Answer:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
Step-by-step explanation:
The distance around the track (400 m) has two parts: one is the circumference of the circle and the other is twice the length of the rectangle.
Let L represent the length of the rectangle, and R the radius of one of the circular ends. Then the length of the track (the distance around it) is:
Total = circumference of the circle + twice the length of the rectangle, or
= 2πR + 2L = 400 (meters)
This equation is a 'constraint.' It simplifies to πR + L = 400. This equation can be solved for R if we wish to find L first, or for L if we wish to find R first. Solving for L, we get L = 400 - πR.
We wish to maximize the area of the rectangular region. That area is represented by A = L·W, which is equivalent here to A = L·2R = 2RL. We are to maximize this area by finding the correct R and L values.
We have already solved the constraint equation for L: L = 400 - πR. We can substitute this 400 - πR for L in
the area formula given above: A = L·2R = 2RL = 2R)(400 - πR). This product has the form of a quadratic: A = 800R - 2πR². Because the coefficient of R² is negative, the graph of this parabola opens down. We need to find the vertex of this parabola to obtain the value of R that maximizes the area of the rectangle:
-b ± √(b² - 4ac)
Using the quadratic formula, we get R = ------------------------
2a
-800 ± √(6400 - 4(0)) -1600
or, in this particular case, R = ------------------------------------- = ---------------
2(-2π)
-800
or R = ----------- = 200/π
-4π
and so L = 400 - πR (see work done above)
These are the dimensions that result in max area of the rectangle:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
Please help me help please please help me please
Answer:
y = 3x + 1 is the answer
Hello there! :)
The slope of this line is 3.
There are lots of ways to calculate the slope.
Here's one of them:
Rise/Run
Here, the rise is 3 (we move up 3 units)
And the run is 1 (we move 1 unit to the right)
3/1=3
So the slope is 3.
Now, the y-intercept is where the graph touches the y-axis.
Here, the y-intercept is 1.
So the equation is
y=3x+1
Hope this helps!
~Just a determined gal
#CarryOnLearning
Please mark brainliest!
[tex]MysteriousNature :)[/tex]
What is 9÷8/9 in simplest form?
Answer:
10 1/8 or 81/8
Step-by-step explanation:
-15(-4)
pls solve, this is page 237 in 7th grade math book, problem 2
Answer: 60
Step-by-step explanation:
The negatives cancel each other out and you are left with 15 times 4
pls find prism if you find it your littearly a pro hacker
Answer:
24 cubic unitsStep-by-step explanation:
Given, in picture,It is a rectangular prism.
It's length in units = 4
It's breadth in units = 2
It's height in units = 3
Therefore,Volume of the given rectangular prism
= length × breadth × height
= 4 units × 2 units × 3 units
= 24 cubic units (Ans)
Amazon Inc. has been sued for following three alleged infringements of law: (1) Unauthorized use of a trademark; the claim is for $100 million (2) Nonpayment of end-of-service severance pay and gratuity to 5,000 employees who were terminated without Amazon Inc. giving any reason; the class action lawsuit is claiming $3 million (3) Unlawful environmental damage for dumping waste in the river near its factory; environmentalists are claiming unspecified damages as cleanup costs (4) Legal counsel is of the opinion that not all the legal cases are tenable in law and has communicated to Amazon Inc. this assessment of the three lawsuits: (5) Lawsuit 1: The chances of this lawsuit are remote. (6) Lawsuit 2: It is probable that Amazon Inc. would have to pay the displaced employees, but the best estimate of the amount that would be payable if the plaintiff succeeds against the entity is $2 million. (7) Lawsuit 3: There is no current law that would compel the entity to pay for such damages. There may be a case for constructive obligation, but the amount of damages cannot be estimated with any reliability. Required: What should be the provision that Amazon Inc. should recognize or the contingent liability that it should disclose in each of the lawsuits, based on the assessments of its legal counsel?
The International Financial Reporting Standards developed standards can
be implemented to ascertain the provisions and disclosures to be made.
The correct responses are;
According to the financial reporting standard, the contingent liability that
Amazon Inc. should disclose and the provision that Amazon Inc. should
recognize, based on the legal consent are;
Lawsuit 1: It is not required to make provision or disclosure because the
probability of the lawsuit progressing is remote and therefore, the
Company will not be required to payout money or lose economic benefits.
Lawsuit 2: The likelihood of the Company having pay the displaced
employees is high however, the amount payable is $2 million, and
therefore, a provision of $2 million is required in the financial reporting.
Lawsuit 3: The Company is not legally obliged to pay for or perform the
cleanup, but based on the relationship between the Company's waste
location, the river, and the community, there is a constructive obligation,
the amount of which cannot be determined with reliability.
Therefore, there is a requirement for disclosure as a contingent liability,
and not a provision as the claim cannot be classified as a provision.
Learn more here:
https://brainly.com/question/17371330
Which inequality represents this sentence?
A number is no less than 48.
n < 48
n > 48
n < 48
n>48
The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.
Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.
It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.
Read related link on:
https://brainly.com/question/25701252
Answer: The correct answer is n≥48
Step-by-step explanation: Give me the brainiest
Would love it if your able to help me :)
Answer:
x = 2.83163
Step-by-step explanation:
Have a nice day!
and if you have questions on how I found it please ask.
The graph of f(x) = x² is transformed to create the graph of g(x) = f(x + 6). Which
statement is true?
A The graph of g(x) reflects the graph of f(x) across the x-axis.
B The graph of g(x) reflects the graph of f(x) across the y-axis.
CThe vertex of the graph of g(x) is 6 units to the left of the vertex of the graph of f(x).
DThe y-intercept of the graph of g(x) is 6 units above the y-intercept of the graph of f(x).
Answer:
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=-f\left(x\right)g(x)=−f(x) is a vertical reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about (or over, or through) the x-axis.
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=f\left(-x\right)g(x)=f(−x) is a horizontal reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about the y-axis.
Step-by-step explanation:
please answer fully///////////////
Answer:
14
Step-by-step explanation:
(4+(16-1)/5)*2
(4+15/5)*2
(4+3)*2
7*2
14
Please help me solve this asap.
(step by step explanation)
Will the answer to the addition problem below be odd or even?
2156 +992 = ?
Answer:
Even
Step-by-step explanation:
When two even numbers are added there will be an even result. To check this adding 2156 and 992 gets 3148 which is an even number.
1. Leonardo da Vinci asserted that a person's height is proportional to the length of the
person's palm. Don's palm is 5 centimeters in length and he is 120 centimeters tall. Mateo's
palm is 7.5 centimeters in length. Assuming that da Vinci's theory is correct, how tall, in
centimeters, is Mateo?
Answer:
120 : 5 = 24 suy ra 24 x 7,5 = 180
Step-by-step explanation:
Natural numbers are ? Integers
Answer:
natural numbers are the positive numbers that begins from 1 ...
but integers include natural numbers , it's negative and zero
Use the drop down to chose the inequality that makes each statement true. A. -17 - 8 B. -27 - -32 C. 110 - -212 D. -432 - 375
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Guide \#1}\huge\boxed{\downarrow}\\\\\large\text{2 negatives = [\bf positive]}\\\large\text{2 positives = \bf [positive]}\\\large\text{1 positive \&1 negative = \bf [negative]}\\\large\text{1 negative \& 1 positive = \bf [negative]}[/tex]
[tex]\huge\textsf{Guide \#2 }\huge\boxed{\downarrow}\\\large\text{Negatives are BELOW 0.}\\\large\text{Positives are ABOVE 0.}[/tex]
[tex]\huge\textsf{Guide \#3 }\huge\boxed{\downarrow}\\\large\text{Positives are on the RIGHT side of the number line.}\\\large\text{Negatives are on the LEFT side of the number line.}[/tex]
[tex]\huge\textsf{Guide \#4 }\huge\boxed{\downarrow}\\\large\text{Positives are bigger than 0}\\\large\text{Negatives are smaller than 0.}[/tex]
[tex]\huge\text{Answering \textsf{your question(s)....}}[/tex]
[tex]\huge\textsf{Option A.}\\\\\large\text{-17 - 8}\\\large\text{= \bf -25}[/tex]
[tex]\huge\textsf{Option B.}\\\large\text{-27 - -32}\\\large\text{= -27 - (-32)}\\\large\text{= -27 + 32}\\\large\text{= \bf 5}[/tex]
[tex]\huge\textsf{Option C.}\\\large\text{110 - -212}\\\large\text{= 110 - (-212)}\\\large\text{= 110 + 212}\\\large\text{= \bf 322}[/tex]
[tex]\huge\textsf{Option D.}\\\large\text{-432 - 375}\\\large\text{= \bf -807}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\large\boxed{\frak{Amphitrite1040:)}\ \bf \heartsuit}[/tex]Find the equation of the line which passes through (0,7) at a gradient of 3
Answer:
y=3x+7
Step-by-step explanation:
y=mx+c
we have (0,7). (x,y)
so y-7/x-0=3
multiply by (x-0) both sides to get
y-7=3x take -7 to the other side of equal sign
it will be: Y=3X+7
If (x + 4) is a factor of f(x), which of the following must be true?
Group of answer choices
f(-4) = 0
Neither x = -4 nor x = 4 are roots of f(x).
Both x = -4 and x = 4 are roots of f(x).
f(4) = 0
PLEASE HURRY WILL GIVE BRANLESIT
Function 1 is represented by the equation y = 6x + 25
Function 2 is represented by the table.
x y
5 31
10 41
15 51
20 61
Which statement about the two functions is true?
The rate of change for Function 2 is 5 times the rate of change for Function 1.
The rate of change for Function 2 is three times the rate of change for Function 1.
The rate of change for Function 2 is one third the rate of change for Function 1.
The rate of change for Function 2 is the same as the rate of change for Function 1.
Answer:
The rate of change for Function 2 is one third the rate of change for Function 1.
Please mark brainliest if possible :)
which function is equivalent to f(n)=(n+2)^2+n^2-4
Evaluate f(x) at x =-3/4
f(x) = 2 - 6x - 4x^2
Answer:
4.25 is the final answer!!!
A long distance phone company charges a flat rate of $1.01 and then $0.09 for each minute. If
a call cost $9.56, how long did it last?
Answer:
30
Step-by-step explanation:
Answer:
95 minutes
Step-by-step explanation:
Deduct the flat rate from the total to see how much was spent on minutes
9.56 - 1.01 = 8.55
to get minutes divide that by the cost per minute
8.55/0.09 = 95
95 minutes
Plz help me well mark brainliest only if u are correct!
Answer:
B
Step-by-step explanation:
Since x is being multiplied by -4/5, you need to multiply both sides of the equation by the reciprocal of -4/5 which -5/4.
Answer: B
In the diagram, <4 and <5 are what type of angles?
A. corresponding angles
B. Alternate interior angles
C. Alternate exterior angles
D. Consecutive interior angles
Answer:
B. Alternate interior angles
Step-by-step explanation:
A local high school has both male and female students.
Each student either plays a sport or doesn't.
The two-way table summarizes a random sample of 70 students.
Female
Male
No sport
10
7
Sport 32 21
Let no sport be the event that a randomly chosen student (from the table) does not play a sport.
Let male be the event that a randomly chosen student (from the table) is male.
Find the following probabilities. Write your answers as decimals.
(a) P(male) = 0
(6) P(no sport and male) = 0
(c) P(no sport male) = 0
Answer:
a. P(male) = 0.4
b. P(no sport and male) = 0.1
c. Unclear question (isn't it the same as b.?)
Step-by-step explanation:
The data below is what I've worked according to, which isn't very clear from the question so the answers are only correct if this is the correct table of data;
[tex]\left[\begin{array}{ccc}&No \ Sports&Sports\\Female&10&32\\Male&7&21\end {array}\right][/tex]
a.
[tex]P(male) = \frac{7 + 21}{70} \\\\ = \frac{28}{70} \\\\ = \frac{2}{5}[/tex]
b.
Using the tree diagram in the picture;
[tex]P(no \ sport \ and \ male) = \frac{2}{5} * \frac{1}{4} \\\\ = \frac{1}{10}[/tex]
What is the value of x?
Answer:
Step-by-step explanation:
45
Answer:
x=44°
Step-by-step explanation:
It's an Isosceles triangle, it has two equal sides (DC=CE) so also its two equal angles of 44 degrees
Hope this helps
Write the equation of the function graphed below:
a. f(x) = 2x−−√3 –4
b. f(x) = 2x−−√3 + 4
c. f(x) =x−−√3 + 4
d. f(x) =x−−√3 – 4
Answer:
I have a couple questions before I answer, what do the 2 dashes represent and are the 4s also under the square root?
BEST ANSWER GETS BRAINLIEST!!!!
A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $31. For 5 pounds of trail mix and pounds of 2 jelly beans, the total cost is 12. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
3x + 8y = 31
5x + 2y = 12
Let's solve your system by elimination.
Multiply the second equation by -4, then add the equations together.
(3x + 8y = 31)
−4 (5x + 2y = 12)
Becomes:
3x + 8y = 31
−20x − 8y = −48
Add these equations to eliminate y:
−17x = −17
Then solve −17x = −17 for x:
−17x = −17
−17x −17 = −17 − 17 (Divide both sides by -17)
x = 1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x + 8y = 31
Substitute 1 for x in 3x + 8y = 31:
(3)(1) + 8y = 31
8y +3 = 31 (Simplify both sides of the equation)
8y + 3 − 3 = 31 − 3 (Add -3 to both sides)
8y = 28
8y8 = 288 (Divide both sides by 8)
y = 7/2
A car travels a constant speed of 45 km/h
3.4.1 The distance travelled in 6 hours?
3.4.2 The time it takes to travel 495 km?
Answer:
1 hour
Step-by-step explanation:
because i divided
Help me out cause this very difficult for me
9514 1404 393
Answer:
a) 37
b) n+d
Step-by-step explanation:
This is a reading comprehension problem. You are asked to understand what you are reading, and to think about what question is being asked.
Given:
a) someone bought 20 notebook computers and 17 desktop computers
b) someone bought n notebook computers and d desktop computers
Find:
a) the total number of computers bought
b) the total number of computers bought
Solution:
a) The total number bought is found by adding together the numbers of each kind:
20 +17 = 37 . . . total computers
__
b) The total number bought is found by adding together the numbers of each kind:
n + d . . . total computers
All of the points in the picture are on the same line *help asap*
Answer:
yes all of the points are on the same line
Step-by-step explanation:
Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are whole numbers, so the definitional formula works well: X Y 4 5 0 2 1 1 3 4
Applying the formula, it is found that the SP for both numbers is of 7.
The first step is finding the mean for both sets, hence:
[tex]M_x = \frac{4 + 0 + 1 + 3}{4} = 2[/tex]
[tex]M_y = \frac{5 + 2 + 1 + 4}{4} = 3[/tex]
Then, the SP(sum of products of deviations) is the sum of the multiplications between each value x and the mean, with each respective value of y(same index) and the mean, hence:
[tex]SP = (4 - 2)(5 - 3) + (0 - 2)(2 - 3) + (1 - 2)(1 - 3) + (3 - 2)(3 - 4) = 7[/tex]
The SP for both numbers is of 7.
A similar problem is given at https://brainly.com/question/20640860
