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

Find the length of the rectangle if the perimeter is 244 yards the length is 18 less than three times the width?

Answers

Answer:

The Length of rectangle is 87 yards.

Step-by-step explanation:

Let width = w

Length = 3w-18

Perimeter of rectangle = 244 yards

We need to find length of rectangle.

First we need to find value of w

The formula used will be: [tex]Perimeter=2(length+width)[/tex]

Putting values and finding w

[tex]Perimeter=2(length+width)\\244=2(3w-18+w)\\244=2(4w-18)\\244=8w-36\\244+36=8w\\8w=280\\w=\frac{280}{8}\\w=35[/tex]

So, w= 35

The width of rectangle w = 35 yards

The length of rectangle l = 3w-18 = 3(35)-18 = 105-18 = 87 yards.

So, the Length of rectangle is 87 yards.

CAN SOMEONE PLEASE HELP ME!!
Consider the polynomial function h(x) = -7x6 + 3x4 – 5x2.
What is the end behavior of the graph of h ?

Answers

Answer: As x -> ♾, h(x) -> -♾, and as x -> -♾,h(x) -> -♾

Step-by-step explanation:

The end behavior is x ----> ∞ then h(x) ----> -∞, and when x ----> -∞ then h(x) -----> -∞.

What is Function?

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

h(x) = -7[tex]x^6[/tex] + 3 [tex]x^4[/tex]– 5x².

If we plot the Equation on the Graph we can see a parabolic Curve.

This Curve tells as x tends to ∞ the value of h(x) tends to -∞.

and, when x tends to -∞ the value of h(x) tends to -∞.

Hence, the end behavior is x ----> ∞ then h(x) ----> -∞.

and, when x ----> -∞ then h(x) -----> -∞.

Learn more about Function here:

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A car covers a distance of 600 m in 2 minutes whereas a train covers a distance of 75 km in 50 minutes. Find the ratio of their speed.​

Answers

answer

1:5

Step-by-step explanation:

To find speed use the formula

speed=distance/time

The car's speed is 600m ÷2mins(120secs)

(600÷120)

5m/s

The trains speed will be

speed=distance/time

=75÷50mins(5/6hrs)

=90km/hr

Ratio of their speed should be

first change the speed of the car 5 m/s to km/hr. 5×18/5 = 18km/hr

the speed of the train is 90km/hr

18:90 simplified it will be 1:5

i really need help asap

Answers

answer is d (-3,1) hope i helped:)

Answer:

D (-3, 1)

Step-by-step explanation:

help asap!!! it’s due in 20 minutes .

Answers

Answer:

ab

Step-by-step explanation:

Mr. Stip bought a new pair of Jordans and 4 new polo shirts. The price of one pair of jordans were double the amount of one polo shirt. If Mr. Stip spent $510, determine the price he paid for the Jordans.

Answers

9514 1404 393

Answer:

  $170

Step-by-step explanation:

If the price of a pair of Jordans is the same as the price of two shirts, the total purchase has a value equivalent to that of 3 Jordans.

  pair of Jordans = $510/3 = $170

Answer:

$170

Step-by-step explanation:

Spencer bought gas for his four-wheeler from Gas World on Saturday. On Sunday, he bought the same amount of gas from Fuel Stop for less money. Now, Spencer has $20 to spend on gas for his car. Fuel Stop is on his way home. If the gas prices haven't changed, will Spencer be able to get more or less gas at Fuel Stop than at Gas World?

Answers

Answer:

Step-by-step explanation:

spencer bought the same amount of gas from gas world and fuel stop. since the gas cost less money at fuel stop, the gas is cheaper at fuel stop at gas world.

spencer has $20 to spend on gas for his car at fuel stop.

since the gas is cheaper at fuel stop, spencer will get MORE gas from fuel stop with his money.

hope this helped

If the gas prices haven't changed, will Spencer be able to get more gas at Fuel Stop than at Gas World

What is Number system?

A number system is defined as a system of writing to express numbers.

Given,

Spencer bought gas for his four-wheeler from Gas World on Saturday

He bought the same amount of gas from Fuel Stop for less money on Sunday

Now, Spencer has $20 to spend on gas for his car.

since the gas cost less money at fuel stop, the gas is cheaper at fuel stop at gas world. spencer has $20 to spend on gas for his car at fuel stop. since the gas is cheaper at fuel stop, spencer will get MORE gas from fuel stop with his money.

Hence if the gas prices haven't changed, will Spencer be able to get more gas at Fuel Stop than at Gas World

To learn more on Number system click:

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What is the equation in slope intercept form of the line that passes through the point (2,2) and is perpendicular to the line represented by y=2/5x + 2

Answers

Answer:

y=

Step-by-step explanation:

Perpendicular means opposite reciprocal of the slope. This means that the slope would change from 2/5 to 5/2 and add a negative, so it is -5/2.

y=-5/2x+b

2=-5/2 (2) +b

7=b

y=-5/2x+7

Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of and costs an additional per mile driven. The second plan has an initial fee of and costs an additional per mile driven. How many miles would Tom need to drive for the two plans to cost the same?

Answers

Complete question :

Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $57.98 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $53.98 and costs an additional $0.16 per mile driven. How many miles would Tom need to drive for the two plans to cost the same?

Answer:

200 miles

Step-by-step explanation:

Let miles driven = x

First option :

57.98 + 0.14x

Second option :

53.98 + 0.16x

First option = second option

57.98 + 0.14 = 53.98 + 0.16x

57.98 - 53.98 = 0.16x - 0.14x

4 = 0.02x

x = 200

200 miles

Determine the simple interest paid to the nearest cent for each loan, interest rate, and time. $2,650, 3.65%, 2 1/2 years

Answers

9514 1404 393

Answer:

  $241.81

Step-by-step explanation:

The interest is given by the formula ...

  I = Prt

Filling in the values and doing the arithmetic, we have ...

  I = $2650×0.0365×2.5

  I = $241.81

The simple interest paid is $241.81.

MARKING PEOPLE AS BRAINLIST ARE THE TRRIANGLES CONGRUENT HOW DO YOU KNOW? Please help thank you :)

Answers

All of the angles and sides are the same

Show work too I’ll mark you brainlist hurry lol

Answers

Answer:

1

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

[tex]e(x)=\frac{1}{5}x\\\\e(5)= \frac{1}{5}*5\\\\\boxed{e(5)=1}[/tex]

Hope this helps.

ANSWER ASAP look at pic and answer #18

Answers

Answer:

Four

Step-by-step explanation:

Answer: will have to be 4

why does math have to be so hard

Answers

I felt this, I’m currently failing even tho I’m trying but that could also be because my teacher doesn’t like me

Answer:

Math seems difficult because it takes time and energy. Many people don't experience sufficient time to "get" math lessons, and they fall behind as the teacher moves on. Many move on to study more complex concepts with a shaky foundation. We often end up with a weak structure that is doomed to collapse at some point.

Math is hard because it is a non-intuitive, non-natural activity. Math don't happen by chance only, it only happens with deliberate, focused work. For this you expend a lot of energy and cause a lot of mental strain, you put yourself on an uncomfortable condition for hours, days, sometimes weeks to solve a problem.

But some people love math, like me, because they study math more than others. If you study more and learn more about math, then you’ll start to feel more comfortable because you’ll be ahead of the class when your teacher teaches you something.

The most important thing is to keep trying and never give up.

Hope this helps! :)

An 8-ounce bottle of lotion costs $4.50. Find the Unit Rate. hint: What is the cost per ounce?

Answers

Answer:

approximately 56 cents

Step-by-step explanation:

4.5/8

I am doing a percent equation problem and I need help please here’s the question 20% of blank =10

Answers

Answer:

[tex]50[/tex]

Step-by-step explanation:

Let [tex]x =[/tex] blank (for convenience)

[tex]20\%x=10[/tex]

[tex]0.2x=10[/tex] (change [tex]20\%[/tex] into its decimal form)

[tex]x = 10\div 0.2[/tex] (divide [tex]0.2[/tex] on both sides)

[tex]x=50[/tex]

∴ Blank = 50

Hope this helps :)

Please help me!!!!!! I really neeeeeeed

Answers

Answer:

A-(x+4,y-5)

B- move 1 unit left and 7 units down

Step-by-step explanation:

A- 4 units right is x so

(x+4,y__)

5 units down is y so

(x+4,y-5)

B- move 1 unit left and 7 units down

because (x-1,y__) is going left because of the subtraction sign and its the x-coordinate, and (x-1,y-7) is down because its a Y-coordinate and sub so its going down.

TIP- Going left/down is always subtract/negative going right/up is positive/addition.

find slope and y-intercept formed the graph if the linear equation
y=1/4x-8​

Answers

Answer:

not sure exactly what its asking but if its asking the slope and y-intercept of this equation is here.

Step-by-step explanation:

the slope is 1/4 while the y-intercept is -8 or (0,-8)

Answer: slope: 1/4

y-intercept: (0,-8)

Hope this helps and good luck :)

Step-by-step explanation:

Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of jocelyns estimate?

Answers

Answer:

12%

Step-by-step explanation:

So 5.5 to 5.62 is .12

Then calculate the difference of 5.5 *.12=0.66

Then do “0.66 is what percent of 5.5?”

The answer is 12%

Thank you for reading, and mark this brainliest

What’s the slope of the line that passes through (-9, -4) and (6, 15).

Answers

19/15, look at the attachment for work

The circumefreence of a circle is 37.8. What is the area of the circle? Use 3.14 for pie

Answers

Answer:

b

Step-by-step explanation:

circumference= 2πr

37.8cm = 2πr

r= 6 cm

Area= πr^2

area = 113cm^2

What is the area of rectangle CDEF?
Area= ...square units

Answers

Step-by-step explanation:

I think it's 48 square units

2 1/3 + 3 2/4 =

Fractions

Answers

5 5/6 is the answer I think

Step-by-step explanation:

2 1/3+3 2/4=7/3+14/4

=28/12+42/12 (common denominater)

=70/12

=5 10/12

for a relation to be a function what must never happen

Answers

Answer:

Step-by-step explanation:

A function is a relation in which each input has only one output

so a relation cannot have more than one output

Answer:

each input (x-value) only has one output (y-value)

Step-by-step explanation:

you can use the vertical line test; pretend to draw vertical lines and if there are two point on the graph where the vertical line touches, it cannot be considered function.

Can someone do this please

Answers

ok so umm you need to do 5x4= 20 and divide 20 and 4 you get 5 and multiply 5x4 you get 20 and the answer is 20

There are 12 circles and 15 triangles. What is the simplest ratio of circles to triangles

Answers

Answer:

4:5

Step-by-step explanation:

Sheila has 14 1/2 pounds of potato salad. She wants to divide the potato salad into containers, each of which holds 1 1/4 pounds. How many containers does she need? Complete the explanation.

Answers

Answer:

11 3/5 containers

Equivalent to 11.6 containers

Step-by-step explanation:

Total pounds of potato salad = 14 1/2 pounds

Pounds in each container = 1 1/4 pounds

How many containers does she need?

Number of containers needed = Total pounds of potato salad / Pounds in each container

= 14 1/2 ÷ 1 1/4

= 29/2 ÷ 5/4

= 29/2 × 4/5

= (29×4) / (2×5)

= 116/10

= 11 6/10

= 11 3/5 containers

Equivalent to 11.6 containers

Which system of inequalities describes the graph?

Answers

Answer:

It Would be C (the third one)

Step-by-step explanation:

Please mark me Brainlyest PLZ

i neeed thiss pleaseeeeeee!!!!!!

Answers

2 the answer is two I think

Please help me out!!

Answers

Answer: C or B

Step-by-step explanation:

Answer:

its the first answer

Step-by-step explanation:

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