Farmer Ed has 3,500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answer:
Because it is a rectangle, the area is expressed as A = xy, or length times width.
Step-by-step explanation:
Because it is next to the river, he only needs to fence three sides, so F = x + 2y.
Knowing the amount of fencing available is 7500m, we get:
7500 = x + 2y solve for x
x = 7500 - 2y substitute into the area equation
A = (7500 - 2y)y distribute
A = -2y2 +7500y
You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875
x = 7500 - 2(1875) = 3750
A = 3750(1875) = 7,031,250 m2
If Farmer Ed has 3,500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, Then 7,031,250 is the largest area that can be enclosed.
What is Rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
As it is next to the river, he only needs to fence three sides, so F = x + 2y.
Knowing the amount of fencing available is 7500m, we get:
7500 = x + 2y
solve for x
x = 7500 - 2y
substitute into the area equation
A = (7500 - 2y)y
Distribute
A = -2y2 +7500y
You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875
x = 7500 - 2(1875) = 3750
A = 3750(1875) = 7,031,250 m².
Hence 7031250 is the largest area that can be enclosed.
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State the slope of the line in simplest form.
the tax on a $400 painting is $34 what should be the tax on a $700 painting
The line segment is rotated 270 degrees counterclockwise about the origin to form A'B'. Which statement describes A'B'?
A.) A'B' is parallel to AB.
B.) A'B' is half the length of AB.
C.)A'B' and AB are equal in length.
D.) A'B' is greater than twice the length of AB.
What is the product of −2 1/2 and −3 1/3 ? a−8 1/3 b−616 c6 1/6 d8 1/3
Answer:
d 8 1/3
Step-by-step explanation:
8/9(54x−36)+2=−3/4(−40+16x)+90x solve for x
To make 3.7 a whole number, multiply by ?
What is greater, 7/9, or 7.81 times 10 to the 1 power?
Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $ 2 0 0 $200dollar sign, 200 a month and an additional $ 1 2 $12dollar sign, 12 for each album that he sells. Last month he earned a total of $ 6 4 4 $644dollar sign, 644. Write an equation to determine the number of albums ( a ) (a)left parenthesis, a, right parenthesis Floyd sold last month. Find the number of albums Floyd sold last month.
To find the number of albums Floyd sold last month, we calculate it using the linear equation $644 = $200 + ($12 \u00d7 a), where $644 is the total earnings, $200 is the base rate, and $12 is the amount earned per album. Floyd sold 37 albums last month.
Explanation:To determine the number of albums Floyd sold last month, we can set up a linear equation based on the information provided. Floyd is paid a base rate of $200 per month, and he earns an additional $12 for every album sold. The total amount Floyd earned last month was $644.
Let's let a represent the number of albums sold. The equation that represents the total earnings for the month would be:
Total Earnings = Base Rate + (Number of Albums Sold × Price per Album)
Based on what has been given, we can express this as:
$644 = $200 + ($12 × a)
To find the number of albums sold, we subtract the base rate from the total earnings, then divide by the additional amount earned per album:
$644 - $200 = $12 × a
$444 = $12 × a
a = $444 / $12
a = 37
So, Floyd sold 37 albums last month.
A popular chain of superstores made 3.0479×108 dollars in profit last year. One particular store in the chain made 2.102×106 dollars in profit last year.
How many times greater is the profit made by the entire chain last year than by this particular store?
Drag and drop the values into the boxes to represent the answer in scientific notation.
0.145 1.45 145 10^2 10^14 10^48
____X_____times greater
7 is what percent of 25
Veronica is saving money to buy a saddle for her horse that costs $175. She plans to save $10 the first month and then increase the amount she saves by $5 each month after the first month. How many months will it take her to save $175? (Whoever knows this, YOU ARE A LIFE SAVER
I am 5 more than 6 times 10?what number am i?
Jack is mixing a cleaning solution that is 12% bleach.After mixing the solution,jack has 150 ounces of cleaning solution.how many ounces of bleach did jack use?
Evaluate. 4⋅(1/4^−3)+12
A. 324
B. 290
C. 268
D. 144
which of the following is a solution to 4cos^2x-1=0?
60°
150°
210°
330°
Answer:
Option A- 60°
Step-by-step explanation:
Given : Function - [tex]4cos^2x-1=0[/tex]
To solve the function
Step 1 - Write the function
[tex]4cos^2x-1=0[/tex]
Step 2- Add 1 both side
[tex]4cos^2x=1[/tex]
Step 3- Divide 4 both side
[tex]cos^2x=\frac{1}{4}[/tex]
Step 4 - Taking root both side
[tex]cosx=\sqrt{\frac{1}{4}}[/tex]
Step 5 - solve
[tex]cosx=\pm{\frac{1}{2}}[/tex]
Either [tex]cosx={\frac{1}{2}}[/tex] or [tex]cosx=-{\frac{1}{2}}[/tex]
When [tex]cosx={\frac{1}{2}}[/tex]
[tex]\rightarrow cosx={cos\frac{\pi}{3}}[/tex]
[tex]\rightarrow x={\frac{\pi}{3}} or 60^{\circ}[/tex]
or when [tex]cosx=-{\frac{1}{2}}[/tex]
[tex]\rightarrow cosx={cos(\pi-\frac{\pi}{3})}[/tex]
[tex]\rightarrow x={\frac{2\pi}{3}} or 120^{\circ}[/tex]
Therefore, Option A is correct solution of function is at 60°.
The solution of the given trigonometric ratio for the expression 4cos²x - 1 = 0 is equal to 60°
To find the solutions to the equation 4cos²x - 1 = 0, we first need to isolate the cosine term and then solve for x.
Let's go through the steps,
Add 1 to both sides of the equation:
4cos²x = 1
Divide both sides by 4:
cos²x = 1/4
Take the square root of both sides:
cosx = ±√(1/4)
Now, we have two cases to consider: positive and negative square roots.
Case 1,
cosx = √(1/4)
The cosine of an angle can never be negative when expressed in degrees, so we ignore the negative square root.
cosx = √(1/4) = 1/2
To find the angles for which the cosine is 1/2, we look at the unit circle or use a calculator to find the inverse cosine (arccos) values:
x = arccos(1/2)
The principal angle that satisfies this is x = 60°.
Case 2,
cosx = -√(1/4)
Again, we ignore the negative square root as the cosine is not negative in degrees.
Therefore, the only solution to the equation is:
x = 60°
Therefore, among the given options, the solution to 4cos²x - 1 = 0 is 60°.
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PLEASE HELP BELOW ,,,,,,,
Making an orthographic drawing for the isometric drawing that the right. Assume there are no hidden cubes
In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.
What is orthographic drawing?The orthographic drawing is the 2-D design of the isometric drawing.
Making an orthographic drawing for the isometric drawing that is the right.
The isometric drawing is the 3-D view of the object.
The graph is given below.
In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.
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suppose that Y and Z are points on the number line if YZ=11 and Y lies on -9 where would Z be located
Final answer:
Point Z is located at 2 on the number line, found by adding the distance YZ=11 to the location of Y at -9.
Explanation:
If Y and Z are points on the number line, YZ=11, and Y lies on -9, to find where Z would be located, you simply add the distance between Y and Z to the point Y. Since the distance YZ=11, and Y is at -9 on the number line, you add 11 to -9 to find Z.
Therefore, the location of point Z will be:
-9 + 11 = 2
So, point Z is located at 2 on the number line.
7/4 - 1.76
Please help -.-
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 48 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth are cut from the square?
(π = 3.14)
Answer Choices:
150.72 in2
192.00 in2
1,152.00 in2
1,808.64 in2
Answer:
D). 1,808.64 in2
Step-by-step explanation:
Diameter - 48 in.
Therefore, the radius is half of 48. 48/2 = 24.
Area = 3.14(24) 24 = 1,808.64in2
Hope this helps
Your local bakery charges $6.00 for one dozen of doughnuts. (One dozen is 12 doughnuts). If you purchase any number of doughnuts over one dozen, you will only have to pay $0.40 per doughnut. The total cost of any number of doughnuts is given by the expression below.
6+.40(d−12)
Which part of the expression represents the number of doughnuts purchased at the discounted rate?
A. d
B. (d−12)
C. 6
D. .40(d−12)
0.2(x+50)-6=0.4(3x+20)
( show work please)
Which equation will help you solve this problem?
You have 16 books and 2 shelves to store them.
If you split them equally between the 2 shelves, how many books will be on each shelf?
What is the equation of the graphed line?
Can someone help my do step by step 579 divided by 3
Answer: 193
Step-by-step explanation: an image is included to show you the steps.
From the division of given numbers we get quotient as 193 and the remainder as 0.
The two given numbers are 579 and 3.
Here, 579 divided by 3.
That is, 579/3
3|579|193
3
_____
279
27
_____
09
09
_____
00
So, the quotient is 193 and the remainder is 0.
Therefore, from the division of given numbers we get quotient as 193 and the remainder as 0.
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Tommy rote down all the whole numbers greater than -1 and less than 3. what is the average value of these numbers
suppose 200 students take an exam, graded on a scale of 0-100%. The median exam grade was 78%, the mean exam grade was 68%, and the range of scores was 40%. would you expect this distribution to be symmetric or skewed? Does the distribution have a high or low variation?
in January 2011 the rate of VAT increased from 17.5% to 20%
work out the difference in price of a car worth £15000 +VAT due to increase in VAT
The difference in price of a car is £375 it is due to the rate of VAT increase from 17.5% to 20% and this can be evaluated by the help of unitary method.
Given :
Rate of VAT increased from 17.5% to 20%.
Total price of a car = £15000 + VAT.
In this problem unitary method can be used to determine the difference in price of a car which is due to the increased rate of VAT.
The price of VAT when its' rate is 17.5% can be:
[tex]= \dfrac{15000}{100} \times 17.5[/tex]
= £ 2625
Therefore, the total price of car when VAT is 17.5% is £17625.
The price of VAT when its' rate is 20% can be:
[tex]= \dfrac{15000}{100} \times 20[/tex]
= £ 3000
Therefore, the total price of car when VAT is 20% is £18000.
So, the difference in price of car = 18000 - 17625 = £375.
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Which expression is equal to 4−−√40−3−−√45 ?