The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.
In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ([tex]p[/tex]), in feet, and the area of the rectangular plot ([tex]A[/tex]), in square feet, of land are described below:
[tex]p = 2\cdot (w+l)[/tex] (1)
[tex]A = w\cdot l[/tex] (2)
Where:
[tex]w[/tex] - Width, in feet.[tex]l[/tex] - Length, in feet.In addition, the cost of fencing of the rectangular plot ([tex]C[/tex]), in monetary units, is:
[tex]C = c\cdot p[/tex] (3)
Where [tex]c[/tex] is the fencing unit cost, in monetary units per foot.
Now we apply (2) and (3) in (1):
[tex]p = 2\cdot \left(\frac{A}{l}+l \right)[/tex]
[tex]\frac{C}{c} = 2\cdot (\frac{A}{l}+l )[/tex]
[tex]\frac{C\cdot l}{c} = 2\cdot (A+l^{2})[/tex]
[tex]\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A[/tex]
[tex]\frac{C\cdot l}{2\cdot c} - l^{2} = A[/tex] (4)
We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:
FDT
[tex]\frac{C}{2\cdot c}-2\cdot l = 0[/tex]
[tex]l = \frac{C}{4\cdot c}[/tex]
SDT
[tex]A'' = -2[/tex]
Which means that length leads to a maximum area.
If we know that [tex]c = 8[/tex] and [tex]C = 4000[/tex], then the dimensions of the rectangular plot of land are, respectively:
[tex]l = \frac{4000}{4\cdot (8)}[/tex]
[tex]l = 125\,ft[/tex]
[tex]A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}[/tex]
[tex]A = 15625\,ft^{2}[/tex]
[tex]w = \frac{15625\,ft^{2}}{125\,ft}[/tex]
[tex]w = 125\,ft[/tex]
The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.
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The net price of a hand phone after allowing trade discount of 20% was RM2,000. Find what is the list price of the hand phone.
Answer:
RM1,600
Step-by-step explanation:
2000 * 0.20= 400
2000-400= 1600
a lamp post cast a Shadow 15 feet long while a 6 foot man standing nearby cast a shadow 5 ft long. what proportion can be used to determine the hight of the lamp post
Answer:
6/5=x/15
Step-by-step explanation:
6/5=x/15,where x is hight of the lamp post
x=18
A cone with a radius of 3 feet and a height of 5 feet is placed on top of a cylinder as shown. Find the volume of the total figure in terms of pi
Answer:
5π
Step-by-step explanation:
v=1/3πrh
v=1/3×π×3×5=5π
The volume of the combined solid is given as 69π ft³.
What is a right circular cylinder?A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.
The volume of the combined solid is given as,
Volume of cone + Volume of cylinder
The expression can be written as,
1/3πr²h + πr²H
Where h and H are the heights of cone and cylinder respectively.
Plug r = 3, h = 5 and H = 6 to obtain as,
⇒ 1/3π × 3² × 5 + π × 3² × 6
⇒ 69π
Hence, the volume of the combined solid is obtained as 69π ft³.
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WILL MARK AS BRAINLIEST IF CORRECT
Answer:
A) 1/12
Step-by-step explanation:
for every 1 that x increase f(x) increases 12
Answer:
1
Step-by-step explanation:
Twice the sum of a number and 3 is equal to three times the difference of the number and 6. Find the number.
ENER
The number is a
(ANSWER QUICKLY)
Answer: 5
Step-by-step explanation:
Please answer and explain
Answer:
Step-by-step explanation:
(fog)(x) = f[g(x)]
(fog)(x) = f[(4/x - 5)]
(fog)(x) = 1 / ((4/x - 5) - 9)
(fog)(x) = 1 / (4/x - 14)
(gof)(x) = g[f(x)]
(gof)(x) = g[1/(x - 9)]
(gof)(x) = (4/ 1/(x - 9)) - 5
(gof)(x) = (4•(x - 9)/1) - 5
(gof)(x) = (4x - 36) - 5
(gof)(x) = 4x - 41
A soccer goalpost is to be made of 40 feet of
Jumber. The school has 27 feet. How much
umber should be purchases?
Answer:
13 more should be purchased.
40-27=13
Solve. 3(x-6) - 8x = -2 + 5(2x+1)
Answer: x = -1.4
Step-by-step explanation:
Answer: x = -7/5
Step-by-step explanation: (3)(x)+(3)(−6)+−8x = −2+(5)(2x)+(5)(1) 3x+−8x+−18 = 10x+−2+5 −5x+−18 = 10x+3 −5x−18-10x = 10x+3-10x −15x−18+18 = 3+18 −15x/-15=21/-15 x = -7/5
Last year, Christine opened an investment account with $5600. At the end of the year, the amount in the account had decreased by 26.5%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
Decrease in amount:
$
Year-end amount:
Answer:
Decrease amount: $1484 Year-end amount: $4116
Step-by-step explanation:
26.5% of 5600 is 1484. We then subtract 1484 from 5600 because that is how the percentage of decrease, which gives us 4116 dollars. This means her year-end account is 4116 dollars, and the decrease amount is 1484 dollars. Hope this helps!
What is the best estimate of 687 × 391?
280,000
210,000
240,000
180,000
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Original equation/problem:}[/tex]
[tex]\mathbf{687\times391}[/tex]
[tex]\mathbf{= 391\times687}[/tex]
[tex]\mathbf{= 268,617}[/tex]
[tex]\huge\textbf{Now, we're going to solve for your}\\\huge\textbf{question:}[/tex]
[tex]\huge\text{Assuming you want us to estimate to the}\\\huge\text{nearest hundred. So we will do so, because}\\\huge\text{it is easier to understand it like that.}[/tex]
[tex]\mathbf{687 \rightarrow 700}\\\mathbf{391\rightarrow 400}[/tex]
[tex]\huge\textbf{New equation:}[/tex]
[tex]\mathbf{700 \times 400}[/tex]
[tex]\mathbf{= 400\times700}[/tex]
[tex]\mathbf{= 280,000}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ A.\ 280,000}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]HELPPP LAST ATTEMPT!!
19+0.12x=0.16x
This whole entire unit is pretty simple, but apparently my brain won't think.
Could you please help?
Answer:
0.04x = 19
x = 475
Step-by-step explanation:
19 + 0.12x = 0.16x
Take away 0.12x from both sides
19 = 0.04x
Divide 19 by 0.04 to find x
x = 475
Answer:
475
Step-by-step explanation:
First, you have to simplify the equation by moving all the like terms to one side of the equal sign.
This entails the taking of 0.12x to the right side of the equal sign.
Remember, when we take anything over the equal sign if it was a positive sign like in this case, it becomes a negative one and the opposite is true if the sign was negative.
So we have
19=0.16x - 0.12x
We then simplify further and get the equation
19=0.04x
To obtain the true value of x, we divide both sides of the equation by 0.04x as follows:
19/0.04=0.04x/0.04
We then find that
x= 475
Solve the right triangle. a = 2.2 m, B = 37.7°, C = 90° 4) A) A = 52.3°, b = 0.6 m, c = 2.3 m B) A = 52.3°, b = 1.7 m, c = 2.8 m C) A = 52.3°, b = 3.2 m, c = 3.9 m D) A = 52.3°, b = 3.2 m, c = 2.8 m
Answer:
B) A = 52.3°, b = 1.7 m, c = 2.8 m
Step-by-step explanation:
We know that it is a right angle triangle because C = 90°
because of that we can do 180 - 90 + 37.7
which is a=52.3
Because it is a right angle triangle, we can use sin, cos,tan
I will use sin to find the side of c
2.2 is a
sin 52.3 = 2.2/x
x= 2.2/ sin 52.3
x=2.78
You could do cos or tan but the pythagorean theorem for me is much faster
so it looks like this, a^2+b^2 =c^2
in this case we have both a and c we want b
so we rearrange
c^2-a^2=b^2
2.78^2-2.2^2= b^2
[tex]\sqrt{2.89}[/tex]=b
1.7=b
therefore it would be this option B) A = 52.3°, b = 1.7 m, c = 2.8 m
SOCCER TRACK GOLF 112 74 59 # OF STUDENTS There are 450 7th graders at Lakeside Middle School. The chart above shows the number that participate in a certain sport Find and fix the incorrect statement #1. About 55% of 7 graders do not play a sport #2: Of the students who play a sport, 24% play golf #3: Of the students who play a sport, 46% play soccer #4: About 16% of all 7 graders run track HURRYYYYYYYYYYYYY
Answer: about 14% of the 7 grade don't play sports
Step-by-step explanation: i think
3
Evaluate the expression 2 + 2 x 5 - 3
Answer:
9
Step-by-step explanation:
Please Excuse My Dear Aunt Sally
Answer:
= 10x − 1
Step-by-step explanation:
Let's simplify.
2 + 2x(5) − 3
= 2+10x + −3
Combine Like Terms:
= 2 + 10x + −3
= (10x) + (2 + −3)
= 10x + −1
= 10x − 1
An office manager has 10,000$ to spend on new equipment
300 divided by 72 equals (300 divided by 7) + (300 divided by 2) = 2,100 + 600 = 2,700
cho a,b,c là các số nguyên. Chứng minh rằng nếu a mũ 3 + b mũ 3 + c mũ 3 chia hết cho 9 thì một trong các số a , b ,c chia hết cho 3
Answer:
let a, b, c be integers. Prove that if a to the power 3 + b to the power 3 + c to the power 3 is divisible by 9, then one of the numbers a , b , c is divisible by 3
Step-by-step explanation:
E) Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got
the receipt and saw that the tax was $42.42. What was the sales tax rate for this
purchase?
Translating "The tax is some percent of the phone's price" into an equation, we get:
42.42 = p · 499
If we divide both sides by 499, we get
0.085 ≈ p
We can check by finding 8.5% of 499:
0.085 · 499 = 42.415, which rounds to 42.42
So the tax rate was 8.5%.
grahm's birthday Is on 26th May which day of the week Is his birthday?
Answer:
Wednesday, 2021,Thursday, 2022
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=23(0.292)^x
what is the % increase
Answer:
Decay
since 0.292 is less than 1
% rate of decrease
1 - 0.292 = 0.708
70.8%
What is the value of y in the following system of equation3x-4y=-20 -x+2y=10
solve 2/3 - 6y = - 1 5/6
Answer:
y = 19/36
Step-by-step explanation:
Assuming that what you want is the value of y, you can pass all the right side stuff to the left, and the y to the right:
2/3 + 15/6 = 6y
Then you can sum the fractions on the left by using the same denominators:
4/6 + 15/6 = 6y ==> 19/6 = 6 * y
then you can pass the 6 that is multiplying on the right to the left - now dividing:
y = 19/36
Answer:
y = 5/12
Step-by-step explanation:
2/3 - 6y = -1 5/6 . . . . . given
4 -36y = -11 . . . . . . . . . multiply by 6
15 = 36y . . . . . . . . . . add 36y+11
15/36 = y = 5/12 . . . . divide by 36, reduce the fraction
_____
Check
2/3 -6(5/12) = -1 5/6
4/6 -15/6 = -11/6 . . . . true
Flying Home A bird flies from the bottom of a canyon that is 844 9/10 feet below sea level to a nest that is 55 4/5 feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest? The difference between the elevation of the canyon and the bird's nest is enter your response here feet. (Simplify your answer. Type an integer, proper fraction, or mixed number.)
Answer:
900 7/10
Step-by-step explanation:
you add the numbers to gether
what is 433.54 in terms of pi?
Answer:
The angle value 433.54 π rad (pi radian) in words is "four hundred and thirty-three point five four π rad (pi radian)".
Step-by-step explanation:
got the information from the internet
42 out of 56 students have cell phone. What percent of students said they owned a cell phone
Answer:
75%
Step-by-step explanation:
now we can see that our fraction is 75/100 which means that 42/56 as a percentage is 75%
Please help and only answer if correct!
Answer: So last time it was 1/4 and 4 so it's no different it just going down by one so it's 1/3 and 3 if it's not I give up.
Step-by-step explanation:
PLS HELP NOW! WILL GIVE BRAINLIEST TO WHO EVER ANSWERS FIRST
Answer:
y = 1.6x −5
Step-by-step explanation:
We start with two points, let’s say (0,-5) and (4,1.4).
The equation is:
y=mx+b
m is the slope and b the y-intercept.
We can find the slope by:
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-5-1.4}{0-4} = 1.6[/tex]
Then solve the equation for b:
y = 1.6x + b ->
−5 = 1.6(0) + b ->
b = -5.
So the final equation is:
y = 1.6x −5.
Hope that helps! :)
Let ABC ≃DEF. Find mE
The value of mE is blank degree
Answer:
m∠E = 124°
Step-by-step explanation:
Since the triangles are congruent, B and E are automatically congruent, since they are corresponding angles.
First, we must find the value of y.
Set both measures equal to each other.
98 + y = 6y - 32.
Subtract y from both sides.
98 = 5y - 32
Add 32 on both sides.
130 = 5y
Divide 5 on both sides.
y = 26
Substitute y for angle E.
E = 6(26) - 32
E = 156 - 32
E = 124°
Need help with 17 pre college