MATHEMATICS HIGH SCHOOL

Use quadratic regression to find a function that fits the following points. (-2,-16), (3,11), (0,2).

Answers

Answer 1

Answer:

Answer:

y = -1.2x² +6.6x +2

Step-by-step explanation:

The quadratic regression function of a calculator or spreadsheet can do this for you. The resulting function is ...

y = -1.2x² +6.6x +2

_____

If you want to do this by hand, put the given (x, y) values into the formula ...

ax² +bx +c = y

and solve the resulting system of equations.

The third point tells you c=2, so you can simplify the system of equations to ...

a(-2)² +b(-2) +2 = -16 ⇒ 4a -2b = -18 ⇒ 2a -b = -9

a(3)² +b(3) +2 = 11 ⇒ 9a +3b = 9 ⇒ 3a +b = 3

Adding these equations together gives ...

(2a -b) +(3a +b) = (-9) +(3)

5a = -6 . . . . . . . . simplify

a = -1.2 . . . . . . . divide by 5

b = 3 -3a = 3 -3(-1.2) = 6.6 . . . . from the second equation

Now we know the coefficients are a=-1.2, b=6.6, c=2, so the function is ...

y = -1.2x² +6.6x +2

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Answers

\frac{32}{45} [/tex]

Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.

Answers

f(x) = 3x^2 : axis of symmetry is x = 0.
g(x) = x^2 - 4x + 5 = (x - 2)^2 + 1 : axis of symmetry is x = 2
h(x) = -2x^2 + 4x + 1 = -2(x - 1)^2 + 3 : axis of symmetry is x = 1

Therefore, based on their axis of symmetry, f(x) < h(x) < g(x)

Refer to the figure and find the volume V generated by rotating the given region about the specified line.R3 about AB

Answers

Answer:

Hence, volume is: $(34\pi)/(45)$ cubic units.

Step-by-step explanation:

We will first express our our equation of the curve and the line bounded by the region in terms of the variable y.

i.e. the curve is re $x=(1)/(16)y^4$

and the line is given as: $x=(1)/(2)y$

Since after rotating the given region $R_(3)$ about the line AB.

we see that for the following graph

the axis is located at x=1.

and the outer radius(R) is: $(1)/(16)y^4$

and the inner radius(r) is: $(1)/(2)y$

Now, the area of the graph= area of the disc.

Area of graph= $\pi(R^2-r^2)$

Now the volume is given as:

$Volume=\int\limits^2_0 {Area} \, dy$

On calculating we get:

Volume= $(34\pi)/(45)$ cubic units.

The volume V generated by rotating the given region about the specified line R3 about AB is $\boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.$

Further explanation:

Given:

The coordinates of point A is $\left( {1,0} \right).$

The coordinates of point B is $\left( {1,2} \right).$

The coordinate of point C is $\left( {0,2} \right).$

The value of y is $y = 2\sqrt[4]{x}.$

Explanation:

The equation of the curve is $y = 2\sqrt[4]{x}.$

Solve the above equation to obtain the value of x in terms of y.

$\begin{aligned}{\left( y \right)^4}&={\left( {2\sqrt[4]{x}} \right)^4} \n{y^4}&=16x\n\frac{1}{{16}}{y^4}&= x\n\end{aligned}$

The equation of the line is $x = (1)/(2)y.$

After rotating the region ${R_3}$ is about the line AB.

From the graph the inner radius is ${{r_2} = (1)/(2)y$ and the outer radius is ${{r_1}=\frac{1}{{16}}{y^4}.$

${\text{Area of graph}}=\pi\left( {{r_1}^2 - {r_2}^2} \right)$

$Area = \pi\left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left({(1)/(2)y} \right)}^2}}\right)$

The volume can be obtained as follows,

$\begin{aligned}{\text{Volume}}&=\int\limits_0^2 {Area{\text{ }}dy}\n&=\int\limits_0^2{\pi \left( {{{\left({\frac{1}{{16}}{y^4}} \right)}^2} - {{\left( {(1)/(2)y} \right)}^2}} \right){\text{ }}dy}\n&= \pi \int\limits_0^2 {\left( {\frac{1}{{256}}{y^8} - (1)/(4){y^2}} \right){\text{ }}dy}\n\end{aligned}$

Further solve the above equation.

$\begin{aligned}{\text{Volume}}&=\pi \left[ {\int\limits_0^2 {\frac{1}{{256}}{y^8}dy - } \int\limits_0^2{(1)/(4){y^2}{\text{ }}dy} } \right]\n&= \frac{{34\pi }}{{45}}\n\end{aligned}$

The volume V generated by rotating the given region about the specified line R3 about AB is $\boxed{\frac{{34\pi }}{{45}}{\text{ uni}}{{\text{t}}^3}}.$

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Volume of the curves

Keywords: area, volume of the region, rotating, generated, specified line, R3, AB, rotating region.

Which of the following is a name for an isometry that moves or maps every point of the plane the same distance and direction? select all that applie flip, glide, translation, slide, rotation

Answers

Translation is the isometry that moves or maps every point of the plane the same distance and direction. There are several types of translation which include: glide and slide.

So, the type isometry that would apply are the following:
GLIDE, TRANSLATION, SLIDE

Answer:

The translation is the isometry that moves or maps every point of the plane at the same distance and direction. There are several types of translation which include: glide and slide.

So, the type of isometry that would apply is the following:

GLIDE, TRANSLATION, SLIDE

What other information do you need to prove triangle GHK is congruent to triangle KLG by SAS

Answers

The angles of the shapes
shape
size

Use estimation to chose the correct value for this expression 5.1 X 2

Answers

Answer:

10.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

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