To express the area A of the rectangular garden in terms of its length l, the formula is A = l * (90 - 2l). The maximum area of the garden can be determined by finding the maximum value of this formula.
The length and width of the garden that produce the maximum area when the farmer has 90 meters of fencing are l = 22.5 meters and w = 45 meters. If the farmer has 260 meters of fencing, the length and width that produce the garden with the maximum area will be l = 65 meters and w = 65 meters.
To derive the formula expressing the area A of the rectangular garden in terms of its length l, we need to consider the perimeter constraint. The perimeter is given as 90 meters, which means the total length of the fencing must equal 90 meters.
For a rectangular garden, the perimeter is calculated as 2 * (length + width). Therefore, we have the equation:
2 * (l + w) = 90
Simplifying the equation, we get:
l + w = 45
Next, we express the width w in terms of the length l by rearranging the equation:
w = 45 - l
To find the area A of the garden, we multiply the length l by the width w:
A = l * w = l * (45 - l)
This formula expresses the area A in terms of the length l.
To find the maximum area, we take the derivative of the area formula with respect to l and set it equal to zero:
dA/dl = 45 - 2l = 0
Solving this equation, we find l = 22.5 meters. Plugging this value back into the width equation w = 45 - l, we get w = 45 meters. Therefore, the length and width that produce the maximum area when the farmer has 90 meters of fencing are l = 22.5 meters and w = 45 meters.
If the farmer has 260 meters of fencing, we follow the same steps. The perimeter equation becomes:
2 * (l + w) = 260
Simplifying, we have:
l + w = 130
Expressing the width w in terms of the length l:
w = 130 - l
The area formula remains the same:
A = l * (130 - l)
To find the maximum area, we take the derivative:
dA/dl = 130 - 2l = 0
Solving this equation, we find l = 65 meters. Plugging this value back into the width equation w = 130 - l, we get w = 65 meters. Therefore, when the farmer has 260 meters of fencing, the length and width that produce the maximum area are l = 65 meters and w = 65 meters.
To know more about optimization problems, refer here :
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At the circus, a clown is shot from a cannon. This situation can be modeled by the function: h = – 16t2 + 45t + 15, where 'h' is height in feet and 't' is time in seconds. Height of the clown
Answer:
t = 3.11 seconds
Step-by-step explanation:
Given that,
At the circus, a clown is shot from a cannon. This situation can be modeled by the function :
[tex]h = -16t^2 + 45t + 15[/tex]
Where
'h' is height in feet and 't' is time in seconds
We need to find how long did it take for the clown to reach his highest point. It can be calculated as follows :
[tex]-16t^2 + 45t + 15=0[/tex]
We need to solve for t. It can be calculated as follows :
[tex]t=\dfrac{-45\pm \sqrt{45^2-4(-16)(15)} }{2(-16)}\\\\t=-0.301\ \text{and}\ 3.11\ s[/tex]
So, the required time is 3.11 seconds.
** PLEASE ANSWER I’L GOVE YOU BRAINLYLIST**
Penelope eats 4 chocolates per day, because in one day, 20 chocolates are in the box. Then, after 2 more days, 8 chocolates are eaten. That means, if she eats an even amount of chocolates, she eats 4 chocolates per day. To check this pattern, on the fourth day, there are 8 chocolates left. 12 - 8 = 4, and the pattern would continue. On the fifth day, 4 chocolates would be left, and on the sixth day, 0 chocolates would be left.
Kamila buys a notebook for $1.59 and pens for $0.29 each. She spends $5.07.
Define a variable that can be used to determine how many pens she bought.
Write an equation using the variable and solve to determine how many pens she bought.
Answer:
12 pens
Step-by-step explanation:
Let the variable that can be used to determine the number of pens that Kamila bought be represented by n.
Price of a notebook = $1.59
Price a pen = $0.29
Total amount spent = $5.07
But,
1.59 + 0.29 n = 5.07
So that,
0.29 n = 5.07 - 1.59
0.29 n = 3.48
n = [tex]\frac{3.48}{0.29}[/tex]
= 12
Therefore, Kamila bought 12 pens.
what is the answer to (13x+30)-(20x+6)
A number, n, decreased by 5, is equal to 3 times the number plus 1. Determine the number.
Answer:
-3
Step-by-step explanation:
A number, n, decreased by 5: n - 5
3 times the number +1 = 3*n + 1 = 3n + 1
3n +1 = n -5
Subtract 1 from both sides
3n = n - 5 - 1
3n = n - 6
Subtract 'n' from both sides
3n - n = -6
2n = -6 {Divide both sides by 2}
n = -6/2
n = -3
The number = - 3
Jacob has $100 in his savings account. The interest rate is 5% per year. How much interest will he earn in 1 year?
While eating lunch, Douglas noticed that 15 students chose to eat chicken and 19 chose to eat pizza. What is the ratio of students in his class who chose to eat chicken to the total number of students?
Please help, I have ask it 5 times. Please.
Answer:
Pair 1: GM and LJ
Pair 2:HI and LM
Step-by-step explanation:
The markings on the line show which lines are congruent to each other. This means that line HI and ML are congruent because they have similar markings. And you could say the same for line JL and MG because it has 2 lines that mark it as congruent to eachother.
So basically your answers are GM and LJ as one pair and HI and LM as another
Can someone solve this please?
Answer: x = 1/2
Step-by-step explanation:
Kelsey put 6 gallons of water in the cooler. How many 1-pint water bottles can be filled from the water in the cooler?
Answer:
48 pints
Step-by-step explanation:
1 gal=8 pints
Hope this helps
Vertical angles are a pair of opposite angles made by two intersecting lines and the angles are _________. *
2 points
Equal to each other
Equal to 90°
Equal to 180°
Equal to 360°
Answer:
[tex] \boxed{ \large{ \underline{\tt{Equal \: to \: each \: other}}}}[/tex]
Step-by-step explanation:
When two lines interesect , the angles formed opposite to each other are called vertically opposite angles. Vertically opposite angles [ V.O.A ] are always equal to each other.
Refer to the attachment! In the given figure , [tex] \angle[/tex] p and [tex] \angle[/tex] s are opposite to [tex] \angle[/tex]r and [tex] \angle[/tex]q respectively. Therefore [tex] \angle[/tex]p and [tex] \angle[/tex]r are vertical angles. Similarly , [tex] \angle[/tex]s and [tex] \angle[/tex]q are also vertical angles.
Hence , Our final answer : Vertical angles are a pair of opposite angles made by two intersecting lines and the angles are equal to each other .
Hope I helped ! ツ
Have a wonderful day / night ! ♡
# [tex] \underbrace{ \large{ \tt{Carry \: On \: Learning}}}[/tex] !!▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
2. A bacteria population is modeled by the equation p(n)= 10,000.2", where h is the number of hours since
the population was measured.
About how long will it take for the population to reach 100,000?
Answer: its 3 the answer is 3
Step-by-step explanation:
Helppp plssss this is due soooon
Which decimal is largest?
0.49
0.45
0.48
Answer:
0.49
Step-by-step explanation:
Answer:
0.49
Step-by-step explanation:
its 0.01 larger than 0.48
its 0.04 larger than 0.45
6. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function in the table.
X F(x)
1 -7
2 -10
3 -13
4 -16
A. f(x) = -3x - 4
B. f(x) = x - 7
C. f(x) = -1/3x - 4
D. f(x) = 3x + 4
Answer:
I think the answer is B. f(x) = -1/3x - 4
Step-by-step explanation:
Use the given functions to set up and simplify
4−16.
XF(x)=X
Fx
1 − 7 = −6
2 − 10 = −8
3 − 13 = −10
4 − 16 = −12
Draw a rhombus with diagonals 4 and 6. What is the area of the rhombus?
first of all you have to draw a rhombus
area (d+d)/2
(4+6)/2
5
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
Answer:
£2.4 is the anwser im pretty sure
Step-by-step explanation:
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A farmer has one square mile of land. If he divides his land into square fields that are 1/2 mile long and 1/2
[tex] \frac{1}{2} \times \frac{1}{2} [/tex]
wide, how many fields will he have?
Answer:
1/4
Step-by-step explanation:
Can someone help me please
Answer:
625
Step-by-step explanation:
A line passes through point (-2, 5) and has a slope of 5/2.
Write an equation in Ax + By = C form for this line.
Use integers for A, B, and C.
Answer:
5x-2y=-20
Step-by-step explanation:
y-y1=m(x-x1)
y-5=5/2(x-(-2))
y-5=5/2(x+2)
y-5=5/2x+10/2
y-5=5/2x+5
y=5/2x+5+5
y=5/2x+10
y-5/2x=10
-5/2x+y=10
2(-5/2x+y)=2(10)
-10/2x+2y=20
-5x+2y=20
5x-2y=-20
Please hellppp meeeee
Answer:
Slope = -1
Explanation:
Basically, your rise will be going 1 box up (an arrow upwards) and your run would be 1 box to the left (an arrow to the left). This will give you :-
1/-1 = -1
Hope this helps, thank you :) !!
Answer:
-4/3
Step-by-step explanation:
a. On the map of Arkansas shown, find the actual distance between Clarksville and Little Rock. Use a ruler to measure.
Answer:
1cm/20mi = 4cm/x
1x = 80
x = 80
The answer is 80 miles
15 points + brnlist , need help asap!!! (with a picture)
Answer:
C
Step-by-step explanation:
According to my calculations Its c
Combine like terms.
38y + 15y =
Answer:
53y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
38y + 15y
38 and 15 are coefficients
y is a term
Since they are like terms, they can be combined
Step 2: Add
38 + 15 = 53
53y
Find the median:51,53,49,51,53,50,54,56
Answer:
52
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
49, 50, 51, 51, 53, 53, 54, 56
the middle are (51,53) and when u have 2 numbers in the middle u add them up and divide by two which gives us 52:)
Simplify each of the following.
7^2 x 7^3
9514 1404 393
Answer:
7^5 = 16,807
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
__
Here, we have a=7, b=2, c=3, so ...
(7^2)(7^3) = 7^(2+3) = 7^5 = 16,807
What the rang of the following function is
Answer:
b
Step-by-step explanation:
Answer:
its 5
Step-by-step explanation:
A certain population is initially 8,951 but declines by 8% every second. Find an exponential formula that gives the population as a function of time. What will be the population after half of a minute?
9514 1404 393
Answer:
734
Step-by-step explanation:
The growth factor is 1 -8% = 0.92. This is the base of the exponential formula. The multiplier is the initial value, so you have ...
p = 8951×0.92^t
When t=30, this evaluates to ...
p = 8951×0.92^30 ≈ 733.68
The population after half a minute will be about 734.
What is the volume of the following rectangular prism pls pls pls pls pls pls pls pls p
Answer:
Step-by-step explanation:
V = l * w * h
l = 2
h = 2
w = 7/3
Volume = 2 * 2 * 7/3 = 28/3 = 9 1/3 or 9.3333
Which equation would you use to solve this problem: Laura bought 4 1/3 bushels of apples for $16. How much did each bushel cost? *
Answer: $3.69
Step-by-step explanation:
Laura bought 4 1/3 bushels of apples.
Firs convert this to an improper fraction for easier calculation:
= 13/3 bushels of apples.
If cost $16 altogether, individually they must cost:
= Cost / Quantity purchased
= 16 ÷ 13/3
= 16 * 3/13
= $3.69
Note: You can divide by a fraction by multiplying the inverse of that fraction.