Answer:
a. 20520
b. 12600
Step-by-step explanation:
Given the function S = 600xe^-x² + 600.
a. To find the average, we have to find the definite integral of the function because average, as it is known, is the sum of data points divided by the size of its dataset, this can be used for discrete data. Integral formula is just the continuous form of average, so we are using integral because we were given an interval of x= 0 to X = 30.
Let's integrate 100xe^x² first. Let –x² = u, this means –2xdx = du and we have dx = –du/2x. Also, when x = 0, u = –(0)² = –0 and when x = 30, u = –(30)² = –900. When we make our substitutions we have:
–600(xe^udu)/2x = –600(e^udu)/2 upon integrating that we have –600(e^u)/2. Applying our interval we have
–600[(e^900)/2 – (e^0)/2] ≈ – [– 3.7 – (1/2)] = –600 (–4.2) = 600 x 4.2 = 2520
Now let's integrate 600, with the interval x = 0 to x = 30 (we are using this interval here because the substitution we made didn't affect this).
We have, upon integrating:
600x.
Substituting our intervals we have:
600(30 – 0) = 600 x 30 = 18000.
Adding that up we have: 2520 + 18000 = 20520.
b. The same method is needed, just difference of interval.
Therefore, after integrating the first component with intervals u = 900 to u = 2500 (from x² = u) we have:
–600[(e^2500)/2 – (e^900)/2] ≈ –600[2.7 – 3.7] = –600(–1) = 600.
Then for the second component:
600x using x = 30 to x = 50
600(50 – 30) = 600 x 20 = 12000.
Adding that up we have:
12000 + 600 = 12600.
PLEASE HELP ME QUICK
A serving dish has a parabolic surface with the vertex (0, 0) at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y = ax2. What is the value of a?
1/12
1/3
1/2
1
Answer:
B
Step-by-step explanation:
1/3
The required value of a is 1/3 for parabola [tex]y = 1/3x^2[/tex].
A parabolic dish with vertex (0,0) at the center, width is 6 inches and depth is 3 inches. y = ax² where a is to be determined.
A parabola is a cross-section cut out of the cone and represented by an equation [tex]y=4ax^2[/tex].
Here,
Vertex is at the center of the parabolic plate (0,0),
with the help of the width and depth coordinate of the one corner is(3,3).
Now put these coordinates in y = ax²
3 = a3²
a = 3/3²
a = 1/3
Thus, The required value of a is 1/3 for the parabola [tex]y = 1/3x^2[/tex].
Learn more about parabola here:
brainly.com/question/4074088
#SPJ5
jerry's softball team is made up of 15 players,and 9 of them are boys.On the team,what is ratios to boys to girls?
Answer:
9:6
Step-by-step explanation:
boys= 9 teammates
girls= 6 teammates
There are 42 boys and 48 girls in sixth grade and each student must be assigned a home room. Each homeroom should have the same number of boys and the same number of girls.
what is thegreatest possible number of sixth grade students?
Answer:
50
Step-by-step explanation:
you add 42 and 48 i think
p(n) = -8n^2 + 9n, Find p(10)
Answer:
first
put the value of p(10) in the place n,
2-multiply -8×10^2+9×10
3-:- -8×100+90
4:-800+90=710ans
What is the 97.2x10 for the 4th power
Please give me the correct answer
helpppppppp meeeeeee
Answer:
h represents the Venn diagram for the above question
Write the quadratic function in vertex form, then identify the vertex
h(x)=x^2+20x+90
h(x)=
Vertex:
I need this answered ASAP please !
Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
Given f(x) = 5(2-x), what is the value of f(-3) ?
Answer:
f(-3) = 25
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 5(2 - x)
f(-3) is x = -3
Step 2: Evaluate
Substitute: f(-3) = 5(2 - -3)Simplify: f(-3) = 5(2 + 3)Add: f(-3) = 5(5)Multiply: f(-3) = 25What is the volume of a cylinder, in cubic feet, with a height of 5 feet and a base
diameter of 10 feet? Round to the nearest tenths place
Answer: 392.7
Step-by-step explanation:
K mola ofkg o okdgmbo9k
Answer: c
Step-by-step explanation:
Edmund made a scale drawing of the rectangular floor of his kitchen. In the scale
drawing, 1 inch represents 2.5 feet. The measurements of the scale drawing are
shown in the diagram.
6.4 in.
4.8 in.
what is the perimeter of the actual kitchen floor in feet?
Answer:
324
Step-by-step explanation:
What is the slope of the line graphed below
Find the equation of the line above. Write the equation in slope intercept form.
The base of a triangle is 12 meters and the height is 6 meters. What is the area of the triangle?
Answer:
36
Step-by-step explanation:
What of the following lines is perpendicular to the line passing across the points (1,1) and (-5,-6)?
y = 6/7x + 1
y = -6/7x + 1
y = -6/7x - 1
y = 6/7x - 1
Circle J was dilated to form circle J'. The diameter of circle J is 2 units and the diameter of circle J' is 18 units. What is the relationship between the areas of circle J and circle J'?
9514 1404 393
Answer:
circle J' has 81 times the area of circle J
Step-by-step explanation:
The ratio of areas is the square of the dilation factor. That factor is 18/2 = 9, so the dilated circle has an area that is 9² = 81 times that of the original.
Does this scatter plot show a positive trend, a negative trend, or no trend?
Answer:
no trend
a positive trend would start in the bottom left and go toward the top right
a negative trend would start at the top left and go town the bottom right
this is an example of no trend
Step-by-step explanation:
a "trend" shows an increasing or decreasing relationship between the x and y values, in this they don't have any sort of relationship. you can tell by the repeating y values for multiple different x-values, or the repeating x-values for multiple different y-values.
Emma poured 40 fl oz. of grape juice equally into 5 cups. How much grape juice does each cup contain?
fl oz. per cup ?
Answer:
The correct answer is 8 fluid ounces per cup.
Step-by-step explanation:
To solve this problem, we need to divide the total amount of grape juice that Emma has (40 fl oz) by the number of cups she is pouring the juice into (5).
40 oz total/5 cups = 8 oz/cup
Therefore, each cup contains 8 fl oz.
Hope this helps!
In class, 30 people have brown shoes, 5 have green shoes, and 1 has blue shoes.
What is the unit ratio of people with green shoes to all the people.
Answer:
5 : 36
There are 36 people in total and only 5 have green shoes.
Select the correct answer
Answer:
Option B
Step-by-step explanation:
Domain of a function is represented by the set input values or x-values
Range of the function is represented by the set of output values or y-values.
From the graph attached,
y-values are varying from y = - 9 to y = 8.
Therefore, range of the function from the given graph will be,
-9 ≤ y ≤ 8
Option B will be the correct option.
PLEASE SHOW FULL SOLUTIONS!! Will Mark Brainliest for the best answer. The radius of a spherical balloon is 3.5 cm. What is the volume of air in the balloon? Show your answer in terms of pi or round your answer to one decimal place.
THANKS
9514 1404 393
Answer:
343π/6 cm³ ≈ 179.6 cm³
Step-by-step explanation:
The formula for the volume of a sphere is one of the volume formulas worth memorizing. It is ...
V = (4/3)πr³
For r = 3.5 cm, the volume is ...
V = (4/3)π(3.5 cm)³ = 343π/6 cm³ ≈ 179.6 cm³
The volume of air in the balloon is about 179.6 cm³.
Darnell’s team scored 40 points at the game. Darnell scored 15% of the team’s points. How many points did Darnell score?
Please help me with math ASAP
Answer:
Step-by-step explanation:
Well what's your question
Factor completely 25x +60
Answer:
5(5x+12)
Step-by-step explanation:
So, take everything out.
GCF 25 and 60
5*5 and 5*3*4
5 is the common factor.
5(5x+12)
Hope this helps plz hit the crown :D
#Team Rainbows!
What are the coordinates of point A?
Answer:
-3-6
Step-by-step explanation:
2х + y = 4
у = 3х – 1
its 2 because 2plus is 2
Jose walked 5.3 miles to school. After school, he walked 4.52 miles to the library.
Finally, he walked 2.89 miles home. How far did Jose walk in all?
Answer: Problem worked out in picture
Step-by-step explanation:
Merry Christmas
In how many map squares did we spot less than 20 plant species
help plssss
Answer:
two map squares ☺️☺️☺️☺️
A bacteria culture grows with constant relative growth rate. The bacteria count was 2,560 after 4 hours and 2,621,440 after 12 hours.
(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)
% per hr
(b) What was the initial size of the culture?
bacteria
(c) Find an expression for the exact number of bacteria after t hours, (t).
y(t) =
(d) Find the number of bacteria after 5.5 hours. (Round your answer to the nearest whole number.)
bacteria
(e) Find the rate of growth in bacteria per hour) after 5.5 hours. (Round your answer to the nearest whole number.)
bacteria per hour
(f) How many hours did it take for the population to reach 104,000? (Round your answer to two decimal places.)
hr
Answer:
A. 86.64%
B. 80
C. y(t)= 80[tex]e^{0.8664t}[/tex]
D. y(5.5) = 9388
E. y(t) = 8134 bacteria for every hour
F. 8.28 hours
Step-by-step explanation:
a. The bacteria count after 4 hours y(4) = 2560
The bacteria count after 12 hours y(12) = 2621440
equation 1: ye^4k = 2560
equation 2: ye^12k= 2621440
divide (2) by (1),
e^8k = 1024
Taking ln both sides:
ln(e8k ) = ln(1024)
8k = 6.931
k=0.8664 // after dividing both sides by 8
rate of growth k% = 0.8664*100 = 86.64%
b. substituting for k in equation 2:
ye^4*0.8664 = 2560
Initial bacteria count y(4) = 80
c. y(t)= 80e^0.8664t
d. the number of bacteria after 5.5 hours => y(5.5) = 80[tex]e^{0.8664(5.5)}[/tex] ≈ 9388
e. y'(5.5) = 80*0.8664e^0.8664(5.5) = 69.31e^0.8664(5.5) = 8134
f. for bacteria population = 104000
where ye^0.8664t = 104000
y = 80
80e^0.8664t = 104000 //divide both sides by 80
e^0.8664t = 1300
ln(e^0.8664t = ln(1300)
t = 7.17 / 0.8664 = 8.28 hours
PLEASE HELLPPP MEEEE WITHH MATHHH
Answer:
-1/2y+1/2x
Step-by-step explanation: