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
Karo-lina-s [1.5K]
3 years ago
9

Find constants a , b, and c such that the function

Mathematics
1 answer:
n200080 [17]3 years ago
4 0

Answer: a = -2, b = -2, c = 1.

Step-by-step explanation:

We know that:

y = a*x^2 + b*x + c.

Then:

y' = 2*a*x + b

y'' = 2*a.

Then we can write the equation:

y′′ + y′ − 2y = 4x^2.

as:

2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2

To solve this, the first step is moving all the terms to the same side:

2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0

Now let's group terms with the same power of x.

(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0

Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:

-4 - 2*a = 0

-2*b + 2*a = 0

-2*c + b = 0

From the first equation:

-4 - 2*a = 0

-4 = 2*a

-4/2 = a

a = -2

And from the second equation:

-2*b + 2*a = 0

2*a = 2*b

a = b

b = -2.

From the third equation we have:

-2c + b = 0

-2c = b

c = b/-2 = -2/-2 = 1.

c = 1

Then our equation is:

y = -2*x^2 - 2*x + 1.

You might be interested in
9.)Jeanne has 3 7/8 yards of fabric. She needs 1 1/4 yards to make a pair of
tatuchka [14]

She can make 3 shorts

4 0
2 years ago
Read 2 more answers
You want to place a towel bar that is 24 1⁄4 centimeters long in the center of a door that is 70 1⁄3 centimeters wide. How far s
Leviafan [203]

Heres Is Your Answer Below

<em><u>70 1/3- 24 1/4=?</u></em>

<em><u /></em>

<em><u>70 4/12- 24 3/12= 46 1/12</u></em>

<em><u /></em>

<em><u>46 1/12 /2= 23 1/24</u></em>

<em><u /></em>

<u>23 1/24 Would be Your Answer</u>

<u></u>

<u>Have A Great Day!</u>

3 0
2 years ago
Solve for the 3 sides
mel-nik [20]

Answer:

1. x = 2√3 or 3.46

2. y = 4√3 or 6.93

3. z = 4√6 or 9.80

Step-by-step explanation:

1. Determination of the value of x.

Angle (θ) = 60°

Opposite = 6

Adjacent = x

Tan θ = Opposite /Adjacent

Tan 60 = 6 / x

√3 = 6/x

Cross multiply

x√3 = 6

Divide both side by √3

x = 6 / √3

Rationalise

x = (6 / √3) × (√3/√3)

x = 6√3 / 3

x = 2√3 or 3.46

2. Determination of the value of y.

Angle (θ) = 60°

Opposite = 6

Hypothenus = y

Sine θ = Opposite /Hypothenus

Sine 60 = 6/y

√3/2 = 6/y

Cross multiply

y√3 = 2 × 6

y√3 = 12

Divide both side by √3

y = 12/√3

Rationalise

y = (12 / √3) × (√3/√3)

y = 12√3 / 3

y = 4√3 or 6.93

3. Determination of the value of z.

Angle (θ) = 45°

Opposite = y = 4√3

Hypothenus = z

Sine θ = Opposite /Hypothenus

Sine 45 = 4√3 / z

1/√2 = 4√3 / z

Cross multiply

z = √2 × 4√3

z = 4√6 or 9.80

8 0
2 years ago
Frank’s quarter grades are 82.5, 94.7, and 87.9. What grade, rounded to the nearest percent, will Frank have to earn in the last
Thepotemich [5.8K]
The given final course grade, 88%, is the average of Frank's four quarter grades. The average is the sum of all grades divided among the four quarters. Let x be the average,
                                  (82.5 + 94.7 + 87.9 + x) / 4 = 88
The value of x is equal to 86.9. Thus, the answer is letter C. 87%.

4 0
3 years ago
A certain corporation listed their sales in 100 as 1700. What was their actual volume in thousands?
densk [106]

as I read this one, they listed their sales as 1700, BUT the scale for those numbers are that each 1 is a "100", namely, they're on a 1:100 scale, so the 1700 is really 1700 * 100, or 170000.


170,000 is 170 * 1000, or 170 thousands.

6 0
3 years ago
Other questions:
  • Really need need help on this please
    11·1 answer
  • When using a debit card: Question options: A:There are always fees. b:Identification is always required. c:You still need to rec
    15·1 answer
  • which word equation is used to calculate the acceleration of an object. A)add the initial velocity and final velocity and multip
    15·1 answer
  • Hendrick wants to enlarge a photo that is 4 inches wide and 6 inches tall. The enlarged photo keeps the same ratio. How y'all is
    11·1 answer
  • sandra brown works as a beautician. she earns $1 commission for the first 50 haircuts and a $1.50 for all haircuts over 50. in a
    12·1 answer
  • If f(x)=x^2-x and g(x)=x+1, determine f (g(x)) in simplest from
    8·2 answers
  • Your paycheck (before deductions) varies directly as the number of hours you work. If your paycheck is $211.60 for 23 hours, fin
    12·1 answer
  • Jimmy won 82 super bouncy balls playing basketball at the county fair. At school he gave three to every student in his math clas
    7·2 answers
  • A rhino can run 28 miles per hour. What is that speed in feet per second, to the nearest whole number?
    9·1 answer
  • What is 5.5 feet in centimeters?​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!