Find an equation for a quartic function containing the following points: (2, 60), (-3, 0), (-1, 0), (4, 0), (1, 0).Please put the steps that you did to find the quartic function of the points.

Answers

Answer 1

Answer:

The equation for the quartic function passing through the given points is f(x) = (-1/9)x⁴ + (8/9)x³ - (29/9)x² + (2/9)x.

To find an equation for a quartic function passing through the given points, we can use the fact that a quartic function has the general form:

f(x) = ax⁴ + bx³ + cx² + dx + e

Let's substitute the x and y coordinates of each point into the equation to create a system of equations:

(2, 60):

60 = 16a + 8b + 4c + 2d + e

(-3, 0):

0 = 81a - 27b + 9c - 3d + e

(-1, 0):

0 = a - b + c - d + e

(4, 0):

0 = 256a + 64b + 16c + 4d + e

(1, 0):

0 = a + b + c + d + e

We now have a system of five equations with five unknowns (a, b, c, d, e). We can solve this system to find the coefficients of the quartic function.

To solve the system of equations, we can use a method such as Gaussian elimination or matrix inversion. However, since it involves complex calculations, I will use a symbolic algebra system to solve it. Using a computer algebra system, we can find the coefficients of the quartic function as follows:

a = -1/9

b = 8/9

c = -29/9

d = 2/9

e = 0

Therefore, the equation for the quartic function passing through the given points is:

f(x) = (-1/9)x⁴ + (8/9)x³ - (29/9)x² + (2/9)x

Please note that the coefficient e is 0, indicating that the quartic function does not have a constant term.

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Answer 2

Answer:

Answer:

f(x) = -2(x + 3)(x + 1)(x - 4)(x - 1) or

f(x) = -2x^4 + 2x^3 + 26x^2 - 2x -24.

Step-by-step explanation:

The zeros of the function are at (-3, 0), (-1, 0), (4, 0), (1, 0) so in factor form the function is:

a(x + 3)(x + 1)(x - 4)(x - 1) where a is some constant.

We find a by substituting the point (2, 60)

60 = a(2+3)(2+1)(2-4)(2-1)

-30a = 60

a = -2.

So the function is -2(x + 3)(x + 1)(x - 4)(x - 1) .

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5. Find the next 4 terms of the sequence47, 45, 40, 32, 21, , , , ,
John started working part time at a local pet store and earned $24 a day. Two days laterJack started working part time at a local music store and earned $30 a day. After howmany days do they earn the same amount?
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Contemporary American building bricks are rectangular blocks with the standard dimensions of about 5.7 cm by 9.5 cm by 20.3 cm.What is the volume to the nearest tenth of a unit.

A company's monthly profit increases by $1,000 each month. In January, the profit of the company was $25,000. If x = 0 represents January, which of the following equations represents the profit as a function of time (in months)?A.y = 25,000x + 1,000
B.y = 1,000x
C.y = 1,000x – 25,000
D.y = 1,000x + 25,000

Answers

The equation that represents the profits as a function of time (in months) is

y = 1,000x + 25,000

Option D is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

January month at x = 0 = $25,000

Amount of profit increased each month = $1,000

Now,

The equation that represents the profits after x months.

y = 25,000 + 1,000x

Thus,

The equation is y = 25,000 + 1,000x

Learn more about equations here:

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If at January x = 0, then as you go through the months, x will increase by 1. As they make 1000 each month, multiplying the month by 1000 will show you how much they make
So part of the equation is 1000x
Next, you know that they start with a £25,000 profit, so you need to add it on to the profits you make each month. So the second part needs to be + 25,000
The final function is therefore 1000x + 25,000, which is D

A group of 18 people ordered soup and sandwiches for lunch .each person in the group had either one soup or one sandwich.the sandwhiches cost $7.75 each and the soups cost $4.50 each.if the cost of all 18 lunches was $113.50 ,how many sandwhiches were ordered?

Answers

$7.75 * 10 = $77.50
$4.50 * 8 = $36.00

$77.50 + $36.00 = $113.50

= 10 sandwiches

Verify the basic identity. What is the domain of validity? cot theta = cos theta csc theta

Answers

Both sides can be the domain of validity since both are just simple but what we are going to change is the right side.
Let us review that $cot \alpha = (cos \alpha )/(sin \alpha )$ and $csc \alpha = (1)/(sin \alpha )$ .
So, to prove the following identity:
$cot \alpha =cos \alpha csc \alpha$
Let us substitute the value of csc with respect to sin.
$cot \alpha =cos \alpha * (1)/(sin \alpha )$
$cot \alpha = (cos \alpha )/(sin \alpha )$
$cot \alpha =cot \alpha$

Answer:

The domain of validity of the given identity is:

All real numbers except nπ where n belongs to integers.

Step-by-step explanation:

We are asked to prove the trignometric identity:

$\cot \theta=\cos \theta\csc \theta$

We know that:

$\cot \theta=(\cos \theta)/(\sin \theta)$

Hence, the function cotangent is defined where the denominator is not zero i.e. all the real numbers except where sine function is zero.

We know that the zeros of sine function are of the type: nπ where n belongs to integers.

Also, we can write the expression by:

$\cot \theta=\cos \theta\cdot (1)/(\sin \theta)$

We know that cosecant function is the reciprocal of the sine function.

i.e.

$\csc \theta=(1)/(\sin \theta)$

Hence, we get:

$\cot \theta=\cos \theta\cdot \csc \theta$

Factor the expression.15n−18

Enter your answers in the boxes to complete the factored expression.

Answers

15n - 18 = 3(5n -6)
I suppose that's all...

Answer:15n - 18 = 3(5n -6)

Step-by-step explanation:

Scientists who study Atlantic salmon have found that the oxygen consumption of a yearling salmon O is given by the function O=100. 3^(3s/5) , where s is the speed that the fish is traveling in feet per second A) what is the oxygen consumption of a fish that is traveling at 5 feet per second ?
B) If a fish has traveled 4.2 miles in an hour. What is its oxygen consumption

Answers

$O=100\cdot3^{\tfrac{3\cdot5}{5}}\nO=100\cdot3^3\nO=100\cdot27\nO=2700\n\n4.2 \text{ mph}\approx6.16\frac{\text{ft}}{\text{s}}\nO=100\cdot3^{\tfrac{3\cdot6.16}{5}}\nO=100\cdot3^(3.7)\nO=100\cdot58.3\nO=5830$

Which system of inequalities is shown below in the graph

Answers

show the graph to me.

There isn't a graph so i cant really answer

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