A three-sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. The enclosed area is to equal 288 m². Find the minimum perimeter and the dimensions of the corresponding enclosure. Dimensions: ... m x ... m
Minimum perimeter: ... m
Answers
the minimum perimeter and the dimensions of the corresponding enclosure: Dimensions: 24 m x 12 m
Minimum perimeter: 48 m
To minimize the perimeter of a three-sided fence enclosing a 288 m² rectangular region with the river forming the fourth side, we can use calculus.
Let's denote the length of the fence parallel to the river as x and the lengths of the other two fences as y. So, the area of the rectangular region is given by the equation:
Area = x * y = 288 m²
Since we want to minimize the perimeter, we'll first express the perimeter in terms of one variable. The perimeter of the three-sided fence is given by:
P = x + 2y
Now, express y in terms of x using the area equation:
y = 288 / x
Substitute this expression for y in the perimeter equation:
P(x) = x + 2(288 / x)
To find the minimum perimeter, differentiate P(x) with respect to x:
dP/dx = 1 - 576/x²
Set the derivative equal to zero to find the critical points:
0 = 1 - 576/x²
Solving for x:
x² = 576
x = 24 m
Now, find the corresponding value of y using the expression for y:
y = 288 / 24
y = 12 m
So, the dimensions of the rectangular region are 24 m x 12 m. The minimum perimeter is:
P = 24 + 2(12) = 24 + 24 = 48 m
Dimensions: 24 m x 12 m
Minimum perimeter: 48 m
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Related Questions
what is the measure of
Answers
Answer:
what
Step-by-step explanation:
A mass attached to a vertical spring has position function given by s(t)=5sin(2t) where t is measured in seconds and s in inches:
Find the velocity at time t=1
Find the acceleration at time t=1
Answers
The acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.
To find the velocity and acceleration of the mass attached to a vertical spring at time t=1, we need to differentiate the position function with respect to time.
First, we can find the velocity function v(t) by taking the derivative of the position function s(t) with respect to time t:
v(t) = s'(t) = 5cos(2t) * 2 = 10cos(2t)
Plugging in t=1, we get:
v(1) = 10cos(2) ≈ -3.42 inches/second
Therefore, the velocity of the mass at time t=1 is approximately -3.42 inches/second.
Next, we can find the acceleration function a(t) by taking the derivative of the velocity function v(t) with respect to time t:
a(t) = v'(t) = -20sin(2t)
Plugging in t=1, we get:
a(1) = -20sin(2) ≈ -19.42 inches/second^2
Therefore, the acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.
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please help me find the same denominator
Answers
Answer:
\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)
let us first start with some basic information ~
A fraction can be represented as \(\frac{x}{y}\\\) where ,
x is the numerator and y is the denominator !
the question asks us to do something that will help us get same denominator for both the terms !
so let's see what we should do in such a case ~
\( \frac{9}{10} \: and \: \frac{7}{8} \\ \\ \\ lets \: make \: the \: denominator \: of \: both \\ the \: terms \: reach \: 80 \: , \\ \\ \bold\orange{ \implies \: \frac{9}{10} \times \frac{8}{8} = }\bold\red{ \frac{72}{80}} \\ \\\bold\orange{ \implies \: \frac{7}{8} \times \frac{10}{10} =}\bold\red{ \frac{70}{80}} \)
and we're done !
let's add some more info to be lil more clear ~
while converting the denominator of both the terms , we must multiply the same number ( this number refers to the one we'll have to multiply to the denominator to obtain the desired result ) with the denominator as well as with the numerator !
hope helpful :D
Answer:
Step-by-step explanation:
you have to multiply first fraction with '8' and second fraction with '10' :
the fractions will become 72/80 and 70/80 then you can compare it
•15 POINTS• don’t need to explain.
a.)
b.)
c.)
Answers
Answer: HL
Step-by-step explanation:
HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.
Julie's entertainment budget for the next six months is $150 per month. She enjoys watching the latest movies and loves the ballet. A movie ticket costs $15 while a ballet ticket costs $35. This month Julie already attended one ballet show and three movies. If Julie decides she would rather see ballet shows for the remainder of this month, how many ballet shows can she attend and stay within her budget?
Answers
Movie ticket=$15
Ballet ticket=$35
Money spent
1 ballet ticket=$35
3 movie tickets=(3x15)=$45
Money spent =$80
Money left=(total amount-money spent)
=($150 -$80)
=$70
Ballet shows Julie would be able to attend=$70/$35
=2
Julie would be able to attend two ballet shows and stay in her budget
17x - y < 13
I’m slope-intercept form
Answers
Answer:
y > 17x - 13
Step-by-step explanation:
We want to write the inequality in slope-intercept form
The general slope intercept form is;
y = mx + b
where m is the slope and b is the y-intercept
So what we have to do to the inequality is to make y the subject
Thus, we have that;
17x -13 < y
Flipping this, we have
y > 17x-13
WILL GIVE BRAINLIEST
PLEASE HURRY! I HAVE ONLY 3 HOURS BEFORE EVERYTHING HAS TO BE SUBMITTED AND I HAVE A LOT DUE!!
What is 1/3 of 4/7?
A. 4/21
B. 5/21
C. 4/10
D. 5/10
Answers
you want to multiply 1/3 by 4/7 since the question uses the word “of”
Answer:
The answer is A.
Hope this helps good luck with online class!
Step-by-step explanation:
4 times 1 = 4
3 times 7 = 21
4/21 'of' means multiply or times!
By using only those factors given in interest tables, find the values of the factors that follow, which are not given in your tables. Show the relationship between the factors by using factor notation, and calculate the value of the factor. For example, (F/P,8%,38)=(F/P,8%,30)(F/P,8%,8)=18.6253. Click the icon to view the interest factors for discrete compounding when i=8% per year. (c) Find the value of the (P/A,8%,145) factor. Select the correct choice below and fill in the answer box to complete your choice. A. (P/A,8%,145)= 0.08
1−(P/F,8%,45)
= (Round to four decimal places. ) B. (P/A,8%,145)= 0.08
1−(P/F,8%,100)(P/F,8%,45)
= (Round to four decimal places.) C. (P/A,8%,145)=(P/A,8%,100)(P/A,8%,45)= (Round to four decimal places. ) D. (P/A,8%,145)= 1−(P/F,8%,100)(P/F,8%,45)
0.08
= (Round to four decimal places.) At what rate of interest compounded annually will an investment double in nine years? The investment will double in nine years at \% compounded annually. (Round to two decimal places.)
Answers
The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:
(P/A, i%, n) = (1 - (1 + i)^(-n)) / i
Substituting the values given:
i = 8%
n = 145
(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08
Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:
(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)
Therefore, the correct choice for the value of (P/A,8%,145) is:
C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)
Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:
(F/P, i%, n) = (1 + i)^n
We want the investment to double, so we have:
(1 + i)^9 = 2
Taking the ninth root of both sides:
1 + i = 2^(1/9)
Solving for i:
i ≈ 0.0809 or 8.09% (rounded to two decimal places)
Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
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In a fruit survey, 300 children choose their favorite fruit out of apples, bananas and watermelon. 38% chose apples, 28% chose bananas. How many children chose watermelon?
Answers
There were 10 cards in a bag labeled 0-9 what is the probability of drawing a 3 and then a 5 if the first card is not replaced before the second drawn
Answers
Answer:
1/9 chance
Step-by-step explanation:
you count 55 cells in the picture. the field of view is 1.85 mm x 1.23 mm. estimate how many cells are in your t75 flask.
Answers
Based on the given information, the estimate for the number of cells in a T75 flask can be calculated by comparing the number of cells in the picture to the field of view area and then scaling it up to the size of the T75 flask.
Given that there are 55 cells in the picture, we can use this information to estimate the density of cells in the field of view. The field of view has dimensions of 1.85 mm x 1.23 mm, which gives an area of 2.7095 square millimeters (\(mm^2\)). To calculate the cell density, we divide the number of cells (55) by the area (2.7095 \(mm^2\)), resulting in an approximate cell density of 20.3 cells per \(mm^2\).
Now, to estimate the number of cells in a T75 flask, we need to know the size of the flask's growth area. A T75 flask typically has a growth area of about 75 \(cm^2\). To convert this to \(mm^2\), we multiply by 100 to get 7500 \(mm^2\).
To estimate the number of cells in the T75 flask, we multiply the cell density (20.3 cells/\(mm^2\)) by the growth area of the flask (7500 \(mm^2\)). This calculation gives us an approximate estimate of 152,250 cells in the T75 flask. It's important to note that this is just an estimate, and actual cell counts may vary depending on various factors such as cell size, confluency, and experimental conditions.
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please help determine if these are functions and explain why or why not
Answers
Answer:The first is a function but the second isn’t.
Step-by-step explanation: The numbers in the first circle (domain) should only point to one number in the second circle (range). Meaning the domain should only have one arrow for it to be a function. Therefore the first problem is a function, but the second problem is not. For
example, in the first problem, the 0 is only pointing to one number, the 2. However, in the second problem the 6 is pointing to two different numbers, the 3 and the 5. -Let me know if this helps you or if you want me to explain it more. Hope this helps! :)
4(4a-2b+5)+2(2a-5)=?
Answers
Answer:
=20a-8b+10
Step-by-step explanation:
4(4a-2b+5)+2(2a-5)
0pen parenthesis
=16a-8b+20+4a-10
Collect like terms
=16a+4a-8b+20-10
=20a-8b+10
Factorise
=2(10a-4b+5)
how can we draw it in graph?
\(f(x) = { - 2}^{ - x} \)
Answers
The graph of f(x) = -2⁻ˣ is given as attached.
How was the above graphed?To graph the function f(x) = -2⁻ˣ, we can follow these steps:
1. Choose a set of x-values to plot on the x-axis. Since the function has an exponent that involves negative powers of 2, we should choose values that are evenly spaced on the x-axis, such as -3, -2, -1, 0, 1, 2, and 3.
2. Substitute each x-value into the function to find the corresponding y-value. For example, when x = -3, we have f(-3) = -2⁻³ = -1/8. Similarly, we can find the y-values for the other x-values we chose.
3. Plot the points (x, y) on the graph. Make sure to label the axes and use a ruler or graphing software to ensure accuracy.
4. Connect the points with a smooth curve to show the shape of the function between the plotted points. Since the function has a negative exponent, it approaches zero as x gets larger, so the curve should approach the x-axis as it moves to the right.
The resulting graph should show a decreasing curve that gets closer and closer to the x-axis, without ever touching it, as x gets larger.
Note that the values of y for each x are:
When x = -3, y = -1/8
When x = -2, y = -1/4
When x = -1, y = -1/2
When x = 0, y = -1
When x = 1, y = -2
When x = 2, y = -4
When x = 3, y = -8
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![how can we draw it in graph?[tex]f(x) = { - 2}^{ - x} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/2jVItBkGpjfNEMsDhwrecge9e3un9g5G.jpeg)
Everyday Math
425. Cooking Natalia's pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?
Answers
Answer:
5
Step-by-step explanation:
........................
Answer:
If Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
Then she needs to cook 5 pounds of pasta if she has 2.5 quarts of sauce.
Step-by-step explanation:
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.We need to find pounds of pasta to be cooked if she has 2.5 quarts of sauce.Use the unitary method to find the pounds of pasta to be cooked.Step 1 of 2
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
If one quart of sauce calls for two pounds of pasta,
Then to find how much pasta is needed for 2.5 quarts of sauce we need to form a proportion.
Let the pounds of pasta needed be x .
\($$\begin{aligned}\frac{\text { pasta }(\text { inPounds })}{\text { Sauce }(\text { inQuarts })} &=\frac{\text { pasta }(\text { inPounds })}{\text { Sauce(inQuarts })} \\\frac{2}{1} &=\frac{x}{2.5}\end{aligned}$$\)
Multiplying both sides by 2.5 we get,
\($$\begin{aligned}\frac{2}{1} \times 2.5 &=\frac{x}{2.5} \times 2.5 \\x &=2 \times 2.5 \\x &=5\end{aligned}$$\)
Step 2 of 2
To check if the answer is reasonable, we substitute it back in the formed proportion
\($\frac{2}{1}=\frac{x}{2.5}$$\)
We found x=5 hence,
\($$\begin{aligned}\frac{2}{1} &=\frac{5}{2.5} \\2 &=2\end{aligned}$$\)
Here, LHS =RHS
Hence, our answer is correct.
Can you help me get the answer ?
Answers
Round 7412 to the nearest thousand.
Answers
Answer:
7000 :)
Step-by-step explanation:
The nearest thousand to 7412 is 7000.
Answer: 7000
Step-by-step explanation: When you round 7412 to the nearest thousand you should get 7000.
Simplify the following expression. (0.5x – 3)(0.5x + 3)
Answers
Answer:
0.25x^2-9
Step-by-step explanation:
Difference of squares converse:
0.25x^2-9
Answer:
0.25x^2-9
Step-by-step explanation:
multiply 0.5x with 0.5x which is 0.25x^2. then multiply 0.5x with 3 which is 1.5x. then multiply -3 with 0.5x which is -1.5x. then multiply -3 with 3 which is 9. so you will have 0.25x^2+1.5x-1.5x-9.
1.5x and -1.5x is 0. so you are left with 0.25x^2-9
Al lives 30 mi. from Ann. At the same time, they start biking toward each other on the same road. Al’s constant rate is 12 mph. Ann’s is 8 mph. How long will it take them to meet?
A. 0.5 hour
B. 1 hour
C. 1.5 hours
D. 2.5 hours
Answers
Answer:
c. 1.5 hours
Step-by-step explanation:
12x1.5=18
8x1.5=12
12+18=30
Answer:
1.5
Step-by-step explanation:
i took the test
If I use 1 pound of sausage for 3/4 pound of cheese how much sausage do I need if I use 1 pound of cheese
Answers
Answer:
1.33Step-by-step explanation:
3/4 = 0.75 pound
1 : 0.75 = x : 1
x = 1 * 1 : 0.75
x = 1.33
--------------check
1 : 0.75 = 1.33 : 1
1.33 = 1.33
the answer is good
Answer:
\(1 \frac{1}{3}lb \: sausage\)
Step-by-step explanation:
What Iike to do is make it like a ratio.
So you have one pound of sausage per 3/4lb of cheese
\( \frac{1lb \: sausage}{( \frac{3}{4} )lb \: cheese} = \frac{sausage}{1lb \: cheese} \)
Then you just make that sausage the subject of the equation by multiplying 1lb cheese to both sides of the equation, and you have your answer.
\(1lb \: cheese \times \frac{1lb \: sausage}{0.75 \: lb \: cheese} = sausage\)
Any help on this? ;-;
Answers
Answer:
last one: 20
Step-by-step explanation:
4 divided by 5 is 0.8
so is 20 divided by 25
16. The perimeter of a rectangular garden is 90 feet. The gardens lengin s5 feci less than 4 messen What are the length and width of the garden?
Answers
the ratio of dividends to the average number of common shares outstanding is:
Answers
The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.
To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.
For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.
In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.
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Blank x + 16 + x = – 3 x – 4
Answers
The value of x from given linear equation is -4.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Given that x + 16 + x = – 3 x – 4
To find the value of x solving the given linear equation
x + 16 + x = – 3 x – 4
⇒ 2x + 16 = -3x - 4
⇒ 2x + 3x = -4 -16
⇒ 5x = -20
⇒ x = -20/5
⇒ x = -4
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A cab charges $1.45 for the flat fee and $0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has $35 to spend.
answers are:
A. $1.45 + $0.55x ≥ $35; x ≥ 61 miles
B. $1.45 + $0.55x ≤ $35; x ≤ 61 miles
C. $0.55 + $1.45x ≥ $35; x ≥ 23 miles
D. $0.55 + $1.45x ≤ $35; x ≤ 23 miles
Answers
9514 1404 393
Answer:
B. $1.45 + $0.55x ≤ $35; x ≤ 61 miles
Step-by-step explanation:
The mileage charge for x miles will be $0.55x, so the total charge will be $1.45+$0.55x. This must be less than or equal to $35 for Ariel to be able to pay for her travel. The appropriate inequality is ...
$1.45 +$0.55x ≤ $35 . . . . . matches choice B
__
Comment on selecting an answer
From a "reasonableness" point of view, any answer choice with "≥ $35" can be eliminated immediately. Further, any answer choice with $1.45x can be eliminated, since the mileage charge is not $1.45, it is $0.55. The leaves only the choice shown above.
ILL GIVE U BRANLIEST WHATS THE SLOPE!?!
Answers
Answer: I dont know this, but can you pl give me brainliest, i wanna know what it looks like and what it does
Step-by-step explanation:
A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 11 footballs were filled with helium to the recommend pressure and 12 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 291 yards with a standard deviation of 4 yards. The mean yardage for the air filled footballs was 285 yards with a standard deviation of 2 yards. Assume the populations are normal with equal variances.
(a). Construct a 80% confidence interval for the mean difference in in yardage for the two types of footballs
Lower bound
(use 3 decimal places)
Upper bound
(use 3 decimal places)
(b). What can you conclude about the sports writer's idea that helimum footballs travel farther, on average?
Answers
Evaluate -6y - 5 for y = 1/2
Answers
Answer:
15
Step-by-step explanation:
-6y-5
Substitute 1/2 for y.
-6y-5
-6(1/2)-5
-3(-5)
15
A feed trial to compare three dietary supplements was conducted using 24 pigs of approximately the same body weight. The 24 pigs came from four litters, with each of the four litters containing six pigs. Within a given litter, the six pigs were randomly assigned to the three dietary supplements, with two receiving each supplement. The pigs were housed in 24 identical pens and fed their assigned diets under identical conditions. This is an example of a block design. What are the blocks in this design?a. The 24 different pigsb. The three different dietary supplementsc. The four different littersd. The 24 identical pensIt is don't D
Answers
The blocks in this design are c. the four different litters. The pigs within each litter were grouped together as a block, and the three dietary supplements were randomly assigned to the two pigs within each block.
This helps control for any variation between litters that could affect the results of the feed trial. The 24 identical pens are not the blocks in this design, but rather the units where the treatments were applied.
A litter is defined as the live birth of several young at once in an animal from the same mother and typically from the same pair of parents, especially three to eight young. The term is most frequently used to refer to the offspring of mammals, although it can also refer to any animal that bears numerous offspring.
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4. Tom rides his bike 35km north and then 450 km east. How far is he from his starting
point?
Answers
Answer:
485km
Step-by-step explanation:
Hope this helps:)