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.
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.
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
NEED HELP ASAP I WILL MARK YOU BRAINLIST
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
(8+k³-6k⁴)+(4-3k⁴+8k²)
(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
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
Answer:
im not completely sure but i think its A
Answer:
D . (4,2)
Step-by-step explanation:
i got it right !
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!
Answer:
To the "LEFT", so -6 is "LESS"
Step-by-step explanation:
-6 < -4
plz help this paper is worth 50 points
Answer:
c
Step-by-step explanation:
Answer:
Choice A
Step-by-step explanation:
Help with 3-5 plz I will mark brainliest and plz show steps thx
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
[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]
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?
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
Is the relationship for Camille’s puppy’s weight in terms of time increasing or decreasing? Explain your response.
I NEED HELP
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!! :)
Find the area. Simplify your answer.
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
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
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?
Write an equation in Point Slope Form that has a slope of -5 and passes through the point (4,9)
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 AnsMary 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!!!!!!!!!
3 pages .............................. 12 min
x pages ............................... 60 min
x = 3*60/12 = 15 pages
What is the quotient of 1 +i ? 3 +4i
Step-by-step explanation:
pls check the answer here is ur answer
Answer:
7/25-1/25i
Step-by-step explanation:
I need help with this problem
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?
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
PLS HELP ME PLS whats 2x6x8 (5/8)
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
As more years go by, the prediction (extrapolation) becomes reliable.
Answer:
Less
Step-by-step explanation:
edge 2020
Answer:A.)less
Step-by-step explanation:
edge 2023
NEED HELP FASTTTTT!!! WILL GIVE BRAINLIEST!!!
Answer: -36
Step-by-step explanation:
Im in desperate need of help
I need help with Just ONE question in math specifically 8th grade pls help.
How is (5 , -7) and (-5 , 7) related on a coordinate plane?
Answer:
they are on opposite quadrants and they meet exactly in the origin (0,0)
Find:11/3 ÷ 2/3
the quotient is 5 and _____
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
If m 6=51, then m 7=
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
Carlos and Jonathan shared $40 in the ratio 5:3. How much money did Jonathan get? (Draw a tape diagram).
PLEASE HELP MEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
carlos got 25 and Jonathan got 15.
Step-by-step explanation:
5+3=8 40/8=5
5×5=25. 5×3=15
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
Answer: Answers are in the pictures
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.
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.
What’s the solution to this problem-5/2=3/4+n
Answer:
..................................................
Step-by-step explanation:
I need help plzzzz percent equations blank% of $30 =3
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!