The area of a rectangle is modeled by the graph where y is the area (in square meters) and x is the width (in meters).
What dimensions result in the maximum area?
A rectangle_ meters by_ meters results in the maximum area.
Answers
Answer:
The dimensions that result in the maximum area are therefore;
Width = 3.5
Height = 3.5
Step-by-step explanation:
The given parameters are;
The area of the rectangle, y = x × h
Where;
x = The width of the rectangle
h = The height of the rectangle
By examination, we have;
x + h = 7
Therefore, x = 7 - h
Which gives;
y = x × (x - 7) = x² - 7·x
y = x² - 7·x
At x = 0, y = 0
At x = 7, y = 0
However, at x = 1, y = -6
Therefore, the function should be, y = -(x² - 7·x)
The maximum occurs where dy/dx = 0, which gives;
dy/dx = d-(x² - 7·x)/dx = 0
dy/dx = 2·x - 7 = 0
2·x - 7 = 0
x = 7/2 = 3.5
On second derivative, we have;
d²y/dx² = 2, which gives a local minimum
x = 3.5 at maximum height
Which give, the maximum height, [tex]y_{max}[/tex] = -(x² - 7·x) at x = 3.5
∴ [tex]y_{max}[/tex] = -(3.5² - 7×3.5) = 12.25
The maximum height = 12.25
The dimensions that result in the maximum area are therefore;
Width, x = 3.5
Height, h = 7 - x = 7 - 3.5 = 3.5
Height, h = 3.5.
Related Questions
At noon the temperature was -10° F. Over the next 4 hours the temperature went up 12°. Then every hour until 10 pm the temperature dropped 2°. What was the temperature at 10 pm?
Answers
Answer:
-10 degrees
Step-by-step explanation:
at noon the temp was -10. -10 + 12 = 2 and that is at 4 o'clock 2- 6 hours ( time until 10 pm) x 2. 2 - 12 = -10.
Answer: 0º F.
Step-by-step explanation:
Noon = 12 pm
At Noon it was -10º F, over the next 4 hours it went up to 12º F.
Noon + 4 hours = 4 pm
The temperature dropped 2º F every hour until 10 pm which means for 6 hours the temperature dropped.
6x2º F = 12º F which means the temperature dropped by 12º F.
12º F - 12º F = 0º F
My brother is wondering what 100÷1,000,000 equals.
Thanks to the patient person who answers this!
Answers
Answer:
0.0001
Step-by-step explanation:
Answer: tell your brother 0.0001
Step-by-step explanation:
Anybody know this answer?
Answers
Answer:
x = 29
Step-by-step explanation:
The sum of the 3 angles is 180 degrees since it is a straight line
x-1 + 3x+2 + 2x+5 = 180
Combine like terms
6x +6 = 180
Subtract 6 from each side
6x+6-6= 180-6
6x =174
Divide y 6
6x/6 =174/6
x = 29
Answer:
it's 29
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
The members of a small town's local arts council are selling raffle tickets. The art council decides that the top three raffle ticket sellers will share a portion of the profits. The second-place seller will receive twice as much as the third-place seller. The first-place seller will receive $20 more than second-place seller. How much will each of the top three sellers receive if the profit portion they will share is $200?
Answers
Answer:
Profit shall be distributed as :
First seller = $92
Second seller = $72
Third seller = $36
Step-by-step explanation:
Let the first seller be A
Second seller be B
Third seller be C
Let the profit of third price seller C = "x"
Profit of B = 2x
Profit of A = 2x + $20
Total profit received by all of them = $200
$200 = (2x + $20) + (2x) + (x)
$200 = 5x + $20
$180 = 5x
x = $36
Therefore profit for 3rd seller = $36
Profit for second seller = $36 [tex]\times[/tex] 2 = $72
Profit for first seller = $72 + $20 = $92
what value of x makes the question true? 2x + 9 = 4x - 1
Answers
Answer:
5
Step-by-step explanation:
2x +9 =4x - 1
2x - 4x =-1 - 9
-2x=-10 /(-1)
2x=10
x=10 :2
x=5
if x=4 and y=1 then what is 3x + y + 2x squared minus 3 + y
Answers
Answer:
I think it is 73
Answer: 439
Step-by-step explanation:
Helppppp with angles
Answers
Answer:
61
Step-by-step explanation:
8 and 11 are corresponding angles. therefore they add up to 180.
so, 180-119 = 61
Answer:
61 degrees,
since 8=1 and 1=5, 5+11=180, 5=119 then 11 should equal 61
The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the
decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
Ο Α.
;0.318 kg
y = 487
B.
: 0.847
kg
y=
oc.
: 442.302 kg
y = 487
s(1
»=2(43);
OD
: 0 kg
Answers
Answer:
a(t) = 487(1/2)^(t/36)a(5) = 442.302 kgStep-by-step explanation:
The exponential function for half-life problems is easily written using 1/2 as the base of the exponent.
present value = (initial value) × (1/2)^(t/(half-life))
Then the amount (a) remaining after t days is ...
a(t) = 487 × (1/2)^(t/36)
__
After 5 days, the amount remaining is ...
a(5) = 487×(1/2)^(5/36) ≈ 442.302 kg
_____
Some folks like their exponential function to be written using e as the base for the exponent. Here, that would be ...
a(t) = 487·e^(-0.019254t)
where the constant in the exponent is -ln(2)/36.
Will give brainliest
Answers
Answer:
-6/3= -2
3/-6= -1/2 they are not equal. So false
-8*9= -72
9*-8= -72 They are equal. So true
hope this helps!
PLEASE GOD IM BEGGING YOU LEGITMENTALLY ANWERS THIS QUESTION
Answers
Answer: we can not see the question
5/6 x 48
You get 25 point if you answer
Answers
Answer:
40Step-by-step explanation:
5/6 x 48 =5 x 48/6 =5 x 8 =40The difference
between two and a
number, multiplied by
five
i need help putting it into an equation
example:two added to three x
3x+2
Answers
help me please!! Slope
Answers
2. Y=-1/2+b
3. Y=-3/3+b
4. I can’t quiet remember how to do sorry :/
Jessica had 167 dollars to spend on 6 books. After buying them she had 17 dollars. How much did each book cost ?
Answers
Answer:
6 $
Step-by-step explanation:
167$-17$=150$cost 6 books
150 $:6 =25$cost a book
The following triangles are congruent because ?
Answers
Answer:
Step-by-step explanation:
The triangles are congruent because they are the same shape, size, and angle measure. The lines on the angles show that two angles have the same measure. The line on the line segments shows that it hads the same length.
which table has a constant of proportionality between y and x of 2
Answers
Answer:
B for Khan Academy.
Step-by-step explanation:
Answer:
The answer is B for Khan Academy
Step-by-step explanation:
I just got it right.
What is the slope of a line which passes through the points (-6, 4) and (4, 6)?
A) 5
B)1/5
C)2
D)1/2
Answers
Answer:
1/5
Step-by-step explanation:
To find the slope between two points, we use the formula
m = ( y2-y1)/(x2-x1)
= ( 6-4)/(4 - -6)
= ( 6-4)/(4+6)
= 2/10
= 1/5
Mr. Hill wants to plant a rectangular garden in his backyard. He has 50 feet of fence to enclose his garden. He wants the length to be 5 feet more than the width. Write the equation that you would use to solve this problem and use your equation to find the dimensions.
What are the dimensions, in feet, of the garden?
What is the equation that you wrote to determine the width, x, of the garden?
Answers
Answer:
PERIOD POOOOOOOOOOOOOOO
Step-by-step explanation:
Is zero positive or negative?
Answers
Answer:
its nutral
Step-by-step explanation:
it is in between postive and negative like the barrior pretty much
CALCULATOR COLOR THEME 0 ZOOM 2. Danielle wants to translate triangle XYZ so that vertex Yis mov (-4,2) to (0,-3). Which of the following mappings can be used to coordinates of Xand Z?
Answers
Answer:The answer is (x,y)->(+4,y-5)
Step-by-step explanation:
since -4 to 0 is + 4 and 2 to -3 is -5
The correct mapping is (x, y) ⇒ (x + 4, y - 5)
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Translation is the movement of a point up, down, right or left in the coordinate plane. If a point A(x, y) is moved a units right and b units down, the new location would be at A(x + a, y - b).
Since the vertex Y(-4, 2) was translated to Y'(0, -3), hence the triangle was translated 4 units to the right (-4 + 4 = 0) and 5 units down (2 - 5 = -3). This can be represented by the mapping:
(x, y) ⇒ (x + 4, y - 5)
Therefore to find x and z coordinates, use the mapping:
(x, y) ⇒ (x + 4, y - 5)
Find out more at: https://brainly.com/question/18249265
Write 9 in scientific notation
Answers
The average July temperature in Texas is 99 degrees Fahrenheit. The actual July temperature for a city may be about 5 degrees hotter or cooler. Write an absolute value equation to find the minimum and maximum temperatures.
I forgot how to write absolute value equations plz help asap
Answers
Answer:
| x-99 | =5
Step-by-step explanation:
x equals the temperature on that day
To which family does the function y = (x + 2) Superscript one-half Baseline + 3 belong?
quadratic
square root
exponential
reciprocal
Answers
Answer:
option b: square root
Step-by-step explanation:
just got correct on edge 2020
The family of the function belongs to square root.
We can solve this by understanding some types of functions
What is Function?This is an expression that relates two variable to one another.
In this question, we are looking for the family of the equation.
The function given is
[tex]y = (x + 2)^\frac{1}{2} + 3[/tex]
The options given here are
quadraticsquare rootexponentialreciprocalWhat is a quadratic equation?This is a polynomial that the variable have the highest power of 2. An example of this is [tex]y = ax^2 + bx + c[/tex]
What is a square rootThis a function in which the variable is a square root to the main function.
An example of this is [tex]y = \sqrt{x}[/tex]
What is an Exponential FunctionThis is a function in which one of the variable has an exponential function to the other. An example of this is [tex]y = 2e^x[/tex]
What is a Reciprocal FunctionThis is a function in which one of the variable is inverse to the other one. An example of this is [tex]y = \frac{1}{x}[/tex]
From the above explanation, we can see that the function
[tex]y = (x + 2)^\frac{1}{2} +3\\y = \sqrt{x+2} + 3[/tex]
is a square root function
Learn more on functions here;
https://brainly.com/question/15602982
HELP ME PLS ITS DUE SOON
Answers
Answer:
B
Step-by-step explanation:
Luna mixes 3/4 of orange juice with 3/8 cup of cranberry juice. She gives 5/8 cup of the juice to Mags. How much is left in Lunas glass?
Answers
Answer:
Luna has half a cup (1/2) (0.5) left in her cup
Step-by-step explanation:
3/4+3/8=1.125 1.125-5/8 of a cup=0.5
Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true. Your explanation should use AT LEAST TWO of the following terms: vertical angles, corresponding angles, congruent, supplementary.
please help
Answers
Answer:
m∠b + m∠e = 180°
Step-by-step explanation:
Lines x and y are the parallel lines and a transversal line is intersecting these lines.
∠b ≅ ∠h [Vertical angles]
∠h ≅ ∠f [Corresponding angles]
Therefore, ∠b ≅ ∠f [Congruent angles]
m∠f + m∠e = 180° [Supplementary angles]
m∠b + m∠e = 180° [Since, ∠b ≅ ∠f]
Therefore, equation representing the relation between ∠b and ∠e is,
m∠b + m∠e = 180°
The required equation that represents the relationship between b and e is m<b + m<e = 180
From the given diagram, we can see that the line x and y are cut by a transversal. This shows that the following statements are true;
m<b and m<g are supplementary i.e m<b + m<g = 180
Also m<b and m<f are equal (alternate interior angle)
m<b = m<d (vertically opposite angle)
Also, since m<d and m<e are supplementary angles (angle on a straight line), then m<b and m<e are also supplementary
Hence the required equation that represents the relationship between b and e is m<b + m<e = 180
Learn more here: https://brainly.com/question/22309882
Martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. She earns interest on her initial deposit. The total amount of money in her savings account at the end of each year is represented by the sequence shown.
100, 105, 110.25, ...
Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?
A. f(n + 1) = f(n) + 5
B. f(n + 1) = 5f(n)
C. f(n + 1) = 1.05f(n)
D. f(n + 1) = 0.05f(n)
Answers
1.05 should be it
Step-by-step explanation:
In a recursive formula, each term of the sequence is found by using the previous term. In this case, the sequence is geometric because we are multiplying each term by the same constant, called a common ratio.
To find this common ratio, we find the percent of change between terms. We do this by using the formula
% change = (amount of change)/(original amount)
The amount of change between the first two terms is 105-100 = 5. This makes the percent change
5/100 = 0.05
The amount of change between the second two terms is 110.25-105 = 5.25. This makes the percent change
5.25/105 = 0.05
However, the common ratio in the sequence is not 0.05. This is because multiplying by this decimal would make the terms decrease instead of increasing. In this case, we are taking 100% of the number and adding an extra 5% (0.05 = 5%); this makes our common ratio 105% = 1.05.
This gives us the recursive formula
Answer:
the correct answer is C. f(n + 1) = 1.05f(n)
Step-by-step explanation:
just got it right 2020 edg
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 4.5).
What is the x-intercept?
Answers
Answer:
-4
Step-by-step explanation:
Answer:
The answer is -4
Step-by-step explanation:
just took it
Wyoming has 63,791 fewer people than Washington DC has. What is the population of Washington DC? Wyoming has 582,658 people total.
Answers
Answer:646449
Step-by-step explanation:You can use a calculator if Wyoming has 63781 fewer people than Washington you have to add that number to Wyoming’s population to get Washington’s
Which set of ordered pairs does not represent a function?
\{(2, 7), (1, 7), (0, -8), (5, -1)\}{(2,7),(1,7),(0,−8),(5,−1)}
\{(-1, -9), (-5, -2), (8, 4), (-5, 2)\}{(−1,−9),(−5,−2),(8,4),(−5,2)}
\{(3, 1), (5, 5), (9, 8), (7, 6)\}{(3,1),(5,5),(9,8),(7,6)}
\{(2, 0), (1, -6), (4, 5), (-8, -6)\}{(2,0),(1,−6),(4,5),(−8,−6)}
Answers
Answer:
The second option
Step-by-step explanation:
There can NOT be a function when one x-value coordinate corresponds to multiple x-values. -5 is corresponding with two different y-values, -2 and 2.