What is the largest possible integral value in the domain of the real-valued function

f(x)=[tex]\frac{1}{\sqrt{800-2x} }[/tex]

Answers

Answer 1

Answer:

Max Value: x = 400

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

AntiderivativesIntegral Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Method: U-Substitution[Integration] Reverse Power Rule: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C[/tex]

Step-by-step explanation:

Step 1: Define

[tex]f(x) = \frac{1}{\sqrt{800-2x} }[/tex]

Step 2: Identify Variables

Using U-Substitution, we set variables in order to integrate.

[tex]u = 800-2x\\du = -2dx[/tex]

Step 3: Integrate

Define:                                                                                                            [tex]\int {f(x)} \, dx[/tex]Substitute:                                                                                         [tex]\int {\frac{1}{\sqrt{800-2x} } } \, dx[/tex][Integral] Int Property:                                                                                     [tex]-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx[/tex][Integral] U-Sub:                                                                                           [tex]-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du[/tex][Integral] Rewrite:                                                                                          [tex]-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du[/tex][Integral - Evaluate] Reverse Power Rule:                                                 [tex]-\frac{1}{2}(2\sqrt{u}) + C[/tex]Simplify:                                                                                                         [tex]-\sqrt{u} + C[/tex]Back-Substitute:                                                                                            [tex]-\sqrt{800-2x} + C[/tex]Factor:                                                                                                           [tex]-\sqrt{-2(x - 400)} + C[/tex]

Step 4: Identify Domain

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.


Related Questions

Please help!

Select the correct answer from each drop-down menu.
On a horizontal number line, -6 is located to the [blank] of -4. So, -6 is [blank] than -4.

First blank- left, right,
Second blank- greater, less,

CORRECT ANSWER GET'S BRAINLIEST!

Answers

Answer:

To the "LEFT", so -6 is "LESS"

Step-by-step explanation:

-6 < -4

PLS HELP ME PLS whats 2x6x8 (5/8)

Answers

Answer:

96 5/8?????

if its wrong i sorryyy

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

If you mean multiplying them all, then:

2x6x8=96

5/8=0.625

0.625x96=60

yay its 60

If the area of the base of a cone is 58 pi square inches, and the height is 3 inches, then which expression represents the volume of a cylinder?

Answers

43

I need help guys go to my account and answer my question pls I need help pls,pls,pls pls pls,

Help with 3-5 plz I will mark brainliest and plz show steps thx

Answers

Answer:
-2
Step by step:
If yu create a number line and start at 3 and go back 5 times it’ll take yu to -2

Write an equation in Point Slope Form that has a slope of -5 and passes through the point (4,9)

Answers

Answer:

I hope that will be help full to u

Step-by-step explanation:As we know point slope form , (Y- Y1) = m (X- X1) As given data ,  m = -5(X1,Y1) =  (4, 9) X1= 4 , Y1= 9putt in the above equation these values, we get Y-9 = (-5) ( X-4) Y-9= -5X +20Y= -5X+29  Ans

As more years go by, the prediction (extrapolation) becomes reliable.

Answers

Answer:

Less

Step-by-step explanation:

edge 2020

Answer:A.)less

Step-by-step explanation:

edge 2023

NEED HELP FASTTTTT!!! WILL GIVE BRAINLIEST!!!

Answers

Answer: -36

Step-by-step explanation:

Eli wanted to order candy online. Company A 2 1/2 pounds of chocolate for $32.50. How much is Company A charging per pound of chocolate?

Answers

Answer: Company A is charging $13 per pound of chocolate

Step-by-step explanation:

32.5/2.5=13= 1 pound

Check:

13*2.5=$32.5

NEED HELP ASAP I WILL MARK YOU BRAINLIST

Answers

Answer:

The correct answer is: Option H: 14.4 units

Step-by-step explanation:

CD is a line segment and let M be the mid-point of the line segment.

As we know that a mid-point divides the line in two equal parts, this means that the length of line segment will be the double of distance between one end and mid-point

Given

C( 2,-1) => (x1,y1)

M(8,3) => (x2,y2)

The distance formula is given by:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Putting the values

[tex]|CM|= \sqrt{(8-2)^2+(3-(-1))^2}\\|CM| = \sqrt{(8-2)^2+(3+1)^2}\\= \sqrt{(6)^2+(4)^2}\\=\sqrt{36+16}\\=\sqrt{52}\\= 7.211[/tex]

We know that

[tex]CD = 2CM\\CD = 2 * 7.211\\CD = 14.422\\CD = 14.4[/tex]

Hence,

The correct answer is: Option H: 14.4 units

I need help with this problem

Answers

i need help in life

Stephen gathered data about the average rainfall in two cities. He organized his data in the given graph.
Average Rainfall
5
City A
ul.
City B
0
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Month
Click on all the true statements about the data.
A. The range of the data for City B is higher than City A.
B. The range of the data for City A is higher than City B.
O C. The median of the data for City B is higher than City A.
UD. The range of the data is the same for both City A and City B.
E. The median of the data is the same for both City A and City B.

Answers

Answer: B.The range Is Higher for city A than City B

E. The median is the same for city A and City B

According to the calculations, the correct statements are B and C.

Given that Stephen gathered data about the average rainfall in two cities, and he organized his data in the graph, to determine which statements are correct, the graph must be analyzed and the following mathematical reasoning must be carried out:

The average rainfalls of City A range from 0.5 to 4.5 per month, with a variable range of 4 points. In turn, the average rainfalls of City B range from 1 to 4 per month, with a variability range of 3 points. Therefore, the range of the data for City A is higher than City B, so option B is correct, and options A and D are incorrect.

Regarding the median rainfalls, City A has a cumulative total of 27 points over 12 months, that is, an average of 2.25 per month. In turn, City B has a cumulative total of 28.5 points over 12 months, that is, an average of 2,375 per month. Therefore, the mean of City B is higher, so option C is correct.

Learn more in https://brainly.com/question/20982963

From two cities that are 500 mi apart, two cars left simulaneously moving towards each other. The speed of one car was 10 mph greater than the speed of the other car. In 5 hours the cars met. Find the speed of each car.

Answers

Given:

Distance between to cities = 500 mi

Two cars left simultaneously moving towards each other.

The speed of one car was 10 mph greater than the speed of the other car.

They meet in 5 hours.

To find:

The speed of each car.

Solution:

Let x mi/h be the speed of one car.

So, speed of second car = (x + 10) mi/h

Two cars left simultaneously moving towards each other.

So, their relative speed = x + (x+10) = (2x+10) mi/h

We know that,

[tex]Speed =\dfrac{Distance}{Time}[/tex]

On substituting the values, we get

[tex]2x+10=\dfrac{500}{5}[/tex]

[tex]2x+10=100[/tex]

[tex]2x=100-10[/tex]

[tex]2x=90[/tex]

Divide both sides by 2.

[tex]x=\dfrac{90}{2}[/tex]

[tex]x=45[/tex]

Now,

Speed of one car = 45 mi/h

Speed of other car = 45+10

                                = 55 mi/h

Therefore, the speeds of two cars are 45 mi/h and 55 mi/hr.

4. Express each of the following in m/s.
(a) 65 cm/s
(b) 367 km/h
(c) 1000 cm/min (d) 86 km/min​

Answers

[tex]{ \large{ \purple{ \sf{Hello \: there!}}}}[/tex]

As we know that, 1 cm = 0.01 m

So,

(a) 65 cm/s = 0.65 m/s

b) 367 km/h = (367 × 5 ÷ 18) m/s

c) 1000 cm/min = (1000 × 60 ÷ 100) m/s

d) 86 km/min = (86 × 60 ÷ 1000) m/s

[tex] \star \:{ \underline{ \boxed{ \sf{ \blue{Thank \: you : ) }}}}}[/tex]

(8+k³-6k⁴)+(4-3k⁴+8k²)​

Answers

(8 + k³ - 6k⁴) + (4 - 3k⁴ + 8k²)

8 + k³ - 6k⁴ + 4 - 3k⁴ + 8k²

(8 + 4) + (8k²) + (k³) + (-6k⁴ -3k⁴)

(12) + (8k²) + (k³) + (-9k⁴)

12 + 8k² + k³ - 9k⁴

I need help plzzzz percent equations blank% of $30 =3

Answers

Answer:

10%

Step-by-step explanation:

Hello I can help you with this question. Lets start.

The question is asking what percent of $30 is 3

so i think u actually meant $3 right but anyways

30 is 10 times 3

then clearly it would be 10%

gogo that's the answer!

Solve each of these equations. Explain or show your reasoning.

2b+8−5b+3=-13+8b−5
2x+7−5x+8=3(5+6x)−12x
2c−3=2(6−c)+7c

Answers

Answer: Answers are in the pictures

If m 6=51, then m 7=

Answers

Answer:

m 7=129

Step-by-step explanation:

if 6 and 7 are right next to each other. it makes 180 degrees so you would take 180-51 to get your answer

What is the quotient of 1 +i ? 3 +4i​

Answers

Step-by-step explanation:

pls check the answer here is ur answer

Answer:

7/25-1/25i

Step-by-step explanation:

Is the relationship for Camille’s puppy’s weight in terms of time increasing or decreasing? Explain your response.
I NEED HELP

Answers

Answer: Increasing because it is gaining weight

Answer:

It's increasing.

Step-by-step explanation:

Camille's puppy is gaining weight as shown in the graph not loosing weight. If Camille's puppy was losing weight it'd be decreasing.

Hope this helps!! Good luck!! :)

Josh is playing golf he has 1 white golf balls 2 yellow golf balls , 3 orange balls , 2 green golf balls in his golf bag at the first hole he randomly draws a ball from his bag , what is the theoretical probability of drawing a orange ball

Answers

Answer:  3/8

Step-by-step explanation:

1+2+3+2= 8

he has 8 balls in total

he has 3 orange balls so the probability is 3/8

Find:11/3 ÷ 2/3

the quotient is 5 and _____​

Answers

Answer:

5.5 quotient 5 and rest 1

But I would answer quotient is 5 and half

Step-by-step explanation:

11/3 ÷ 2/3 = 11/3 * 3/2 = 11/2= 5.5

So the quotient is 5 and rest is 1

Hope this helps, have a good day

Answer:

5 1/2

Step-by-step explanation:

11/3÷2/3

Applying the fractions formula for division,

=11/3×3/2

=33/6

Simplifying 33/6, the answer is

=5 1/2

What’s the solution to this problem-5/2=3/4+n

Answers

Answer:

..................................................

Step-by-step explanation:

The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -6<= x <= 6?

Answers

Answer:

- 1

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ - 6, 6 ]

From the graph

f(b) = f(6) = - 2

f(a) = f(- 6) = 10 , thus

average rate of change = [tex]\frac{-2-10}{6-(-6)}[/tex] = [tex]\frac{-12}{12}[/tex] = - 1

step by step explanation:

I don't know

sorry really wanna help

Mary types 3 pages in 12 minutes. If she continues this same speed, How many pages should she type in 60 minutes? Show your work/ Use a double number line, HELP PLEASE!!!!!!!!!

Answers

3 pages .............................. 12 min

x pages ............................... 60 min

x = 3*60/12 = 15 pages

Question
What is the solution to this system of equations?
ly
101
y=x-2
y=-0.5x + 4
8
6
2.
6
10
O A. (2,4)
O B. (1,2)
O C. (2,1)
O D. (4,2)
PLS HELP

Answers

Answer:

im not completely sure but i think its A

Answer:

D . (4,2)

Step-by-step explanation:

i got it right !

Im in desperate need of help

I need help with Just ONE question in math specifically 8th grade pls help.

Answers

I don’t see a problem but repost it and I can see if I know it

Find the area. Simplify your answer.

Answers

ill need a photo?!! try pasting a photo so i can see it

How is (5 , -7) and (-5 , 7) related on a coordinate plane?

Answers

Answer:

they are on opposite quadrants and they meet exactly in the origin (0,0)

Carlos and Jonathan shared $40 in the ratio 5:3. How much money did Jonathan get? (Draw a tape diagram).
PLEASE HELP MEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

carlos got 25 and Jonathan got 15.

Step-by-step explanation:

5+3=8 40/8=5

5×5=25. 5×3=15

plz help this paper is worth 50 points

Answers

Answer:

c

Step-by-step explanation:

Answer:

Choice A

Step-by-step explanation:

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