Fit a quadratic function of the form f(t)=c0+c1t+c2t2f(t)=c0+c1t+c2t2 to the data points (0,−5)(0,−5), (1,5)(1,5), (2,−3)(2,−3), (3,11)(3,11), using least squares.

Therefore the required quadratic polynomial is

Step-by-step explanation:

Given quadratic function is

Given data (0,-5), (1,5) , (2,-3) and (3,11)

Its means f(0)= -5, f(1)= 5, f(2) = -3 and f(3)=11

Let

  ,        and

We can write this system as

Since

we have ,ker A= {0}

Therefore

Putting the values of in the given quadratic equation

Therefore the required quadratic polynomial is

let's solve your equation step-by-step.

24−3x=−27

step 1: simplify both sides of the equation.

24−3x=−27

24+−3x=−27

−3x+24=−27

step 2: subtract 24 from both sides.

−3x+24−24=−27−24

−3x=−51

step 3: divide both sides by -3.

−3x

−3

=

−51

−3

x=17

answer:

x=17

step-by-step explanation:

mark brainliest and have a great day!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240