Answers
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
Related Questions
Write a phrase in words to match each expression.
5+3
——
n
Answers
Answer:
sum of five and 3 is divided by n
Team members Corinne, Kevin, and Tomas decide to share the cost
of 2 motor controllers and 4 wheels equally. How much does each
member need to contribute?
Please help(write step by step and upload pic or do it here please I appreciate it so much !
Answers
Answer:
each member needs to put in 91.70 dollars in.
Step-by-step explanation:
you add the costs of all the tools needed. in this case the two controllers and wheels which adds up to 275.1.
then you divide by the amount of people which is three. so 275.1/3 and you get 91.7
20. It takes Zach 15 minutes to walk 7 blocks to the swimming pool. 7 At this rate, how many blocks can he walk in one minute? Circle the letter of the correct answer. how do I do this step by step to solve it by myself
Answers
Answer:
Zach chose C as the correct answer
7 divided by 15 is 0.47, that’s the amount of miles divided by the number of minutes. I’m really sleep deprived so sorry if this answer is wrong 3
If sin theta equals to a divided by b what is the value of sec square theta minus tan square theta
Answers
Answer:
Square is the answer
hope it helps u
plz mark it as brainliest
Rewrite the expression using rational exponents .
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt[5]{(3y)^{4}} = [(3y)^{4}]^{\frac{1}{5}}=(3y)^{4*\frac{1}{5}}=(3y)^{\frac{4}{5}}[/tex]
Find the length of side xx in simplest radical form with a rational denominator.
Answers
Answer:
Solution given:
Relationship between perpendicular and hypotenuse is given by sin angle
Sin 30°=opposite/hypotenuse
½=[tex]\frac{x}{9}[/tex]
x=[tex]\frac{9}{2}[/tex]
The value of x is [tex]\frac{9}{2}[/tex]
Find the missing angle in the image below. Do not include spaces in your answers ** Can somebody help me fr everybody keep giving me the wrong answer
Answers
Answer:
measure of angle V + measure angle W = VUF
Answer:
∠ VUF = 94°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles
∠ VUF is an exterior angle of the triangle, then
∠ VUF = 71° + 23° = 94°
hello can you help me with this?
Answers
Answer:
x = 25.5
Step-by-step explanation:
suppose RS and MQ are parallel the sum of angle MRS and RMN would be 180 degrees
2x + x + x 78 = 180 add like terms then subtract 78 from both sides
4x = 102 divide both sides by 4
x = 25.5
If a= 5-2 root 6 then find the value of root a - 1/root a
Answers
Answer:
2\sqrt2
Step-by-step explanation:
a=5-2√6 ...(1)
[tex]\frac{1}{a}=\frac{1}{5-2 \sqrt{6} } \times\frac{5+2\sqrt{6} }{5+2\sqrt{6} } =\frac{5+2\sqrt{6}}{(5-2\sqrt{6})(5+2\sqrt{6})} =\frac{5+2\sqrt{6}}{5 ^2-(2\sqrt{6})^2} =\frac{5+2\sqrt{6}}{25-24} =5+2\sqrt{6}\\a+\frac{1}{a}=5-2\sqrt{6}+5+2\sqrt{6}=10[/tex]
[tex](\sqrt{a}-\frac{1}{\sqrt{a}})^2=(\sqrt{a})^2+(\frac{1}{\sqrt{a}})^2-2 \times \sqrt{a} \times \frac{1}{\sqrt{a}}=a+\frac{1}{a}-2=10-2=8\\\sqrt{a}-\frac{1}{\sqrt{a}}=\sqrt{8}=2\sqrt{2}[/tex]
Find the measure of the indicated angle
Answers
Answer:
Step-by-step explanation:
This is an isosceles triangle because 2 of the sides are the same length (marked with single slashed through them). The Isosceles Triangle Theorem tells that if 2 sides are congruent to each other, then the angles opposite those sides are congruent to each other as well. That means that the bottom left angle measures 68. According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180, so:
x = 180 - 68 - 68 so
x = 44
Chad gets an annual salary of 25,000. He and his family spend 3500 per year on food. What percent of his salary is spent on food
Answers
Answer:
[tex]\frac{x}{100}[/tex] x 25000 = 3500
[tex]x[/tex] x 250 = 3500
x = 3500/250
x = 350/25
x = 14%
Janna is using a cone-shaped cup to fill a cylindrical container. The cup has the same height and radius as the container. How many rimes will she have to fill the cone-shaped cup to completely fill the cylindrical container.
Answers
Answer:
3 times
Step-by-step explanation:
Step 1: Express the volume of the cup in terms of "r" (radius) and "h" (height)
The formula for the volume of a cone is:
Vcone = 1/3 × h × π × r²
Step 2: Express the volume of the container in terms of "r" and "h"
The formula for the volume of a cylinder is:
Vcylinder = h × π × r²
Step 3: Calculate how many times the volume of the cone is contained in the volume of the cylinder
Vcylinder/Vcone = (h × π × r²) / (1/3 × h × π × r²) = 3
1. Describe the graph of the line x=5
Answers
Answer: a Line going up and down
Step-by-step explanation:
Answer:
See explanation below
Step-by-step explanation:
The line x = 5 would be vertical and lies on x = 5 within the x-axis.
Is 3a = 9 true or false when x is 3?
Answers
X
2
4
00
12
V
4
2.
1
2/3
Answers
Answer:
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5
Step-by-step explanation:
Select the correct answer.
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table
Find the area
Please help me
Answers
Answer: 24 square cm.
8*6=48
48/2=24
Answer:
24 cm^2
Step-by-step explanation:
(w*h)/2
pls help w this
√2x+1 = 4
In the equation above, what is the value of 2x +1?
A) 3/2
B) 2
C) 4
D) 16
Answers
Answer:
[tex]\boxed {\boxed {\sf D. \ 16}}[/tex]
Step-by-step explanation:
We are given the following equation and asked to solve for 2x+1.
[tex]\sqrt {2x+1}=4[/tex]
We want to isolate the entire expression of 2x+1. Notice that it is under the square root. If we want to isolate it, we have to perform the inverse operation. The inverse of a square root is a square, so we square both sides of the equation.
[tex](\sqrt{2x+1} )^2= (4)^2[/tex]
[tex]2x+1=(4)^2[/tex]
[tex]2x+1=16[/tex]
We could continue solving for x, then plug the answer back into the expression 2x+1. However, hopefully you notice that we already found the answer!
We only had to do one step to find the answer, but you could complete many other steps to get the same answer:
[tex]2x+1-1=16-1\\2x=15\\2x/2=15/2\\x= 7.5[/tex] (Solve for x)
[tex]2x+1\\2(7.5)+1\\15+1\\16[/tex] (Plug the answer in for x)
The value of 2x+1 is 16 and the correct answer is 16.
A washer and a dryer cost $587 combined. The washer costs $63 less than the dryer. What is the cost of the dryer?
Answers
Answer:
The dryer costs $325.
Step-by-step explanation:
Let w represent the cost of the washer and d represent the cost of the dryer.
They cost $587 combined. In other words:
[tex]w+d=587[/tex]
The washer costs $63 less than the dryer. Therefore:
[tex]w=d-63[/tex]
Thus, we have the system of equations:
[tex]\displaystyle \begin{cases} w+d = 587 \\ w=d-63\end{cases}[/tex]
We can solve it using substitution. Substitute the second equation into the first. Hence:
[tex](d-63)+d=587[/tex]
Combine like terms:
[tex]2d-63=587[/tex]
Add 63 to both sides:
[tex]2d=650[/tex]
And divide both sides by two. Hence:
[tex]d=325[/tex]
The dryer costs $325.
Further Notes:
And since the washer is $63 less, the washer costs:
[tex]w=(325)-63=262[/tex]
The washer costs $262.
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
Answers
Answer:
3
Step-by-step explanation:
We are going to be using cofunction identity cos(90-x)=sin(x).
Apply to either side but not both.
cos(22f − 1) = sin(7f + 4)
sin(90-[22f-1])=sin(7f+4)
90-[22f-1]=7f+4
Distribute
90-22f+1=7f+4
Combine like terms
91-22f=7f+4
Add 22f on both sides
91=29f+4
Subtract 4 on both sides
87=29f
Divide 29 on both sides
3=f
f=3 is between 0 and 90
Answer:
The answer is "3."
Step-by-step explanation:
Just submitted the test and got the answer correct!
Can someone help me with this math homework please!
Answers
Answer:
x = 48.125
Step-by-step explanation:
Explanation in progress! (●'◡'●)
Answer:
48.25
Step-by-step explanation:
first wirte the same qa and write long qa and write the ans in procesa
an object falls from a height, h m, varies directly as the square of its time, t s on planet Q. given that the object falls from the height of 5 m in 2 s, calculate the time taken in seconds, for the object to fall from a height of 45 m on the planet.
Answers
Answer:
18 seconds
Step-by-step explanation:
5x9=45 so 2x9=18
Find the value of cos C rounded to the nearest hundredth, if necessary
Answers
[tex]\bold{\frac{5}{13} or 0.38}[/tex]
Answer:
Solution given:
here
by using Pythagoras law
hypotenuse =
[tex]\displaystyle\sqrt{adjacent ²+opposite ²}\\=\sqrt{15²+36²}=39[/tex]
Cos C=[tex]\frac{adjacent} {hypotenuse}=\frac{15}{39}=\frac{5}{13} or{0.38}[/tex]
solve the simultaneous equation: y=2x²+3x-31 y= x= 21-2x
Answers
Answer:
1. x =(3-√257)/4=-3.258
2. x =(3+√257)/4= 4.758
Step-by-step explanation:
irst add
x
to both sides of the second equation to get:
y = x + 3
Then substitute this expression for y into the first equation to get:
29 = x 2 + ( x + 3 ) 2 = 2 x 2 + 6 x + 9
Subtract 29 from both ends to get:
0 = 2 x 2 + 6 x − 20
Divide both sides by 2 to get:
0 = x 2 + 3 x− 10 = ( x+ 5 ) ( x − 2 )
So x = 2 or x = − 5
If x = 2 then y = x + 3 = 5 .
If x = − 5 then y=x + 3 = − 2
So the two solutions
( x, y ) are ( 2 , 5 ) and ( − 5 , − 2 )
Can someone help with this problem
Answers
y=60
If you add the opposite side values of the triangle (not the one touching the y), you get the value of y). 35+25=y
This works because y+x= 180 and the three angles of a triangle add to 180.
Step-by-step explanation:
x+35+25=180
x+60 =180
x = 120.
y+x =18
Suppose that the scores on a statewide standardized test are normally distributed with a mean of 64 and a standard deviation of 2. Estimate the percentage of scores that were (a) between 60 and 68.
Answers
Answer:
95. 45%
Step-by-step explanation:
Given :
Mean score, = 64
Standard deviation = 2
Score between 60 and 68
P(Z < (x - mean) / standard deviation)
P(Z < (60 - 64) / 2) = P(Z < - 2) = 0.02275 (Z probability calculator)
P(Z < (68 - 64) / 2) = P(Z < 2) = 0.97725 (Z probability calculator)
P( score between 60 and 68)
P(Z < 2) - P(Z < - 2)
0.97725 - 0.02275 = 0.9545
Score between 60 and 68 = 0.9545 = 0.9545 * 100% = 95.45%
Grafico de deportes: fútbol 30%, atletismo 25%, tenis 5%, voleibol 10%, basquetbol 20%. Si 165 jóvenes prefieren el fútbol ¿cuantos prefieren el basquetbol?
Answers
Answer:
33 jóvenes prefieren el basquetbol.
Step-by-step explanation:
Hay 165 jóvenes.
De estos, 20% prefieren el basquetbol.
¿cuantos prefieren el basquetbol?
20% de 165, entonces:
[tex]20\% = \frac{20}{100} = 0.2[/tex]
[tex]0.2*165 = 33[/tex]
33 jóvenes prefieren el basquetbol.
Intercept Form
Point (-3,4)
Slope 5/3
m= b=
Answers
Answer:
y = 5/3x + 9
Step-by-step explanation:
y = 5/3x + b
4 = 5/3(-3) + b
4 = -5 + b
9 = b
Can someone help solve the problems 2-4
Answers
Answer:
1234567891011121314151617181920
Step-by-step explanation:
you just count
An amusement park has discovered that the brace that provides stability to the ferris
wheel has been damaged and needs work. The arc length of steel reinforcement that
must be replaced is between the two seats shown. The sector area is 28.25 square
feet and the radius is 12 feet.
Brace that provides
A: 4.708
B: 2.669
C: 9.417
D: 2.354
stability to the ride
What is the length of steel that must be replaced?
04.708 feet
Answers
Answer:
Hence the correct answer is option (A) 4.708.
Step-by-step explanation:
Solution:-
Now, we need to find the angle of the sector by using sector formula,
[tex]A = 28.25 ft^{2} \\r = 12ft.\\\\28.25 = \frac{\theta}{360^{o} } \times \pi \times 12^{2} \\\\\theta=\frac{28.25\times 360}{12 \times12 \times \pi} \\\\\theta =( \frac{70.625}{\\pi} )^{o}[/tex]
We now convert the angle to radian
[tex]\theta = \frac{70.625}{\pi} \times \frac{\pi}{180}\\\\\theta = 0.39236 radian[/tex]
Now we calculate the length of arc by arc formula
[tex]\theta=\frac{I}{12} \\\\0.39236 =\frac{I}{12}\\\\I = 4.708 feet.[/tex]
So, The length of steel that must be replaced is 4.708 ft.
Find the value of `x´ in the given parrallelogram.
Answers
3x-12=x+6
2x-12=6
2x=18
X=9
Step-by-step explanation:
=> (3x-12) =(x+6)
or,3x - x = 6 + 12
or,2x = 18
or,x = 18/2
•: x=9#
