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4vir4ik [10]
2 years ago
10

A bullet is shot straight upward with an initial speed of 925 ft/s. The height of the bullet after t seconds is modeled by the f

unction h(t) = −16t2 + 925t where h is measured in feet. Use the function h to find the average speed of the bullet during the given time intervals
Mathematics
1 answer:
never [62]2 years ago
7 0

Answer:

462 ft/s  

Step-by-step explanation:

The height of the bullet is modeled by:

h(t) = -16t² + 925t------------------------------------ (1)

The speed of the bullet is modeled by the first derivative of equation (1)

dh/dt= -32t + 925------------------------------------ (2)

At maximum height,  dh/dt = 0

0 = -32t  + 925

32t = 925

  t  =   925/32

     =   28.91 seconds

This means that the total time to reach maximum height is 28.91 seconds

Substituting into equation (1) we can calculate the maximum  height:

h = -16 (28.91)² +925 (28.91)

  =   -13,372.61 + 26,742.675

  =  13,367.065 ‬ft

Average speed =  Total distance/ Total time

                         =    13,367.065/28.91

                         =  462.368

                         ≈ 462 ft/s  

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KATRIN_1 [288]

Answer:

300

Step-by-step explanation:

5 0
1 year ago
Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of
ehidna [41]

Answer:

The required system of equations is,

y=25+x

y=20+2x.

Step-by-step explanation:

Let the number of hours spent by Lucy = x

It is given that,

Local zoo charges initial fee $25 and per hour fee $1.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=25+x in dollars.

Also, Local citcus charges initial fee $20 and per hour fee $2.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=20+2x in dollars.

Since, the objective function for the situation is to 'minimize the cost'.

So, upon solving the equations, we will get the minimum value as,

25+x = 20+2x

i.e. x= 5

Thus,

y=25+x implies y=25+5 i.e. y= $30

y=20+2x implies y=20+2\times 5 i.e. y=20+10 i.e. y= $30

Thus, the minimum value is $30.

The required system of equations is,

y=25+x

y=20+2x.

8 0
2 years ago
Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.
butalik [34]
(a) Data with the eight day's measurement.
Raw data:      [60,58,64,64,68,50,57,82], 
Sorted data:  [50,57,58,60,64,64,68,82]
Sample size = 8 (even)
mean            = 62.875
median         = (60+64)/2 = 62
1st quartile   = (57+58)/2 = 57.5
3rd quartile  = (64+68)/2 =  66
IQR = 66 - 57.5 = 8.5

(b) Data without the eight day's measurement.
Raw data:      [60,58,64,64,68,50,57]
Sorted data:  [50,57,58,60,64,64,68]
Sample size = 7 (odd)
mean            = 60.143
median         = 60
1st quartile   = 57
3rd quartile = 64
IQR = 64 -57 = 7

Answers:
1. The average is the same with or without the 8th day's data.  FALSE
2. The median is the same with or without the 8th day's data.  FALSE
3. The IQR decreases when the 8th day is included.                  FALSE
4. The IQR increases when the 8th day is included.                   TRUE
5. The median is higher when the 8th day is included.              TRUE

8 0
2 years ago
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5 0
2 years ago
calculeaza lungimea segmentului ab in fiecare dintre cazuri:A(1,5);B(4,5);A(2,-5),B(2,7);A(3,1)B(-1,4);A(-2,-5)B(3,7);A(5,4);B(-
Tatiana [17]

Answer:

1. 3; 2. 12; 3. 5; 4. 13; 5. 10; 6. 10

Step-by-step explanation:

We can use the distance formula to calculate the lengths of the line segments.

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}

1. A (1,5), B (4,5) (red)

d = \sqrt{(x_{2} - x_{1}^{2}) + (y_{2} - y_{1})^{2}} = \sqrt{(4 - 1)^{2} + (5 - 5)^{2}}\\= \sqrt{3^{2} + 0^{2}} = \sqrt{9 + 0} = \sqrt{9} = \mathbf{3}

2. A (2,-5), B (2,7) (blue)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(2 - 2)^{2} + (7 - (-5))^{2}}\\= \sqrt{0^{2} + 12^{2}} = \sqrt{0 + 144} = \sqrt{144} = \mathbf{12}

3. A (3,1), B (-1,4 ) (green)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-1 - 3)^{2} + (4 - 1)^{2}}\\= \sqrt{(-4)^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25} = \mathbf{5}

4. A (-2,-5), B (3,7) (orange)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(3 - (-2))^{2} + (7 - (-5))^{2}}\\= \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = \mathbf{13}

5. A (5,4), B (-3,-2) (purple)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-3 - 5)^{2} + (-2 - 4)^{2}}\\= \sqrt{(-8)^{2} + (-6)^{2}} = \sqrt{64 + 36} = \sqrt{100} = \mathbf{10}

6. A (1,-8), B (-5,0) (black)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-5 - 1)^{2} + (0 - (-8))^{2}}\\-= \sqrt{(-6)^{2} + (-8)^{2}} = \sqrt{36 + 64} = \sqrt{100} = \mathbf{10}

6 0
1 year ago
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