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SSSSS [86.1K]
3 years ago
5

PLZZZZZZ NEED HELP!!!!!!!

Mathematics
1 answer:
tatyana61 [14]3 years ago
3 0
The answer is (4,-3.4)
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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40
malfutka [58]
PART A

The given equation is

h(t) = - 16 {t}^{2} + 40t + 4

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4

We add and subtract

- 16(- \frac{5}{4} )^{2}

to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4

We again factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4

This implies that,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4

The quadratic trinomial above is a perfect square.

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4

This finally simplifies to,

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29

The vertex of this function is

V( \frac{5}{4} ,29)

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

29

PART B

When the ball hits the ground,

h(t) = 0

This implies that,

- 16 ( t- \frac{5}{4}) ^{2} +29 = 0

We add -29 to both sides to get,

- 16 ( t- \frac{5}{4}) ^{2} = - 29

This implies that,

( t- \frac{5}{4}) ^{2} = \frac{29}{16}

t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }

t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}

t = \frac{ 5 + \sqrt{29} }{4} = 2.60

or

t = \frac{ 5 - \sqrt{29} }{4} = - 0.10

Since time cannot be negative, we discard the negative value and pick,

t = 2.60s
8 0
3 years ago
Julie runs 1 1/2 miles in 1/3 hour.How many miles will she run per hour at the same speed?
konstantin123 [22]
Multiply 3 * 1 1/2 to find how many miles she runs per hour

1 1/2 * 3

3/2 * 3

9/2

4 1/2       She will run 4 1/2 or 4.5 miles per hour.
4 0
3 years ago
Which expression could be used to determine the area of the square? A square has side lengths of 10.75 meters. (2)(10.75) (4)(10
kolezko [41]

Answer:

Step-by-step explanation:

area of square=10.75² m²

or A=(10.75)(10.75)  m²

3 0
3 years ago
Solving by factoring
puteri [66]

Answer:

3

Step-by-step explanation:

6 0
3 years ago
PLEASE HELP!
Ierofanga [76]

Answer:

even number can be divided by two without areminder

3 0
3 years ago
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