Mathematics High School

Determine the area of the region bounded by f(x)=√x and g(x)=x/2 on the interval [0,16]. Area =64.

Answers

Answer 1

The area bounded by f(x) = √x and g(x) = x/2 on the interval [0,16] is 64.

To find the area bounded by the given functions, we need to determine the points of intersection. Setting f(x) = g(x), we get:

√x = x/2

Squaring both sides, we get:

x = 0 or x = 16

So the points of intersection are (0,0) and (16,8).

Next, we need to determine which function is on top in the interval [0,16]. We can do this by comparing the values of the two functions at x = 8, which lies in the middle of the interval. We have:

f(8) = √8 = 2√2

g(8) = 8/2 = 4

Since f(8) < g(8), the function g(x) is on top in the interval [0,16]. Therefore, the area bounded by the two functions is given by:

∫[0,16] (g(x) - f(x)) dx

= ∫[0,16] (x/2 - √x) dx

= [x^2/4 - (2/3)x^(3/2)] [0,16]

= (16^2/4 - (2/3)16^(3/2)) - (0 - 0)

= 64

Hence, the area bounded by the two functions is 64.

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Related Questions

Jordan bought 3 bags of chips and 4 bars of chocolate and paid $7.25. Diego bought 2 bags of chips and 3 bars of chocolate and paid $5.25. What is the cost of a bag of chips and a bar of chocolate?

Answers

Answer:

Step-by-step explanation:

Please help..........

Answers

Maybe try

[tex] \frac{z - y}{x} [/tex]

If that doesn't work, tell me.

The range for the set of data represented by the following box-and-whisker plot is 8.

Answers

Answer:

True

Step-by-step explanation:

The range is the difference between the lowest and the highest values of the set:

19 - 11 = 8

The answer is TRUE

Answer:

true

Step-by-step explanation:

A population numbers 15,500 and grows at 3.75% per year. Write an exponential model for the growth of this population.

Answers

Answer: [tex]f(x)=15500(1.0375)^x[/tex]

Step-by-step explanation:

The exponential model for growth is given by :-

[tex]f(x)=A(1+r)^x[/tex], where A = initial value , r = growth rate (in decimal), x = time  (in years).

Given: A= 15,500      r= 3.75% = 0.0375

The exponential model for the growth of this population will be :

[tex]f(x)=15500(1+0.0375)^x\\\\\Rightarrow\ f(x)=15500(1.0375)^x[/tex]

hence, the required model: [tex]f(x)=15500(1.0375)^x[/tex]

Mike's car holds 14 2/5 g of gas, averages 20mpg. About how far can Mike's travel if his tank is 1/4 full?

Answers

Solution :

It is given that :

The car of Mike's can hold = [tex]$14 \frac{2}{5}$[/tex] g of gas.

                                            [tex]$=\frac{72}{5}$[/tex] g of gas

∴ [tex]$=\frac{1}{4} $[/tex] th of [tex]$\frac{72}{5}$[/tex] g of gas is  [tex]$=\frac{1}{4} \times \frac{72}{5}$[/tex]

                                          [tex]$=\frac{18}{5}$[/tex] g of gas

                                         

The average distance that the car can travel when the tank is full is = 20 mpg

∴ In  [tex]$\frac{72}{5}$[/tex] g of gas, the car travels = 20 mpg

   In 1 g of gas, the car travels = [tex]$20 \times \frac{5}{72} $[/tex] mpg

   So in  [tex]$\frac{18}{5}$[/tex] g of gas, the car travels = [tex]$20 \times \frac{5}{72} \times \frac{18}{5} $[/tex] mpg

                                                          = 5 mpg

is 3+5(9+2n)equal to48+5n

Answers

Answer: No
There is no logical way to get ‘5n’

Choose ALL the angles with a measure less that 90 degrees.

Answers

Answer:

Top left    Top middle     Bottom Left       Bottom right

Step-by-step explanation        

If the angle makes an "L" it is a 90 degrees angle or a right angle

If the angle makes a "V" it is less than 90 degrees or an acute angle

If the angle makes a "Stretched out  V" it is more than 90 degrees or an obtuse angle

The option that represents the acute angle will be option A, option B, option D, and option F.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The types of angles are as follows:

If the angle is less than 90° then the angle is known as an acute angle.If the angle is equal to 90° then the angle is known as a right angle.If the angle is more than 90° then the angle is known as an obtuse angle.

Then the option that represents the acute angle will be option A, option B, option D, and option F.

More about the angled link is given below.

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Por un tubo de 2.5 cm de diámetro fluye agua con una repidez de 20 cm/s ¿Cuál es el valor del flujo y el gasto del agua?

Answers

Answer:

El flujo y gasto de agua es aproximadamente 98.175 centímetros cúbicos por segundo.

Step-by-step explanation:

El gasto del agua ([tex]Q[/tex]), medido en centímetros cúbicos por segundo, es el flujo que pasa a través del tubo. La ecuación para determinar el gasto es:

[tex]Q = \frac{\pi}{4}\cdot D^{2}\cdot v[/tex] (1)

Donde:

[tex]D[/tex] - Diámetro del tubo, medido en centímetros.

[tex]v[/tex] - Velocidad del flujo, medida en centímetros por segundo.

Si sabemos que [tex]D = 2.5\,cm[/tex] y [tex]v = 20\,\frac{cm}{s}[/tex], entonces el flujo y gasto del agua es:

[tex]Q = \frac{\pi}{4}\cdot (2.5\,cm)^{2}\cdot \left(20\,\frac{cm}{s} \right)[/tex]

[tex]Q \approx 98.175\,\frac{cm^{3}}{s}[/tex]

El flujo y gasto de agua es aproximadamente 98.175 centímetros cúbicos por segundo.

in a week 13 hens laid 78 eggs what is the unit rate for eggs per hen?

Answers

Answer:

6 eggs per hen

Step-by-step explanation:

78/13=6 eggs per hen

Pls help FAST I’m giving brainliest

Answers

The answer to this would be 15-4x

This is a short answer question.
Describe what the graph and equation look like for each of the parent functions.

Answers

Answer:

there you go there's your answers

Step-by-step explanation:

→A parent function is the simplest function of a family of functions. of this form is y = x2. The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II.

€xample→

For example, you can simplify "y=2*sin(x+2)" to "y=sin(x)" or "y=|3x+2|" to "y=|x|." Graph the result. This is the parent function. For example, the parent function for "y=x^+x+1" is just "y=x^2," also known as the quadratic function.


The Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week,
he sold $4,500 worth of stocks. How much did he make last week in commission? If he averages
that same amount each week, how much did he make in commission in 2011?

Answers

I’m pretty sure it’s 33,390

Hello
I have to write at least 20 words to say hi.

Answers

Hi

I have to write at least 20 words to say hello.

PLEASE HELP WILL MARK BRAINLIEST!!!
Select all that are equivalent to sin∠GFH

Answers

Answer:

I think sin<GEJ IS equivalent to sin∠GFH

All that are equivalent to sin∠GFH is

D) cos(&lt;EGJ)

"Corresponding angles"

sin(&lt;GEJ)cos(&lt;FGH)cos(&lt;EGJ)

From the image JE and HF are parallel.

So angle GFH and angle GEJ are corresponding angles.

So they are equal.

so, sin(&lt;GFH) = sin(&lt;GEJ).

From triangle GFH, &lt;GFH+&lt;FGH = 90.

So, sin(&lt;GFH) =cos(&lt;FGH).

Again &lt;FGH = &lt;EGJ.

So, sin(&lt;GFH) =cos(&lt;EGJ)

All that are equivalent to sin∠GFH is cos(&lt;EGJ).

Thus, the correct answer is D.

Learn more about corresponding angles: https://brainly.com/question/2009183

An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth

Answers

Answer:

Step-by-step explanation:

X = distance between eagle and mouse.

sin(15°) = 280/x

X = 280/sin(15°) = 1,081.837 ft

can someone answer this for me please and thank you !!

Answers

Answer:

gfcdxgstez5xdyrfctugv-

_=+86545

Step-b57645745y-step explanation:

uygtf57d4ftv

Help Please is the answer zero? I’m not good with algebra

Answers

Answer:

should be 0 because it isnt increasing or decreasing

Help me please :)....

Answers

Answer:

a = 6, b = 12, c = 18, d = 12

Step-by-step explanation:

9^6 * 9^3 =


Give the answer in exponent form

Answers

Step-by-step explanation:

1,983593e11

Answer:

9^18

Step-by-step explanation:

Since the bases are the same digit, all you have to do is multiply the exponents to get your answer

The cactus grill has decided to run a special on Wednesday night where every table gets 10% off their bill find the total for this table

Answers

B? I pretty sure it’s b

Exponent shown below

Answers

I believe that it’s 7^16

7^14*1 * 7^2

x ^ a+b
7^16

The mid point of a given line segment must lie on the given line segment

true or false

Answers

Answer: The answer is true .

(3x +7x² + 2x + 3) + (x + 1)

Answers

Answer:

=7x2+6x+4

Step-by-step explanation:

3x+7x2+2x+3+x+1

Combine Like Terms:

=3x+7x2+2x+3+x+1

=(7x2)+(3x+2x+x)+(3+1)

=7x2+6x+4

Answer:

=7x2+6x+4

What is the value of x? 5 + 1/5x = 5

Answers

Pretty sure that’d be 0 or No Solution

Answer:

x = 0

Step-by-step explanation:

5 + 1/5x = 5

Subtract 5 from both sides.

1/5x = 0

Divide both sides by 1/5

x = 0

I hope this helps!

Solve the equation. 8| n | − 1 = 15
A.n=2
B.n=2 or n=-2
C.n=8 or n=-8
D. No solution

Answers

Answer:

8n=15+1

8n=18

divide both sides by 8

n=2 A

The price of a plain bowl plus the price
of
extra ingredients equals $

Answers

Answer:3,13

Step-by-step explanation:the price of the bowl is 10$ then you add 3 extra ingredients for a dollar each 10+3=13

Answer:

3,13

Step-by-step explanation:

The price of a television is $567.31. The state sales tax rate is 8.3%.

What is the total cost of the television?

Answers

 

that in the image could be your answer but i rlly dont know thats the way I was taught

What is a numerical expression? Give an example.

Answers

Answer:

Step-by-step explanation:

The term numerical expression is made up of two words, numerical meaning numbers, and expression meaning phrase. ... A numerical expression in mathematics can be a combination of numbers, integers combined using mathematical operators such as addition, subtraction, multiplication, or division.

[tex]tan(0)=\frac{5\sqrt{20} }{11}[/tex]

Answers

Answer:

0.035°

Step-by-step explanation:

We need to find the value of  [tex]\theta[/tex] for the given expression. So,

[tex]\tan\theta=\dfrac{5\sqrt{20}}{11}[/tex]

or

[tex]\theta=\tan^{-1}\tan\left(\frac{5\sqrt{20}}{11}\right)\\\\=-2.0083\ radian[/tex]

Or we can write as :

[tex]\theta=0.035^{\circ}[/tex]

So, the value of [tex]\theta[/tex] is equal to 0.035°.

Mr. Berger assigned the following system of equations to be solved for homework.

2 x minus 3 y = negative 12. 4 x + y = negative 10.

Which is the x-coordinate of the correct solution?
x = negative 3
x = negative one-fifth
x = StartFraction 9 Over 7 EndFraction
x = 2

Answers

Answer:

x=-3

Step-by-step explanation:

2 x - 3 y = -12.

4 x + y =  -10.

Answer:

X=3

Step-by-step explanation:

Trust me ;))

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