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Maru [420]
3 years ago
9

A ball is thrown straight up from the top of a building 124 ft tall with an initial velocity of 64 ft per second. The height s(t

) (in feet) of the ball from the ground, at time t (in seconds), is given by s(t) = 124 + 64t − 16t2. Find the maximum height attained by the ball.
Mathematics
1 answer:
algol133 years ago
6 0

Answer:

246 ft is the maximum height

Step-by-step explanation:

The height h given above is a quadratic function. The graph of h as a function of time t gives a parabolic shape and the maximum height h occur at the vertex of the parabola. For a quadratic function of the form h = a t² + bt + c, the vertex is located at t = - b / 2a. Hence for h given above the vertex in the question s(t) = 124 + 64t − 16t², is at t

t = -64/2(-16) = 64/32 = 2 seconds

Thus, 2 seconds after the object was thrown, it reaches its highest point (maximum value of h) which is given by

h = -16(2)² + 64 (2) + 124 = 246eet

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Two kinds of crated cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200
BlackZzzverrR [31]

Answer:

The correct answer is option b)

50a+10b<1000; 200a+360b < 7200; a> 0; b>0

Step-by-step explanation:

We are given that Two kind of crated cargo namely A and B to be shipped by truck.

<u>Cargo A:</u>

Volume of each crate of cargo A = 50 cubic ft

Weight of each crate of cargo A = 200 pounds

Let number of crates of cargo A to be shipped = a

Total volume of 'a' crates of cargo A = 50a cubic ft

Total weight of 'a' crates of cargo A = 200a pounds

<u>Cargo B:</u>

Volume of each crate of cargo B = 10 cubic ft

Weight of each crate of cargo B = 360 pounds

Let number of crates of cargo B to be shipped = b

Total volume of 'b' crates of cargo B = 10b cubic ft

Total weight of 'b' crates of cargo B = 360b

Total volume allowed in the truck is 1000 cubic ft

Total volume of 'a' crates of Cargo A and Total volume of 'b' crates of Cargo B = 50a+10b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

50a+10b ....... (1)

Total weight allowed (load limit) in the truck is 7200 pounds

Total weight of 'a' crates of Cargo A and Total weight of 'b' crates of Cargo B = 200a+360b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

200a+360b ....... (1)

And number of crates of cargo A and B are always a positive number.

So, a > 0 and b > 0.

So, the correct answer is option b.

<em>b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0</em>

3 0
3 years ago
Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at colleg
zhenek [66]

Answer:

96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is  [335.89 , 356.10].

Step-by-step explanation:

We are given that a group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during winter 2018.

During March 2018, they randomly sampled 314 BYU students and found that on average, students paid $346 for rent with a standard deviation of $86.

So, the pivotal quantity for 95% confidence interval for the average age is given by;

           P.Q. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = average rent paid by 314 BYU students = $346

            s = sample standard deviation = $86

            n = sample of students = 314

            \mu = population mean monthly rent of all unmarried BYU students

So, 96% confidence interval for the population mean monthly rent, \mu is ;

P(-2.082 < t_3_1_3 < 2.082) = 0.96

P(-2.082 < \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } < 2.082) = 0.96

P( -2.082 \times {\frac{s}{\sqrt{n} } } < {\bar X - \mu} < 2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

P( \bar X -2.082 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ) = 0.96

96% confidence interval for \mu = [ \bar X -2.082 \times {\frac{s}{\sqrt{n} } } , \bar X +2.082 \times {\frac{s}{\sqrt{n} } } ]

                                                = [ 346 -2.082 \times {\frac{86}{\sqrt{314} } } , 346 +2.082 \times {\frac{86}{\sqrt{314} } } ]

                                                = [335.89 , 356.10]

Therefore, 96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is [335.89 , 356.10].

5 0
3 years ago
Given that (2,8) is on the graph of f(x),find the corresponding point for the function -3/4 f(x)
yuradex [85]

Answer:

Corresponding point to (2,8) along -3/4 f(x) = ( -1.5 , -6 )

Explanation:

 When a graph f(x) is multiplied by a factor k, the points on the graph also changes by (kx, ky).

Here it is given that (2,8) is on the graph of f(x)

Now we need to find corresponding point to (2,8) along -3/4 f(x)

x - coordinate = \frac{-3*2}{4} =-1.5

y - coordinate = \frac{-3*8}{4} =-6

So corresponding point to (2,8) along -3/4 f(x) = ( -1.5 , -6 )

8 0
3 years ago
Is it bad to have a foot fettish lol please be honest
Marizza181 [45]

Answer:

i think taht yes my dear friend lol

Step-by-step explanation:

8 0
2 years ago
Brendan is adding to his book collection. He buys 6 books for $15 each. How much money does Brendan spend on the books?
kogti [31]
$90

6 multiplied by 15 is 90, thus $90
7 0
3 years ago
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