find the maximum area of the rectangle inscribed in the triangle formed by the x x-axis, the y y-axis and the line y
Answers
A shape's highest possible area is called its maximum area.The size of the rectangle that will result in the greatest area is 4 by 2 units.
What is meant by rectangle?Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side. Rectangles are two-dimensional shapes, and as such, they have length and breadth as their defining characteristics. The rectangle's shorter side is its width, while its longer side is its length.How to calculate a rectangle's area. The size of a rectangle. A = l × b. Once the length and breadth are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.The equation is given as:
x + 2y - 8 = 0
Rewrite as:
2y = 8 - x
Divide both sides by 2,
y = [tex]\frac{8 - x}{2}[/tex]
y = 4 - [tex]\frac{x}{2}[/tex]
The area (A) of the rectangle is:
A = xy
Substitute
y = 4 - [tex]\frac{x}{2}[/tex]
A = x[tex](4 - \frac{x}{2})[/tex]
Expand
A = 4x - [tex]\frac{x^{2} }{2}[/tex]
Differentiate
A' = 4 - x
Set the derivative to 0,
4 - x = 0
Collect like terms
x = 4
Recall that:
y = 4 - [tex]\frac{x}{2}[/tex]
Substitute 4 for x,
y = 4 - [tex]\frac{4}{2}[/tex]
y = 4 - 2
y = 2
So, we have:
x = 4 and y = 2
Hence, the dimension of the rectangle that will produce the maximum area is 4 units by 2 units.
The complete question is:
A rectangle is inscribed in the region bounded by the x-axis, the y-axis, and the graph of x+2y-8=0. Approximate the dimensions of the rectangle that will produce the maximum area.
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Related Questions
Jeremy has a stand in the farmer's market where he sells strawberries by the pound. The table shows the weights of the strawberries and the prices per quantity. The relationship between the amount of strawberries in pounds and the price is a proportional relationship.
Which statement is true?
A.)The table does not represent a proportional relationship because the differences between consecutive terms in each column do not have the same ratio.
B.)The table does not represent a proportional relationship because the ratio between the price column and the weight column is not the same for each row.
C.)The table represents a proportional relationship because the differences between consecutive terms in each column have the same ratio.
D.)The table represents a proportional relationship because the ratio between the price column and the weight column is the same for each row.
Answers
Solve using substitution y = -4x + 10 y = -x + 1.
will give brainleist if correct
Answers
Answer:
Hi! The answer to your question is (3,-2)
Step-by-step explanation:(
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Hope this helps!!
- Brooklynn Deka
Find m∠ABC = 7x - 4 and m∠BDC = 9x - 1 and and m∠ABC = 107°, find x, m∠ABC and m∠BDC.
Answers
Answer:
m<BDC = 62 degrees
Step-by-step explanation:
Using the expression;
<ABC = <ABD + <DBC
107 = 7x-4 + 9x - 1
107 = 16x-5
16x = 107 + 5
16x = 112
x = 112/16
x = 7
Get m<DBC
m<BDC = 9x - 1
m<BDC = 9(7)-1
m<BDC = 63 - 1
m<BDC = 62 degrees
An aquarium is to be drained. The aquarium is shaped like a rectangular prism with length 40 in, width 22 in, and height 16 in. Suppose
water is pumped out of the aquarium at a rate of 704 in per minute. If the aquarium starts completely full, how many minutes does it take
to empty the aquarium?
Answers
9514 1404 393
Answer:
20 minutes
Step-by-step explanation:
The volume is given by ...
V = LWH
V = (40 in)(22 in)(16 in) = 14,080 in³
If water is removed at the rate of 704 in³/minute, the time to remove it all is ...
t = quantity/rate = (14,080 in³)/(704 in³/min) = 20 min
It takes 20 minutes to empty the aquarium.
express your answer in scientific notation 4.9x 10^5 - 5.8x 10^4
Answers
Answer:
4.32×10^5
first calculate the left side and the calculate the right side.
finaly substract the result you get when you calculate at the first the result is 4.32 ×10^5
can anyone help me with this please! Serious plz lol
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I hope this helps you
pleaseeee helpppppp meeee
Answers
Remember: Rise/Run
When you have 1/4, you rise once and run to the right four times.
Since there is no room to plot that, do the opposite. Go down one and to the left four times.
7.
A company is able to sell 600 of its product in the first year of business.
products it is able to sll decreases by 20%. If this trend continues:
Each year however, the amount of
a) How many products will it be able to sell in year 5?
b) How many products will it have sold over the course of 5 years?
Answers
9514 1404 393
Answer:
246 products in year 52017 products over 5 yearsStep-by-step explanation:
The n-th term of the geometric series is ...
an = a1(r^(n-1))
for first term a1 and common ratio r. The common ratio here is the growth factor: 1 -20% = 0.8. This means the 5th term (5th year sales) will be ...
a5 = 600(0.8^(5-1)) ≈ 246 . . . . . products sold in year 5
The sum is given by ...
sn = a1(1 -r^n)/(1 -r) = 600(1 -0.8^5)/(1-0.8) = 2017
The company will have sold about 2017 products over 5 years.
What value will make the equation true -21 - ? = 1and1/2
Answers
Answer:
the answer would be -21 - (-22 1/2)= 1 1/2
The value that will make the equation true would be -21 - (-22 1/2)= 1 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the equation as;
-21 - (-22 1/2)
Now the mixed fraction is 22 1/2 = 45/2
The difference of the equation is;
-21 - (-22 1/2)
-21 - (-45/2)
= 1 1/2
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Can someone help me pls
Answers
Answer:
PΔJKL=66
Step-by-step explanation:
so we are given the line segments JK, KL, and LJ which are tangent to k(O), and also that JA=9, AL=10, and CK=14
JL=JA+AL (parts whole postulate)
JL=9+10=19 (substitution, algebra)
JA=JB=9 (tangent segments from the same point are congruent)
CK=KB=14 (tangent segments from the same point are congruent)
JK=JB+KB (parts whole postulate)
JK=9+14=23 (substitution, algebra)
LA=LC=10 (tangent segments from the same point are congruent)
LK=LC+CK (parts whole postulate)
LK=10+14=24 (substitution, algebra)
Perimeter of ΔJKL=LK+KL+LJ (perimeter formula for triangles)
Perimeter of ΔJKL=23+24+19=66 (substitution, algebra)
Need the answer for x and y
Answers
Answer:
x = 2
BD = 41
Step-by-step explanation:
18x + 5 = 15x + 11
combine like terms:
3x = 6
x = 2
BD = 15(2) + 11 = 41
I HATE MATH so if u help me I’ll give y a kiss muah
Answers
Find the area of each figure.
Answers
1536in (for rectangle). 288in (for triangle)
Area of rectangle: 48in* 32in = 1536 in
Area of triangle: 48in*12in÷1/2= 576/2=288in
Formula of area of triangle is b*h divided by 2
Formula of area of rectangle is length*width
Hope this helps!
Saeed wants to have his birthday at an amusement park with a few of his friends but he can't spend no more then $80. The amusement park charge6a flat admission fee of $35 for a private party and 6.50 per person for food and drinks
Write an inequality that represents the total cost of seeds birthday for n people given his budget
Answers
Answer:
T=35X6.50
Step-by-step explanation:
can someone please help me of really appreciate it , i’ll give you brainliest !!
Answers
Answer:
It would be the second answer, x=-3
Step-by-step explanation:
Exponents: 7-3= 4
3 to the power of 4 = 81
If the probability of a chance event is 0.96, it is less likely to happen than which of the following probabilities of another chance event ?
1. 0.95
2. 0.75
3. 0.85
4. 1
Answers
Please answer the question in the picture because it would paste correctly thanksss
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
146 is equal to 12.08
12 3/4 is 12.75
12 5/8 is 12.63( I rounded it.Before it was 12.625)
Then you put it in order.
What is the answer to 1+1 ?
Answers
Answer:
2
Step-by-step explanation:
1+1=2
Thank you for coming to my TED Talk
Answer:
22
Step-by-step explanation:
Find the least common multiple (LCM) for the pair of numbers 6 and 18
Answers
Answer:
the lcm is 6
Step-by-step explanation:
6 divided by 3 is 1
18 divided by 3 is 6
6 becomes 3 and 2
Answer:
18
Step-by-step explanation:
Since the question is asking for the least common multiple, you factor out the 6 in 18 and 6. This gives you 631 as the LCM because you have factored out 6 and this is the GCF because there are no more common factors between 3 and 1. Since 631 equals 18, 18 is the LCM
HELP NEEDED ASAP! Thanks :)
Answers
Answer:
3
Step-by-step explanation:
First we must find the total boxes of pens
15 + 9 = 24
Then we can divide the total cost by the total number of boxes of pens
$72 / 24 boxes = 3
What is the volume of a sphere with a surface area of 16pi ft^2?
Answers
Answer:
B
Step-by-step explanation:
Sphere Surface Area = 4 • π • r²
For it to equal 16 PI, then radius must equal 2
4*PI*2*2 = 16 PI
Sphere Volume = 4/3 • π • r³
Sphere Volume = 4/3 • π • 2^3
Sphere Volume = 4/3 *PI * 8
Sphere Volume = 32 / 3 PI
Sphere Volume = 10.666 PI cubic feet AND I think that is answer B
which SHOULD read 10 (2/3) PI ft^3
The possible values of x
are given by x+8≤6
The greatest possible value of 7x is
Answers
Answer:
if you help me with this ill help u with that problem
its very simple
https://brainly.com/question/22760971
Step-by-step explanation:
Please Help!!! 15 Points!!! Will Mark Brainliest!!! Please show your work!!
A pick-up truck if fitted with new tires which have a diameter of 40 inches. How fast will the pick-up truck be moving when the wheels are rotating at 365 revolutions per minute? Express your answer in miles per hour rounded to the nearest whole number.
Answers
Answer:
14
Step-by-step explanation:
365*40=14600*60 minutes = 14 miles per hour
Find the slope of the line passing through the points (4,1) and (4,-5)
Answers
Answer:
Step-by-step explanation:
(4 , 1) ; x₁ = 4 and y₁ = 1
(4 , -5) ; x₂ = 4 and y₂ = -5
The slope of the the line is undefined as the line is parallel to y-axis
Need HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
9514 1404 393
Answer:
x = 6
Step-by-step explanation:
The similarity statement tells you ...
TR/TP = XZ/XP
TR = x = TP(XZ/XP) = 12(18/36)
x = 6
A town has a population of 7000 and grows at 4% every year. What will be the population after 13 years, to the nearest whole number?
Answers
Answer:
The population would be 11,656 after 13 years.
Step-by-step explanation:
We can do the equation 7000(1+4/100)^13
Hope it helps :)
solve for Angles 1 and 2 please
Answers
Answer:
angles 1 and 2 measure 118°
Step-by-step explanation:
Isaiah has 2 3/5 cups of dough to make dumplings. If he uses 1/5 cup of dough for each dumpling, how many dumplings can Isaiah make?
Answers
Now that you have 13/5, you will see it’s much easier to divide! There are thirteen fifths cups of dough and he needs one fifths cups of dough for each dumpling. This means he can make 13!
Answer:
Step-by-step explanation:
You can convert 2 3/5 into 13/5 because 5/5 = 1 and 10/5 = 2.
Now that you have 13/5, you will see it’s much easier to divide! There are thirteen fifths cups of dough and he needs one fifths cups of dough for each dumpling. This means he can make 13!
Find the 12th term of the arithmetic sequence whose common difference is d=-7 and whose first term is a = 10.
Answers
Answer:
87
Step-by-step explanation:
tn= a + (n-1)d
t12 = 10 + (12-1)7
=87
please help me I really need it
Answers
Answer:
Step-by-step explanation:
Because of the givens (a right angle a common Hypotenuse and a leg in each triangle) ΔSUT and ΔSUV are congruent. HL
That means that < SUT = < SUV so what you get out of that is
w + 10 = 3w Subtract w from both sides.
w - w + 10 = 3w - w
10 = 2w Divide both sides by 2
10/2 = 2w/2
w = 5
I don't know what A with a check mark below it is.