Answer:
1. Express the width of the rectangle in terms of the length X.
width = 500 - X
2. Express the surface area of the rectangle in terms of X.
area = -X² + 500X
3. What value of X gives the maximum surface area?
maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250
X = 250 ft
4. What is the maximum surface area?
maximum surface area = X² = 250² = 62,500 ft²
Step-by-step explanation:
since the perimeter = 1,000
1,000 = 2X + 2W
500 = X + W
W = 500 - X
area = X · W = X · (500 - X) = 500X - X² or -X² + 500X
The area of a shape is the amount of space it occupies.
The width in terms of x is 500 - xThe surface area in terms of x is x(500 - x)The value of x that gives maximum surface area is 250 feetThe maximum area is 62500 square feetThe length is represented as x.
Let the width be y.
So, we have:
[tex]\mathbf{Perimeter =2(x + y)}[/tex]
This gives
[tex]\mathbf{2(x + y) = 1000}[/tex]
Divide both sides by 2
[tex]\mathbf{x + y = 500}[/tex]
Make y the subject
[tex]\mathbf{y = 500 -x}[/tex]
So, the width in terms of x is 500 - x
The surface area is calculated as:
[tex]\mathbf{A = xy}[/tex]
Substitute [tex]\mathbf{y = 500 -x}[/tex]
[tex]\mathbf{A = x(500 - x)}[/tex]
So, the surface area in terms of x is x(500 - x)
Expand [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 500x - x^2}[/tex]
Differentiate
[tex]\mathbf{A' = 500- 2x}[/tex]
Equate to 0
[tex]\mathbf{500- 2x = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = 500}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 250}[/tex]
So, the value of x that gives maximum surface area is 250
Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]
[tex]\mathbf{A = 250 \times 250}[/tex]
[tex]\mathbf{A = 62500}[/tex]
Hence, the maximum area is 62500
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Solve for n: 0.22n = 6.6.
Answer:
30
Step-by-step explanation:
Solve for n: 0.22n = 6.6.
6.6/0.22 (because for example 3/3 and n/n= 1 so 0.22/0.22 = 1 so we have to divide 6.6 since it is part of the equation and we have to do it on both sides.)=30
What is the quotient of -3/8 and -1/3?
A. -1 1/8
B. -1/8
C. 1/8
D. 1 1/8
Answer:
d. 1 1/8
Step-by-step explanation:
-3 -1
---- ÷ -----
8. 3
Keep, Change, Flip.
-3/8 stays the same.
Division becomes multiplication.
-1/3 becomes -3/1
-3. -3. = 9
----- × ----- ------
8. 1. = 8
9/8 = 1 1/8
Answer:
D. 1 1/8
Step-by-step explanation:
The sum of two numbers is 14 and their difference is 4. What are the two numbers (02 6 8 Larger number Smaller number
Answer:
The two numbers are 9 and 5
Step-by-step explanation:
If u try adding 9 and 5 u will get 14
And if u subtract them u will get 4
I hope the answer is helpful
Please help me thanks.
y=(-2x)+5
Step-by-step explanation:
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 25 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)width ________ ftheight _______ ft
Answer:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
Step-by-step explanation:
This question is better understood with an attachment.
See attachment for illustration.
Given
Represent Perimeter with P
[tex]P = 25ft[/tex]
Required
Determine the dimension of the rectangle that maximizes the area
First, we calculate the perimeter of the rectangular part of the window.
From the attachment, the rectangle is not closed at the top.
So, The perimeter would be the sum of the three closed sides
Where
[tex]Width = 2x[/tex]
[tex]Length = y[/tex]
So:
[tex]P_{Rectangle} = y + y + 2x[/tex]
[tex]P_{Rectangle} = 2y + 2x[/tex]
Next, we determine the circumference of the semi circle.
Circumference of a semicircle is calculated as:
[tex]C = \frac{1}{2}\pi r[/tex]
From the attachment,
[tex]Radius (r) = x[/tex]
So, we have:
[tex]C = \frac{1}{2}2\pi * x[/tex]
[tex]C = \pi x[/tex]
So, the perimeter of the window is:
[tex]P = P_{Rectangle} + C[/tex]
[tex]P =2y + 2x + \pi x[/tex]
Recall that: [tex]P = 25[/tex]
So, we have:
[tex]25 =2y + 2x +\pi x[/tex]
Make 2y the subject
[tex]2y = 25 - 2x - \pi x[/tex]
Make y the subject:
[tex]y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}[/tex]
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Next, we determine the area (A) of the window
A = Area of Rectangle + Area of Semicircle
[tex]A = 2x * y + \frac{1}{2}\pi r^2[/tex]
[tex]A = 2xy + \frac{1}{2}\pi r^2[/tex]
Recall that
[tex]Radius (r) = x[/tex]
[tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
Substitute [tex]\frac{25}{2} - x - \frac{\pi x}{2}[/tex] for y in [tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
[tex]A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2[/tex]
Open Bracket
[tex]A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \frac{1}{2}\pi x^2[/tex]
To maximize area, we have to determine differentiate both sides and set A' = 0
Differentiate
[tex]A' = 25 - 4x - \pi x[/tex]
[tex]A' = 0[/tex]
So, we have:
[tex]0 = 25 - 4x - \pi x[/tex]
Factorize:
[tex]0 = 25 -x(4 + \pi)[/tex]
[tex]-25 =-x(4 + \pi)[/tex]
Solve for x
[tex]x = \frac{-25}{-(4+\pi)}[/tex]
[tex]x = \frac{25}{4+\pi}[/tex]
Recall that
[tex]Width = 2x[/tex]
[tex]Width = 2(\frac{25}{4+\pi})[/tex]
[tex]Width = \frac{50}{4+\pi}[/tex]
Recall that:
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Substitute [tex]\frac{25}{4+\pi}[/tex] for x
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}[/tex]
[tex]y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}[/tex]
[tex]y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{50}{2(4 + \pi)}[/tex]
[tex]y = \frac{25}{4 + \pi}[/tex]
Recall that:
[tex]Length = y[/tex]
So:
[tex]Length =\frac{25}{4 + \pi}[/tex]
Hence, the dimension of the rectangle is:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.
Answer:
$0.36
Step-by-step explanation:
Let the cost per unit of electricity = e
Let the cost per unit of gas = g
a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390;
600e + 100g = 390 ----- i
400 units of electricity and 250 units of gas were used for a total cost of $326.
400e + 250g = 326 ----- ii
Now we have two equations, and we solve for g;
600e + 100g = 390 ----- i
400e + 250g = 326 ----- ii
Multiply equation i by 4 and equation ii by 6;
2400e + 400g = 1560 ---- iii
2400e + 1500g = 1956 ---- iv
Subtract equation iii from iv;
1100g = 396
g = [tex]\frac{396}{1100}[/tex] = 0.36
Cost per unit of gas $0.36
82 63 44 25 sequence
Answer:
the next number is 6
Step-by-step explanation:
i'm assuming you want to find what comes next after 25 so pretty much each number decreases by 19
The 10th term of the arithmetic sequence will be –89.
What is the arithmetic sequence?Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as
[tex]\rm a_n = a_1 + (n - 1)d[/tex]
The sequence is given below.
82, 63, 44, 25, ......
The first term is 82 and the common difference will be
d = 63 – 82
d = –19
Then the equation will be
[tex]\rm a_n =82- (n - 1) \times 19[/tex]
Then the 10th term of the sequence will be
a₁₀ = 82 – (10 – 1) x 19
a₁₀ = 82 – 171
a₁₀ = –89
The complete question is 82 63 44 25 sequence. What is the 10 term of the sequence?
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HELPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
its the first third and fith
Step-by-step explanation:
For Carly's birthday celebration her family took her out to eat at her favorite restaurant. The total bill was $135.
Her dad wants to leave an 18% tip.
How much money is the tip?
$
Clara’s school awarded 1900 raffle tickets as incentives. The principal will draw one winning ticket. The winner will receive an iPad pro. Clara received 5 tickets for good attendance, 4 for making the honor roll, and 8 for tutoring other students.
What is the probability that one of Clara’s tickets will be selected by the principal? (write your answer as a %, once it is in % form round to the hundredths place)
Answer:
0.89%
Step-by-step explanation:
Given that :
Total number of raffle tickets = 1900
Total number of Clara's tickets (5 + 4 + 8) = 17
Probability that one of Clara's tickets will be picked :
Probability = (required outcome / Total possible outcomes)
Required outcome = total number of Clara's ticket
Total possible outcomes = total number of raffle tickets
Hence,
P(picking one of Clara's tickets) = 17 / 1900
17 / 1900 = 0.0089473
0.0089473 * 100%
= 0.8947%
= 0.89%
Suppose that you are asked to pick a card from a deck of 52 cards. Once you have selected a card, you place it face down on the table. You are then asked to selected another card from the deck. Is the event of you picking the first card going to affect the probability of the second card selected, why or why not? Are these events independent or dependent?
Answer:
Step-by-step explanation:
The second card is influenced by the first only in that you have not replaced the first card. That makes a difference.
1/52 is the probability for the first card.
1/51 is the probability for the second card.
They are independent events. Drawing the 7 of diamonds does not make the chances of drawing the Ace of Spades other than the 7 came first and the probability of getting the Ace is slightly larger.
Step-by-step explanation:
The only way the second card is influenced by the first is if you did not swap out the first card. That alters everything.
The likelihood of getting the first card is 1/52.
The odds of getting the second card are 1/51.
They happen separately. Other than the fact that the 7 came first and the odds of receiving the Ace is a little bit higher, drawing the 7 of diamonds does not increase the chances of drawing the Ace of Spades.
Emilio wants to find 2/3 of 50. explain how emilio could estimate the answer
Answer:
Emilio could estimate the answer by thinkinng of 50 as 100. Then 2/3 of 100 is 66.66666666. Divide this by 2 to get 33.33333333
Step-by-step explanation:
Hopefully this helps! I kind of just thought of what ran through my head so I would say it's an estimate.
Error Analysis A contractor purchases 4 dozen pairs of padded work gloves for $54.24. She
incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct
unit price? What is the error?
The correct unit price is $
per pair.
Answer:
the unit rate for each pair is $1.13
Step-by-step explanation:
Okay this is how you would do this problem correctly:
we know that 4 dozen pairs of gloves cost $54.24 however we want to know what the cost is for one pair so we have to make a equation by dividing total cost by the number of glove pairs.
$54.24/4 dozen
the reason we are putting 4 dozen instead of just dividing $54.24 by 4 is because we want to know the unit price for each pair of gloves so it would actually look like this:
$54.24/4(12)
Dozen = 12
so we multiply 12 by 4 to get 48 pairs of gloves, we then divide $54.24 by 48 to find our unit rate of pricing for each pair:
$54.24/48 = 1.13
so now we place a dollar sign in front of 1.13 to get your answer:
for every pair bought it costs $1.13
So how did the Analysis A contractor get the wrong answer? well when she had bought the 4 dozen gloves she divided $54.24 by 4, which in this case would make it seem as though the gloves came in a 12 pack of gloves. However she was buying the gloves individually so she would have to multiply 4 by 12 before dividing the total number of gloves from $54.24.
a drawer contains 8 blue socks and 8 black socks. it is dark and you cannot tell the difference between colors
Answer:
yes
Step-by-step explanation:
i will trun on the light and see what color the socks are
please write complete question
what is 25+30 pleas help me
Plz help me with this
hi!
so you're trying to find the value of n, I assume.
(n +2) / 5 = -3
n + 2 = -3 * 5
n + 2 = -15
n = -17
hope this helped!
The new Xbox series gaming console sells for 499 all units are sold out at stores but can be found online for 34% more than the original price how much would it cost to get it online at the marked up price
Use the ten blocks to draw a quick picture to solve the following division problem: 165/11.
Step-by-step explanation:
[tex]\begin{array}{c|c c|c} 11 & 165 & & 15 \\ \cline {2-3} & 11 & & \\ & & 55 & \\ \cline {2-3}& & 55 & \\ & & 0& \end {array}[/tex]
At a university, Todd deposits $100 into his cafeteria account. He spends $5 on dinner every day. Seth deposits $140 into his account. He spends $5 on lunch and $5 on dinner every day. After how many days will Todd and Seth have the same amount of money in their accounts? 16 8 4 2
Answer:
The answer is 8 days.
Step-by-step explanation:
By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table
Day - Todd - Seth
1 - 95 - 130
2 - 90 - 120
3 - 85 - 110
4 - 80 - 100
5 - 75 - 90
6 - 70 - 80
7 - 65 - 70
8 - 60 - 60
The radius of a circle is 10 meters. What is the angle measure of an arc bounding a sector
with area 150 square meters?
Which of the following offers the least price per ounce of shampoo?
A) $6 for 8 ounces of shampoo
B) $4 for 5 ounces of shampoo
C) $8 for 12 ounces of shampoo
D) $12 for 16 ounces of shampoo
The required offer is the least price per ounce of shampoo is $8 for 12 ounces of shampoo. Option C is correct.
Given that,
To determine the offer the least price per ounce of shampoo.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
A) $6 for 8 ounces of shampoo
6 / 8 = $0.75 per ounces of shampoo
B) $4 for 5 ounces of shampoo
4/ 5 = $0.80 per ounces of shampoo
C) $8 for 12 ounces of shampoo
8/12 = $0.67 per ounce of shampoo
D) $12 for 16 ounces of shampoo
12/16 = $0.75 per ounce of shampoo
Thus, the required offer is the least price per ounce of shampoo is $8 for 12 ounces of shampoo. Option C is correct.
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Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. Complete the table using equivalent ratios. help me pleaseeee
Answer:
21/6 = 7/2 = 14/4
Step-by-step explanation:
Answer:
21:6 7:2 14:4
Step-by-step explanation:
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At a certain school,5/9 of the students are boys. Today, 2/3 of the boys brought their lunch. What fraction of the students are boys who brought their lunch
The fraction of the students are boys who brought their lunch is 5/6.
It is required to find the fraction of the students are boys who brought their lunch.
What is fraction?A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
At a certain school, students are boys =5/9
students are boys brought their lunch=2/3
According to given question we have,
Divide 5/9 by 2/3
[tex]\frac{5/9}{2/3} \\\\\frac{5}{6}[/tex]
Therefore, the fraction of the students are boys who brought their lunch is 5/6.
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evaluate the expression when x=4/5 and y=-2/9: 3y-x
Answer:
-2/15
Step-by-step explanation:
PLS HELP!!! Which statement about numbers is true?
All whole numbers are rational numbers
All rational numbers are integers
All rational numbers are whole numbers
All integers are whole numbers
First to answer will be voted brainliest!!
Answer:
all integers are whole numbers
Please could you show the working out as well:)
Answer:
( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{2 + 5}{15}[/tex] = [tex]\frac{7}{15}[/tex]
[tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{18-7}{21}[/tex] = [tex]\frac{11}{21}[/tex]
[tex]\frac{7}{15}[/tex] , [tex]\frac{1}{2}[/tex] , [tex]\frac{11}{21}[/tex]
LCD (2, 15, 21) = 210
[tex]\frac{98}{210}[/tex] , [tex]\frac{105}{210}[/tex] , [tex]\frac{110}{210}[/tex]
105 - 98 = 7
110 - 105 = 5 ⇒ [tex]\frac{11}{21}[/tex] is closer to [tex]\frac{1}{2}[/tex] ⇒ ( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
what is an equation for the translation of y=|x| left 7 units?
Answer:
y,x-7
Step-by-step explanation:
I think this is it
Answer:
y=x-7
Step-by-step explanation:
Classify the shape as precisely as possible based on its markings.
Question 11 options:
A)
Rhombus
B)
Quadrilateral
C)
Parallelogram
D)
Rectangle
Answer:
c is wrong
Step-by-step explanation:
The given shape is a rhombus.
Hence the correct option is A.
Given is a shape we need to identify its type,
Since all the sides are congruent shown, so we can conclude that the shape is a Rhombus.
A rhombus is a quadrilateral (a polygon with four sides) in which all four sides have equal length. Additionally, the opposite sides of a rhombus are parallel to each other.
The rhombus is also a special type of parallelogram, as it has all the properties of a parallelogram, including opposite sides being equal in length, all the sides being equal and opposite angles being equal in measure.
Hence the correct option is A.
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Y-p=m(x-8) solve for x
Answer:
x = Y /m − p /m +8
Step-by-step explanation: