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Fantom [35]
3 years ago
14

An object is launched directly in the air at a speed of 48 feet per second from a platform located 12 feet above the ground. The

position of the object can be modeled using the function f(t)=−16t2+48t+12, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Mathematics
1 answer:
anastassius [24]3 years ago
6 0

9514 1404 393

Answer:

  48 ft

Step-by-step explanation:

For the quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the given quadratic, which defines a parabola opening downward, the axis of symmetry defines the time at which the maximum height is reached.

  t = -48/(2(-16)) = 1.5

Then the maximum height is ...

  f(1.5) = (-16·1.5 +48)1.5 +12 = (24·1.5) +12

  f(1.5) = 48

The maximum height the object will reach is 48 feet.

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5a - 2(4a + 1) + 6(4a - 1)​ show work pls
Mekhanik [1.2K]

Answer:

21<em>a</em> − 8

Step-by-step explanation:

6 0
3 years ago
1. What is the median of the data set?
Tamiku [17]

Answer: 1. 7

2. 100

3. 193.8

4. 0.8

5. 90.6

Step-by-step explanation:

1. Given the data  9,3,10,12,4,5,12,2

For finding the median we arrange it in ascending order

2,3,4,5,9, 10,12,12

Since the no of observations are even

∴ median =\frac{n/2 th term + (n/2 + 1)th term}{2}

= \frac{5+9}{2}

=\frac{14}{2}

=7

i.e. Median =7

2. Given the data

23, 95,100,23,100,100

Since the no 100 is repeated thrice i.e. the maximum no of times

∴ Mode=100

3.

Given the data

108, 305,252,113, 191

Mean=\frac{108+305+252+113+191}{5}

=\frac{969}{5}

=193.8

4. Money spent in the first week

= $11.52, $6.48, $5.99, $14.00, and $9.50

Total for the first week

=11.52+6.48+5.99+14.00+9.50

=$47.49

Now she spent $4 more in the second week

i.e.$47.49+4

=51.49$

Increase in mean =\frac{4}{5}

=0.8

5.

Given

2 students scored 100 each

9 students scored 95 each

10 students scored 90 each

3 students scored 80 each

1 student scored 70

Total score of students =2\times100+ 9\times 95+10\times90+3\times80+70\times1

=2265

The average score

=\frac{2265}{25}

=90.6

8 0
3 years ago
Please help with this pls.
allochka39001 [22]

Answer:

x = 9

(5x9) - 1° = 45 - 1 or 44°

Step-by-step explanation:

the little square indicates the angle is a right angle, measuring 90°

therefore, you can solve for 'x' by creating this equation:

46 + 5x-1 = 90

45 + 5x = 90

5x = 45

x = 9

5 0
3 years ago
Niko has an orange tree and a lemon tree in his backyard the orange tree is 7 feet tall 9 inches tall the lemon tree is 1 yard 2
Dennis_Churaev [7]
We can solve this by converting both measurements to inches.

Orange tree:
1 foot=12 inches
7 feet=84 inches
84 inches + 9 inches = 93 inches total

Lemon tree:
1 yard=3 feet=36 inches
2 feet=24 inches
36 inches + 24 inches + 5 inches=65 inches total

Therefore, the orange tree is taller than the lemon tree.
8 0
3 years ago
Expand and simplify 6(2x - 3) – 2(2x + 1)
Charra [1.4K]

Answer 8x - 20

Step-by-step explanation:

6(2x - 3) - 2(2x + 1)

Distribute

6(2x) -6( 3) - 2(2x) -2( 1)

12x -18 -4x -2

Combine like terms

12x -4x    -18 -2

8x-20

3 0
3 years ago
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