write an equation for an exponential function, in the form y=axb^x, whose graph passes through the coordinate points (1, 7.5) and (3, 16.875).

Answers

Answer 1

Answer: 7.5 = a*b^1

16.875 = a* b^3

Divide the last equation by the former

16.875/7.5 = b^ (3-1)

2.25 = b^(2)

extract square root from both sides

b = 1.5

From 7.5 = a*b ⇒ a = 7.5/ (1.5) = 5

The requested function is y = 5 (1.5)^x

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Which equation has an a-value of 1, a b-value of –3, and a c-value of –5?

Answers

Answer:

$x^2-3x-5$

Step-by-step explanation:

The standard quadratic equations are given in the form of

$ax^2+bx+c$

Comparing the values of a , b and c and putting a=1 , b=-3 and c=-5 in the equation we get our quadratic polynomial as

$x^2-3x-5$

c-b=-2a If that is a possibility.

Earlier this year in a drug bust in Shanghi, China, police seized 2.4 tons of methamphetamines. If a typical dosage is 50mg, how many doses is that bust, which the Chinese police prevented from being sold to the public?

Answers

2.4 tons=2.4 tons*(1,000 Kg / 1ton)*(1,000,000 mg / 1 kg)=
=2,400,000,000 mg=2.4 x 10⁹ mg

Now, we solve this problem by the rule of three.

50 mg ---------------------1dose
2.4x10⁹ mg---------------- x

x=(2.4 x 10⁹ mg * 1 dose) / 50 mg=48,000,000 doses.

Answer: 48,000,000 doses

Fifteen tickets cost $193.75. what is the average cost of each ticket

Answers

15 tickets cost = 193.75
So, 1 ticket costs = 193.75 / 15 = 12.92

In short, Your Answer would be $12.92

Hope this helps!

Answer:

$12.92

Step-by-step explanation:

What 2 numbers add up to get 17 and multiply to get -200

Answers

There is no fixed equation when I arrived at these numbers.

I just did trial and error. I came up with 25 and -8 as the numbers.

200 ÷ 25 = 8 ⇒ the sum of 17 depends on the signs of each numbers.

-8 x 25 = -200

-8 + 25 = 17

What is the solution of -11m = -132

Answers

There is one solution to the equation, so let's solve it :D1

Step - Divide both sides of the equation by -11

-11m/-11 = -132/-11

FINAL ANSWER --

m = 12

↑ ↑ ↑ Hope this helps! :D

-11m=-132 / * (-1)
11m=132
m=132:11
m=12

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.

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