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Paul [167]
3 years ago
7

The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the

object is 150 feet.
Mathematics
1 answer:
jolli1 [7]3 years ago
6 0
If you've started pre-calculus, then you know that the derivative of  h(t)
is zero where h(t)  is maximum.

The derivative is            h'(t) = -32 t  +  96 .

At the maximum ...        h'(t) = 0

                                       32 t = 96 sec

                                           t  =  3 sec . 
___________________________________________

If you haven't had any calculus yet, then you don't know how to
take a derivative, and you don't know what it's good for anyway.

In that case, the question GIVES you the maximum height.
Just write it in place of  h(t), then solve the quadratic equation
and find out what  't'  must be at that height.

                                       150 ft = -16 t²  +  96  t  +  6 

Subtract 150ft from each side:    -16t²  +  96t  -  144  =  0 .

Before you attack that, you can divide each side by  -16,
making it a lot easier to handle:

                                                         t²  -  6t  +  9  =  0

I'm sure you can run with that equation now and solve it.    
The solution is the time after launch when the object reaches 150 ft.
It's 3 seconds.  
(Funny how the two widely different methods lead to the same answer.)

The answer is from AL2006

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Baily is training to run a marathon. The number of minutes it takes to run the marathon after t weeks of training is M= 300(0.95
Whitepunk [10]

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3 0
3 years ago
A business executive bought 40 stamps for
alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

x + y =40

<em>(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)</em>

Now, let's make an equation for the cost of these stamps.

0.33x + 0.23y = 12.40

<em>(AKA - The cost of the stamps in total, should equal $12.40).</em>

So now, we have our two equations:

x + y =40\\0.33x+0.23y=12.40

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

x+y=40\\x=40-y

Now, let's put this into our second equation.

0.33x+0.23y=12.40\\0.33(40-y)+0.23y=12.40

Distribute, and solve for y.

13.2-0.33y +0.23y =12.40\\13.2-0.1y=12.40\\-0.1y=-0.8\\y=8

Now, we plug this into one of our equations.

x+y=40\\x+8=40\\x=32

In the end, we have thirty-two 33-cent stamps, and eight 23-cent stamps.

3 0
1 year ago
Question 4
den301095 [7]

Answer:

40.2

Step-by-step explanation:

Diameter = 16, Radius = 16/2 = 8

Central angle = 2π/5 radians = 72°

Sector area,

8²π×(72/360)

= 64π/5

= 40.2 (rounded to the nearest tenth)

Answered by GAUTHMATH

6 0
3 years ago
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