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iVinArrow [24]
3 years ago
10

A rock is launched from a cannon. After 1 second, the rock is 58 feet in the air; after 2 seconds, it is 112 feet in the air. Us

ing the quadratic function, find the height, in feet, of the rock after 10 seconds in the air
Mathematics
1 answer:
max2010maxim [7]3 years ago
8 0

Answer:

Step-by-step explanation: This is the quadratic function:

h(x)=ax²+bx+c

We have two points:

(1,58)

(2,112)

Now, we calculate this quadratic funtion.

we assume that h(0)=0

Therefore:

a(0)²+b(0)+c=0

c=0

(1,58)

a(1)²+b(1)=58

a+b=58  (1)

(2,112)

a(2)²+b(2)=112

4a+2b=112

2a+b=56  (1)

With the equations (1) and (2) we make a system of equations:

a+b=58

2a+b=56

we can solve this system of equations by reduction method.

-(a+b=58)

2a+b=56

---------------------

a=-2

-2(a+b=58)

2a+b=56

-------------------

      -b=-60  ⇒  b=60

The function is:

h(x)=ax²+bx+c

h(x)=-2x²+60x

Now find the height, in feet, of the rock after 10 seconds in the air.

h(10)=-2(10)²+60(10)

h(10)=-200+600=400

Answer: 400 ft.

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Oksana_A [137]

Given:

Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.

He is only allowed to work 13 hours total per week.

He wants to make at least 65 dollars.

To find:

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Solution:

Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.

He is only allowed to work 13 hours total per week.  It means sum of x and y must be less than or equal to 13.

x+y\leq 13

He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.

4x+7y\geq 65

Number of hours can not be negative.

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Therefore, the required system of inequalities contains some equations,  x+y\leq 13,4x+7y\geq 65 and x, y\geq 0.

4 0
3 years ago
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
Kisachek [45]
<span>This is a quadratic equation . We order to equate to zero

</span>2x²<span> – 7 = 9  
 </span>
2x² - 7-9 = 0
2x² - 16 = 0

This equation is a binomial
2* (x² - 8) = 0
<span>We choose the simplest method . The equation with practice it can be calculated in the memory
</span><span>
The product is equal to 0 if one of the factors is zero
</span>
2≠0  ∨     x² - 8 = 0
               x² = √8
               x = √8     ∨  x= - √8

Answer : x = √8 ∨ x = -√8
5 0
3 years ago
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Answer:

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Step-by-step explanation:

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8 0
3 years ago
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Answer:

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Step-by-step explanation:

y=mx+b

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1 because for every 10 it goes to the right, it goes up 10 as well.

b=10 because the function crosses the y-axis at 10

so

y=x+10

4 0
3 years ago
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