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KengaRu [80]
1 year ago
10

A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of

5 feet. The function h(t) = -16t^{2}+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
Mathematics
1 answer:
Flura [38]1 year ago
6 0

The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

Learn more about quadratic equations here:

brainly.com/question/1214333

#SPJ1

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Diane has a rope that is 8 meters long. She cuts away a piece that is 1.67 meters long. How long is the remaining piece of rope?
Readme [11.4K]

Answer:

6.33 m

Step-by-step explanation:

Total length of the rope = 8 m

Cut length of the rope = 1.67 m

We need to find the remaining piece of the rope.

Remaining piece = Total length - cur length

= 8 m - 1.67 m

= 6.33 m

So, 6.33 m is the remaining piece of the rope.

3 0
2 years ago
How much money will she have if she doesn't buy any packs of baseball cards? $16 $18 $19 $20
GrogVix [38]

The amount of money that Carly would have left if she doesn't buy any packs of baseball cards is $20.

<h3>How to calculate the amount of money?</h3>

In order to calculate the amount of money that Carly would have left if she doesn't buy any packs of baseball cards, we would determine the cost of each baseball card as follows:

  • Let the cost of each baseball card be x.
  • Let the number of cards bought be n.

Translating the word problem into an algebraic expression, we have;

x - n = 16

x - 2n = 12

Solving the simultaneous equations by elimination, we have:

n = 4

Therefore, Carly's minimum balance is given by:

x - n = 16

x = 16 + n

x = 16 + 4

x = $20.

Read more on word problems here: brainly.com/question/13170908

#SPJ1

<u>Complete Question:</u>

The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards. How much money will she have if she doesn't buy any packs of baseball cards?

5 0
2 years ago
Factor out the GCF from the terms of the polynomial –4y5 + 6y3 + 8y2 – 2y. A. –2y4 + 3y2 + 4y – 1 B. y(–4y4 + 6y2 + 8y – 2) C. 2
andreyandreev [35.5K]

Answer:

Option D) -2y(2y^4-3y^2-4y+1) is correct

Therefore -4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)

Step-by-step explanation:

Given polynomial is -4y^5+6y^3+8y^2-2y

To factorise the given polynomial by taking out the common terms of the given polynomial :

  • -4y^5+6y^3+8y^2-2y
  • =2y(-2y^4+3y^2+4y-1) ( here 2y is GCF common term so taking outside the terms of the polynomial )
  • =-2y(2y^4-3y^2-4y+1) ( now taking (-) outside )

Therefore -4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)

Option D) -2y(2y^4-3y^2-4y+1) is correct

8 0
3 years ago
Write in simple radical form:
WARRIOR [948]

Answer:

The answer to your question is \frac{2}{3}

Step-by-step explanation:

Here, there is a difference of squares, so just solve it and simplify

              ( 1 + \frac{1}{\sqrt{3} } ) (1 - \frac{1}{\sqrt{3} } )

Multiply the binomials

             = 1 - \frac{1}{3}

Simplify

             = \frac{3 - 1}{3}

             = \frac{2}{3}

7 0
3 years ago
Which of the following points are solutions to the equation 3x - 4y - 8 = 12?
NARA [144]
I got 0-5
Sorry if I’m wrong I try
8 0
2 years ago
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