
t=1.5 seconds
Thus the time taken for the ball to reach the maximum time is 1.5 seconds

b]</span><span> What is the ball’s maximum height?
The maximum height will be:
h(1.5)=-16(1.5)</span>²+48(1.5)+6
h(1.5)=42 fee
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Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc
Mademuasel [1]
Let X is the random number Erik thinks of, and Y is the random number Nita thinks of.
Both X and Y are in the range from 0 to 20.
<span>X<=20
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The difference between the two numbers can be written X-Y, or Y-X depending on which number (X or Y) is greater. But we do not know that. In order not to get negative value, we calculate absolute value of X-Y,  written |X-Y| which will give positive value whether X is greater than Y or not.
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6 0
2 years ago
The square of a number decreased by 3 times the number 28 find all possible values for the number
stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number  

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

a^2 - 3a = 28

a^2 - 3a - 28 = 0

Let us solve the above quadratic equation

\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Using the above formula,

\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28

\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}

Thus the possible values of number are 7 and -4

5 0
2 years ago
Katy had two choices of routes to get her to work. She wanted to choose the route that would get her to work fastest, on average
zmey [24]

Answer:

D. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls within the bounds of the confidence interval.

Step-by-step explanation:

At 5% confidence level, Katy found difference in mean commuting times (Route 1-Route 2) in minutes as (-1,9).

Since no difference in means (0 min) falls within the confidence level (-1,9), we can not reject the hypothesis that there is no difference in mean commuting times when using Route1 or Route2.

A <em>higher</em> significance level(10% etc) may lead a <em>shorter</em> confidence interval leaving 0 outside and may reach a conclusion that Route1 takes longer than Route2

4 0
2 years ago
I'm having trouble on problem 36
denpristay [2]
Jason has x dollars, and Ryan has 5 more dollars than Jason. How many dollars does Ryan have? How many dollars do both boys have?

Jason has x
Ryan has x + 5
both boys have x + x + 5 = 2x + 5


5 0
2 years ago
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