Sai has a garden on the side of his house that will be enclosed with 196 ft. of fencing. The
rectangular plot will be fenced in on all sides except for the side against the house. What
dimensions will maximize the plot of land? What is the maximum area?
PLEASE DO THESE BELOW
-use written and verbal explanination that justifies each step
-Use at least one representation(ex number sentences, diagrams, charts, etc)
Answers
Answer:
49 and 98, with an area of 4802
Step-by-step explanation:
So, let X be one of the sides, and Y be the other
X*Y would be the area of the rectangle since width*length = area, and X is the width and Y is the length
2X+Y would be the perimeter, excluding the wall (since we don't need fencing for the side sticking to the wall)
To find the max area, we can plot our two equations
so, our two equations:
1. 2X+Y=196 (since perimeter)
2. X*Y=area, and we're trying to maximise it
We can re-arrange the first equation to get
3. Y=196-2X
plug our new equation (#3) into the second equation(#2)
to get:
X*(196-2X)=area=196X-[tex]2X^2[/tex]
And now that we have this equation, we can either:
Graph it to see the largest area (the highest point)
Or calculate the max area using calc
We have a quadratic function that goes up, then down as X increases, so we'll try to find the point where the function stops going up, and instead goes down as X increases (image is attached, not to scale). Recall that the first derivative basically tells is the slope of a function/equation at a given X, so when the function is at a slope of 0, we know that the area is at its max point.
Take the first derivative
(196X-2X^2)'=196-2(2X)=196-4X
196-4X is the equation of the slope, so when X = 49, then the slope is 0
This means that one of the side lengths should be 49
To find out which one, we can use trial and error: (there are 2 cases)
1. 49*((196-49)/2)=3601.5
or:
2. 49*(196-2*49)=4802
The second option is correct since the number, or the area is larger.
Side length 1: 49
Side length 2: (196-2*49), or 98
Note: there's definitely another way to do this problem
Related Questions
What is the distance from the shore to the waterfall in the image of the koi pond shown below? All measurements are in yards. Round to the nearest hundredth if needed.
3 yards
99.72 yards
13.8 yards
6.43 yards
Answers
Answer:
6.43 yards
Step-by-step explanation:
a²+b²=c²
x²+5.4²=8.4²
x²+29.16=70.56
-29.16 -29.16
x²=41.4
x=6.43
help me pleeeeeeeeeeeeeeeease
Answers
Answer:
n ≥ 29
She needs to do more than 29 pushups on the sixth day.
Step-by-step explanation:
First, we need to use the formula for finding the average. We currently have numbers for the first 5 days.
(22+26+21+25+27+n)/6 = 25
Multiply both sides by 6.
25*6 = 150
150-27-25-21-26-22=x
x=29
Since it is an inequality, Sarah needs to do more than 29 pushups on the sixth day.
Find the value of a and b so that f(x)=(x-5)(a㏒ₓ3-b)
Answers
Answer: :-p(x) = x⁴ - ax³ -3x² + 2x + bWe have to find the values of "a" and "b"Given :-(x+1) and (x-1)
Which of the following rates is the best deal on a box of cereal?
options:
$3.20 for 20 ounces
$4.50 for 25 ounces
$5 for 40 ounces
$6.50 for 20 ounces
Answers
Answer:
C. $5 for 40 ounces
Step-by-step explanation:
First, we need to find the unit rate for each deal.
To do this, we divide the price of the cereal box by the unit (ounces):
1. $3.20 for 20 ounces
3.20/20 = $0.16 for each ounce
2. $4.50 for 25 ounces
4.50/25 = 0.18 for each ounce
3. $5 for 40 ounces
5/40 = 0.13 for each ounce
4. $6.50 for 20 ounces
6.50/20 = 0.33 for each ounce
As you can see, the third one is the best deal, as it is the least expensive.
Hope this helps!
What is the surface area of this complex figure?
Enter your answer in the box.
ft²
Answers
Answer:
a = side length a
b = side length b = bottom triangle base b
c = side length c
h = height of prism
H = height of bottom triangle
V = volume
Atot = total surface area = all sides
Alat = lateral surface area = all rectangular sides
Atop = top surface area = top triangle
Abot = bottom surface area = bottom triangle
Step-by-step explanation:
Answer:
792ft²
Step-by-step explanation:
Have a blessed day
I hope this helps
God bless
Jenny is studying the growth of a particular type of plant. She is testing the effects of three growth factors: lighting, age, and temperature. Here are the levels she's testing for each.
Growth factor Levels
Lighting Low, Medium, High, Very high
Age month, months, months, months, months
Temperature , , ,
She wants to find the number of ways of combining one level from each of the growth factors. How many ways are there?
Answers
Answer:
80
Step-by-step explanation:
For these types of counting problems, just multiply all of the levels.
For example, this would be
4 choices
5 choices
4 choices
Multiply 4*5*4, and you get 80.
Total number of ways of combining one level from each of the growth factors is equals to 80.
What is fundamental principle of counting?" As per fundamental principle of counting if first event has 'm' number of possible outcomes , second has 'n' number of possible outcomes then total number of ways are m× n ."
According to the question,
Number of growth factors =3
First growth factor: Lightening
Second growth factor: Age
Third growth factor : Temperature
As per the data given we have,
Number of levels in lightening 'm'= 4
Number of levels in age 'n'= 5
Number of levels in temperature 'p' =4
Substitute the value as per the definition of fundamental principle of counting
Total number of ways = m × n × p
= 4 × 5 × 4
= 80 ways
Hence, total number of ways of combining one level from each of the growth factors is equals to 80ways.
Learn more about fundamental principle of counting here
https://brainly.com/question/23905307
#SPJ2
Pls help me with this
Answers
Answer:
Library A: 1500 books
Library B: 900 books
Library C: 3250 books
Library D: 750 books
Library E: 3000 books
From GREATEST to LEAST
Library C, Library E, Library A, Library B, then Library D
What is the volume of a hemisphere with a diameter of 7.6 m, rounded to the nearest tenth
Answers
Answer:
112.9 cubic meters
Step-by-step explanation:
Formula for Sphere: (4/3) * π*r*3
Since the hemisphere is half of the sphere, plug in variables and multiply.
Screenshot attached please help i need the answer quickly there are 2 problems so please solve all of them
Answers
Answer:
Pink: 48 units sq
Blue: 42 units sq
Step-by-step explanation:
Area of a trapezoid: A=(h)(a+b)/2. To see where h, a, and b are located, see the reference image below. Always remember that a is the shorter end and b is the longer end. Since each grid mark goes by 2, we can use the graph to find the missing variables.
PINK trapezoid:
h = 8, a = 4, b = 8A = 8(4 + 8)/2 = 48 units squaredBLUE trapezoid:
h = 6, a = 4, b = 10A = 6(4 + 10)/2 = 42 units squaredHope this helps!
Please help it’s a math question!!
Answers
Answer:
pentagon, octagon and heptagon.
Step-by-step explanation:
pentagon - five sides
hexagon - six sides
heptagon - seven sides
octagon - eight sides
quadrilateral - four sides
nonagon - nine sides
In this question, we have three polygons: pentagon, octagon and heptagon. (in order from left to right)
Hope this helps!
The boys track team needs to keep a count of how many laps they run at practice so they know the distance. Each lap is 400 meters. What is the difference between the teammate who ran the furthest and the teammate who ran the least distance?
Answers
Answer:
9 laps or 3600 meters.
Step-by-step explanation:
First you want to find who has ran the furthest and the least distance.
So we have Rory ran the most with 14 laps or 5600 meters and Daniel who ran the least with 5 laps or 2000 meters.Next we subtract becuase when you say to "find the difference" it means to subtract.We subtract if you want to find the laps we do 14-5 and if you want to find the number of meters we do 5600-2000.
At a pizzeria one day, 12 of the pizzas sold were topped with mushrooms. This represented 15% of all the pizzas sold that day. What was the total number of pizzas sold that day?
Record your answer in the grid. Be sure to use the correct place value.
Answers
Answer:
80
Step-by-step explanation:
So, let's say the total number of pizzas is x
If 15% of x, the total, is 12, then x * 0.15 must = 12
Use this to make an equation
12 = 0.15x
Divide both sides by 0.15 to get x on its own
12 / 0.15 = x0.15 / 0.15
80 = x
80 pizzas were sold
PLS HELP! 15 POINTS!
Answers
Answer:
297
Step-by-step explanation:
3*3*3*11=297
How you find the area is by multiplying all of the sides
KA EASY- correct answers only thx :)
Answers
Answer:
B C
Step-by-step explanation:
not gonna bother, by examination
Pls Help..............
Answers
Answer:
12
Step-by-step explanation:
V = l*w*h
V = 4*1.5*2
V = 12
Hope this helps :)
(25 POINTS) Parallel lines m and n are cut by a transversal t. Which two angles are NOT corresponding angles?
A. 1 and 6
B. 4 and 8
C. 3 and 7
D. 1 and 5
Answers
Explanation: 1 & 6 has different angle measurements. 6 is obviously bigger than 1 if we properly look at it.
Answer:
Answer is A.
Step-by-step explanation:
Solve each equation. Show your work, 1. 5(y + 2/5) =-13
Answers
Answer:
-3
Step-by-step explanation:
5(y+2/5)=-13
5(y+0.4)
5y + 2 =-13
5y=-13+2
5y=-15
y=-15/5
y=-3
5(-3+2/5)=-13
What is the measure of Angle B from the diagram below:
Answers
Answer:
201
Step-by-step explanation:
Can ya'll help me? I have tried to do it but I keep getting it wrong :(
Answers
Answer:
A: 4
Step-by-step explanation:
So first you can move the 2^-5 to the denominator, making the equation (2^2) (4^3) / (2^5) (2)
Then simplify the terms so you end up with (4)(64) / (32) (2)
Then multiply the denominator so you end up with (4) (64) / (64)
Since both the denominator and numerator have 64, those cancel out leaving you with 4
If you need more clarification feel free to ask
Answer:
A) 4
Step-by-step explanation:
Evaluating
(2⁻⁵)(2²)(4³)(2⁻¹)(2)⁻⁵⁺²⁻¹ x (2²)³(2)⁻⁴⁺⁶(2)²4Write the expanded form of the expression (using distributive property). -4(5x + 6)
Answers
Answer:
-20x - 24
you just multiply the factor on the outside by each on the inside.
A __________ is the amount of energy needed to raise the temperature of one __________ of water, ________ degree celcius.
Write the correct words for those missing above (there are two possible correct answers).
Your answer:
Answers
Answer:
calorie, gram, 1
Step-by-step explanation:
this is what I know, good luck:)
Specific heat capacity is the amount of energy required to raise the temperature of 1kg of one degree of any substance ( including water) by one degree Celsius
Hope this helps xx
List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches. find the area of the rectangle the square the triangle and the other rectangle
Answers
Answer:
The area of the square is x^2
The area of the triangle is x*height/2
The area of the rectangle is x*height of rectangle
X is the length of the square named C
You need to measure these yourself because we don't know whether these are to scale or not.
Step-by-step explanation:
A small business spent $23,000 for taxable items last year. The tax was 9.5%. How much did the small business pay in taxes last year?
step by step please!!!!!!
Answers
to find the amount the business paid in taxes, you have to find 9.5% of $23000
9.5% is 0.095 as a decimal
multiply 23000 by 0.095 to get 2185
therefore, the business paid $2,185 in taxes last year
hope this helps!
Im stuck on this one question
Answers
Answer:
8x+6 is less than or equal to 42
Step-by-step explanation:
Answer:
e
Step-by-step explanation:
Cameron pays $6 to rent shoes.
Cameron pays $8 per game.
Cameron has a limit of $42.
Expression: 8x + 6 [tex]\leq[/tex] 42
Cameron must spend less than or equal to $42.
hope this helps :)
hi i need help can somebody answer this question and give an explanation
Answers
Answer:
0.30
Step-by-step explanation:
Each marker costs 30 cents each (0.30$)
you have to divide the amount of money (6) by the amount of markers (20)
6 ÷ 20= 0.30
Stevie is moving up to the attic and wants to paint a wall white. The wall is a triangle with a base of 20 feet and a height of 21 feet. What is the area of the wall?
Answers
Answer - 420 ft
Answer:
Step-by-step explanation:
Remark
Use the formula for the Area of a Triangle to find the number of square feet the paint will have to cover.
Formula
Area = 1/2 base * height
Givens
b = 20 feet
h = 21 feet
Solution
Area = 1/2 * 20 * 21
Area = 1/2 * 420
Area = 210 square feet
Please Help! You will get brainliest as long as it is correct!
Answers
Answer:
Casey's snack mix is slightly cheaper per ounce.
Step-by-step explanation:
Divide the total price per box by the amount of ounces. This results in:
- Kim's snack mix costing $0.16 per ounce.
- Casey's snack mix costing $0.14 per ounce.
Therefore, by $0.02, Casey's snack mix is cheaper even though the total price is higher due to having more mix.
Rectangle QUAD has coordinates Q(0,0), U(0,3), A(6,3), and D(6,0). Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor 6. What are the coordinates of point D'?
Answers
Answer:
Step-by-step explanation:
Since the dilation is centered at the origin, we can multiply each of the coordinates by the scale factor. This gives us that D'(36,0).
coach loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of ______
a. center
b. quantity
c. distribution
d. variation
e. correlation
Answers
Answer:
variation?
Step-by-step explanation:
A car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. Which equation represents the distance, d, that the car travels in m minutes?
A. d = 0.75 m
B. d = 1 1 3 m
C. d = 3.5 m
D. d = 2.625 m
Answers
Answer:
3.5
Step-by-step explanation:
2 5/8 mi=21/8mi 3/12min=7/2min 7/2 as a decimal is 3.5