MATHEMATICS HIGH SCHOOL

Write an equation of the parabola in intercept form that passes through (−18, 72) with x-intercepts of −16 and −2.

Answers

Answer 1
Answer:

y = a(x + 16)(x + 2)

72 = a(-18 + 16)(-18 + 2)

72 = a(-2)(-16)

72 = a(32)

(72)/(32) = a

(9)/(4) = a

Answer: y = (9)/(4)(x + 16)(x + 2)

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WILL GIVE BRAINLIEST FOR RIGHT ANSWER Solve the equation

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no solution is the answer

What is the value of SZT?

Answers

Answer:

\boxed{m \angle SZT = 121 \degree }

Given:

m \angle RZT = 137 \degree \n m\angle RZS = 56 \degree

Step-by-step explanation:

= > m \angle RZT = m\angle RZS + m \angle SZT \n \n = >157 \degree = 36 \degree+ m \angle SZT \n \n = > 157 \degree - 36 \degree = m \angle SZT \n \n = > 121 \degree = m \angle SZT \n \n = > m \angle SZT = 121 \degree

A relation is:A.) the output (y) values of the relation

B.) the input (x) values of the relation

C.) a set of points that pair input values with output values

D.) x and y values written in the form (x,y)

Answers

D. X and y values written in the form of (x,y)
the answer would be D since x,y is a function

Estimate 219 and 445

Answers

Estimation: 200 and 400. If a number is less than 50, depending on whether in the hundreds or thousands (1500 in this case), the number can be estimated to 2000. But since both numbers are less than 250 or 450, the number remains 200 and 400

(picture) Factoring Polynomials: GCF PLEASEE HELP!!!!!
a
b
c
d

Answers

Answer:

Factored form is 4x(2x+3)

Step-by-step explanation:

8x^2 + 12x

The factors are

8x^2 ----> 2*2*2*x*x

12x  -------> 2*2*3*x

GCF is 2 * 2 * x= 4x

Now we factor out GCF from 8x^2 + 12x

When we factor out GCF, divide each term by 4x

4x((8x^2)/(4x) +(12x)/(4x))

4x(2x +3)

Factored form is 4x(2x+3)

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 rex=(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.

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