1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stellarik [79]
2 years ago
6

a rock is launched from a canon. it's height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

After 1 second, the Rock is 58 ft in the air; after 2 seconds, it is 112 feet in the air. find the height, in feet, of the rock after 10 seconds in the air.
Mathematics
2 answers:
ratelena [41]2 years ago
6 0
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.
lakkis [162]2 years ago
5 0
<h2><em><u>Answer: 400 ft.</u></em></h2><h2><em><u>For Plato</u></em></h2>

You might be interested in
When lines intersect in one place, what are they called?
Deffense [45]
Independent
..............
7 0
3 years ago
Read 2 more answers
Khloe and Emma work at a furniture store. Khloe is paid $245 per week plus 9.5% of her total sales in dollars, xx, which can be
ale4655 [162]

Answer: Their weekly pay would be the same if xx equals $1,600

Step-by-step explanation: The first and most important step is to identify what the question requires, and that is, what is the value of the unknown in the equation of their weekly incomes that would make their pay to be the same? Their weekly pay as per individual is given as follows;

Khloe = 245 + 0.095x ———(1)

Emma = 285 + 0.07x ———(2)

Simply put, we need to find the value of x when equation (1) equals equation (2)

245 + 0.095x = 285 + 0.07x

Collect like terms and we now have

0.095x - 0.07x = 285 - 245

0.025x = 40

Divide both sides of the equation by 0.025

x = 1600

Therefore their weekly pay would be at the same level, if x equals $1600

6 0
3 years ago
I need to know a equivalent fraction for number 7
AlekseyPX
9/10 is equivalent to 90/100 and the answer under mine or above or the other answer should be reported. They got points for a question they did not answer correctly.
7 0
3 years ago
The equation 4(x – 3)2 – 5 = 139 has two solutions: one positive and one negative. What is the
AlekseyPX

Answer:

Step-by-step explanation:

4(x-3)2-5 = 139

(4x-12)-5=139

-20x + 60 = 139

-20x +60 - (60) = 139- 60

-20x = 79 divide both sides by -20

x = -3.95

3 0
3 years ago
Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.
lys-0071 [83]

Answer:

16

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Mr. Salazar assigns the same number of homework questions each school day. The ratio table below shows the total
    12·2 answers
  • HELP !! I NEED SOMEONE TO DO THIS TO ME!!
    12·1 answer
  • Be specific and try!
    12·1 answer
  • Need answers for a and b <br> Thank you
    14·1 answer
  • The solution of the equation...and how to explain the answer
    7·2 answers
  • If You write all numbers from 30 to 65 including 30 and 65 how many times would you write the digit 4?
    14·1 answer
  • The length r of a rope should be at least 5 inches how would you write that as an inequality​
    13·1 answer
  • In 1995, there were 85 rabbits in Central Park. The population increased by 12% each year. How many rabbits
    14·1 answer
  • Someone please help me!!
    14·2 answers
  • (b) Rita bought 15 pounds of rice for $7.How many pounds of rice did she get per dollar?pounds per dollar I need help with this
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!