You are using 1000 feet of fence to create a rectangular enclosure. Let X represents length of the rectangle. Please use proper unit in each answer. A rectangle drawing could help. 1. Express the width of the rectangle in terms of the length X. 2. Express the surface area of the rectangle in terms of X. 3. What value of X gives the maximum surface area. 4. What is the maximum surface area?
Answer:
1. Express the width of the rectangle in terms of the length X.
width = 500 - X
2. Express the surface area of the rectangle in terms of X.
area = -X² + 500X
3. What value of X gives the maximum surface area?
maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250
X = 250 ft
4. What is the maximum surface area?
maximum surface area = X² = 250² = 62,500 ft²
Step-by-step explanation:
since the perimeter = 1,000
1,000 = 2X + 2W
500 = X + W
W = 500 - X
area = X · W = X · (500 - X) = 500X - X² or -X² + 500X
The area of a shape is the amount of space it occupies.
The width in terms of x is 500 - xThe surface area in terms of x is x(500 - x)The value of x that gives maximum surface area is 250 feetThe maximum area is 62500 square feetThe length is represented as x.
Let the width be y.
So, we have:
[tex]\mathbf{Perimeter =2(x + y)}[/tex]
This gives
[tex]\mathbf{2(x + y) = 1000}[/tex]
Divide both sides by 2
[tex]\mathbf{x + y = 500}[/tex]
Make y the subject
[tex]\mathbf{y = 500 -x}[/tex]
So, the width in terms of x is 500 - x
The surface area is calculated as:
[tex]\mathbf{A = xy}[/tex]
Substitute [tex]\mathbf{y = 500 -x}[/tex]
[tex]\mathbf{A = x(500 - x)}[/tex]
So, the surface area in terms of x is x(500 - x)
Expand [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 500x - x^2}[/tex]
Differentiate
[tex]\mathbf{A' = 500- 2x}[/tex]
Equate to 0
[tex]\mathbf{500- 2x = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = 500}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 250}[/tex]
So, the value of x that gives maximum surface area is 250
Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]
[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]
[tex]\mathbf{A = 250 \times 250}[/tex]
[tex]\mathbf{A = 62500}[/tex]
Hence, the maximum area is 62500
Read more about areas at:
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9
Use the graph to answer the following questions.
D
175
150
(4.150)
125
Total Cost
100+
(2.100)
75
50 10.50
25
Days
Part C: Write the equation for the line if x = the number of days and y = the total cost.
So
IM 2020
10
Use the graph to answer the following questions.
a
Your equation for the first point will be y=x+50
Explanation...
The x is zero so we just only put x. The y is 50 so we input a 50 giving us y=x+50.
Your equation for the second point will be y=2x+100.
Explanation...
Your slope is 2 so we input that and the y intercept is 100 giving us the equation y=2x+100.
Your equation for the third point will be y=4x+150
Explanation...
Your slope is 4 so we input that. Your y intercept is 150 so we input that. It gives us the equation y=4x+150.
Please help it’s urgent!!!!
Find the arc length of the partial circle.
How do you solve this: 2x(3-a)=a(2-b) to find b?
Answer:
b=-2(3x-xa-a)/a
Step-by-step explanation:
2x(3-a)=a(2-b)
6x-2xa=2a-ab
b=-2(3x-xa-a)/a
You can simplified to top because im a little lazy, sorry
a mass of 25kg on a ramp at an angle of inclination 30 degrees to the horizontal, is oulled with a force of 75 kg an angle of 20 degrees to the ramp what is the frictional force if it is pulled up the ramp at constant speed
Decompose the forces into components that are parallel or perpendicular to the plane. Then the fricitional force (magnitude f ) is only included in the net force parallel to the surface. The other two are the parallel components of the box's weight (mag. w ) and the pulling force (mag. p)
The box is moving at constant speed, so there is no acceleration and the box is in equilibrium. By Newton's second law,
∑ F = p cos(20º) - w sin(30º) - f = 0
We're given p = 75 N, and
w = m g = (25 kg) (9.80 m/s²)
so
f = (75 N) cos(20º) - (25 kg) (9.80 m/s²) sin(30º)
f ≈ -52 N
That the magnitude is negative makes me think there's a mistake in the question.
The entrance to a museum in Paris is shaped like a square pyramid. The base of the pyramid has a side length of 35 meters, and the height of the pyramid is 22 meters
Answer:
the total Hight would be 42 meters
Step-by-step explanation:
What is the slope of a line perpendicular to the line passing through the points P (2,5) and Q (-3,7)?
Answer:
2/5
Step-by-step explanation:
perpendicular line means the two lines' slope when multiplied together gives a answer of -1.
hence, we just need to find the slopw of the line connecting the 2 points and form an equation with -1 to get the slope the question wants.
slope of the line PQ:
(7-5)/(-3-2) = -2/5 (slope formula)
slope of the perpendicular line:
-2/5 x slope = -1
slope = (-1)/(-2.5) = 2/5
2.
If the sun is approximately 1.5 x 1011 meters from Earth, what is the approximate distance from Earth to Mars?
It was supposed to be 10 to the 11 power but it didn’t do it. It out 1011
Answer:
The distance from Earth to Mars is 8×10¹¹ m.
Step-by-step explanation:
Given that,
The speed of light is 3×10⁸ m/s. The sun is approximately 230,000,000,000 m from Mars. If the sun is approximately 1.5 x 10¹¹ meters from Earth, what is the approximate distance from Earth to Mars.
The sun is approximately 2.3 × 10¹¹ m from Mars.
The sun is approximately 1.5 x 10¹¹ m from Earth.
The distance between from Earth to Mars is :
d = 2.3 × 10¹¹ m - 1.5 x 10¹¹ m
= 8×10¹¹ m
Hence, the distance from Earth to Mars is 8×10¹¹ m.
If 4/5 – 3/10 = x + 11/2, find the value of
X.
Answer:
x = 85/60 or 17/12
Step-by-step explanation:
4/5 - 3/10 = x + 11/12
=> 8/10 - 3/10 = x + 11/12
=> 5/10 = x - 11/12
=> x - 11/12 = 5/10
=> x = 5/10 + 11/12
=> x = 5 * 6 / 10 * 6 + 11 * 5 / 12 * 5
=> x = 30 / 60 + 55/60
=> x= 85/60
If my answer helped, kindly mark me as the brainleist !!
Thank You!!
Answer:
maybe -5
Step-by-step explanation:
4/5-3/10=x+11/2
1/2-11/2=x
-10=2x
x=-5
Can anyone please help with this problem ASAP ?
Answer:
4 would be $55.00 and 8 would be $75.00
Twice the sum of a number and five is equal to six
Answer:
-2
Step-by-step explanation:
Let the no. be x
So, By question,
2(x+5)=6
x+5=3
x=-2
Answer:
2(n+5)=6
Step-by-step explanation:
twice=2*
the sum of a number and five= (n+5)
equals six-=6
------------------------------------------
DISTRIBUTE= 2n+10=6 (Distributive Property)
subtract 10 on both sides= 2n=-4 (subtraction Property of Equality)
divide by two on both sides= n=-2 (Division Property)
I WILL GIVE YOU 20 POINTS AND THE BRAINLYEST
all of the points in the picture are on the same line.
Find the slope on the like exain or show your reasoning
write and equation for the line.
find the values for A and B. Explain your reasoning.
Answer:
Step-by-step explanation:
Find the slope and then the equation of line.
(x₁ , y₁) = (2 , 2) & (x₂, y₂) = (6 , 10)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{10 - 2}{6 - 2}\\\\= \frac{8}{4}\\\\= 2[/tex]
m = 2
Equation of the line: y - y₁ = m(x - x₁)
y - 2 = 2 (x - 2)
y - 2 = 2x - 4
y = 2x - 4 + 2
y = 2x - 2 --------------(I)
(a, 8)
Plug in x = a & y = 8 in (I)
8 = 2a - 2
8 + 2 = 2a
10 = 2a
a = 10/2
a = 5
(4 , b)
Plug in x = 4 & y = b in (I)
b = 2*4 - 2
b = 8 - 2
b = 6
Answer:
dog peas
Step-by-step explanation:
donkey peas
How to solve (10 points)
Answer:
side 1: 10 = 15
side 2: 6 = 11
im not 100% sure this is correct
Step-by-step explanation:
13-8 = 5
so we add 5 on each side
10 + 5 = 15
6 + 5 = 11
There are 90 girls and 60 boys in the sixth grade at a middle school. Of these students, 7 girls and 2 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed?
Answer:
6%
Step-by-step explanation:
90 + 60 = 1507 + 2 = 9Set up a proportion: [tex]\frac{9}{150} = \frac{x}{100}[/tex] Cross multiply, then divide: 9 × 100 = 900, 900 ÷ 150 = 6So, 6% of students in 6th grade were left-handedI hope this helps!
Step-by-step explanation: Ok so if there are 90 girls and 7 are left handed u use this method 6/90 multiply by 100 and u get 7.77%
Does the graph represent a function?
57x2.3 what is the anser pls help
Answer:
285.00
Step-by-step explanation:
Because you change 57 to a decimal (57.0) then you multiply.
57.0×2.3=285.00
today is my birthday wish me a happy birthday
Into a mixed number btw. Marcos talks to his grandfather in Alabama for about 95 minutes per month about how long does her talk each day on average? (Hint: use 1 month=30 days)
Answer:
The answer is 3.16666667 its simple u just divide 95 by 30
Step-by-step explanation:
Answer:
3.06451613
Step-by-step explanation:
You divide 95 by 31 to get 3.06441613
Use row 3 to write an equivalent ratio for the amount of apple juice to orange juice used in 3 smoothies. To create this ratio, what did Sarah do to each number in row 1?
1:1.2 as a fraction pls tell me in one minute
Hello!
the answer is 83/100!
Hopefully this helps ^^
(Conditionals)
TRUE OR FALSE:
If a number is a perfect square, then it has only 3 factors.
Answer:
False
I hope this helps!
P(x)=x^4 - 2x^3 - 3x^2 + 4
What is the remainder when P(x) is divided by (x-3)?
Answer:
The given polynomial is p(x)=x
4
−2x
3
+3x
2
−ax+3a−7
Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19
Therefore, p(−1)=19 (By Remainder theorem)
=>(−1)
4
−2×(−1)
3
+3(−1)
2
−(−1)a+3a−7=19
=>1+2+3+a+3a−7=19
=>4a−1=19
=>4a=20
=>a=5
The value of a is 5
Now,
p(x)=x
4
−2x
3
+3x
2
−5x+3×5−7
=x
4
−2x
3
+3x
2
−5x+15−7
=x
4
−2x
3
+3x
2
−5x+8
Remainder when the polynomial is divided by (x+2)
=p(−2) (By Remainder Theorem)
=−2
4
−2(−2)
3
+3(−2)
2
−5(−2)+8
=16+16+12+10+8
=62
Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62
Step-by-step explanation:
The remainder when P(x) is divided by (x-3) is 8
What is the quotient remainder theorem?The quotient-remainder theorem says that when any integer n is divided by any positive integer d, the result is a quotient q and a nonnegative remainder r that is smaller than d.
Given here, P(x)=x⁴ - 2x³ - 3x² + 4
Now we know from the polynomial remainder theorem that the remainder on dividing by (x-a) is f(a)
Thus P(3)=8
Hence, The remainder is 8
Learn more about the remainder theorem here:
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#SPJ2
Cindy is selling circus tickets. On the first day she sells 6 adult tickets and 5 children tickets for total of 112.50. On the second day she sells 8 adult tickets and 4 children tickets for the total 130. Determine the cost of adult and child tickets. Used a to represent adult and c to represent child tickets. Write an equation to represent the sales of day 1 and day 2. Used the elimination method.
Answer: Children tickets cost 7.50
Adult tickets cost 12.50
Step-by-step explanation:
Let a represent adult tickets
Let c represent child tickets
On the first day she sells 6 adult tickets and 5 children tickets for total of 112.50. This can be written as:
6a + 5c = 112.50 ...... equation i
On the second day she sells 8 adult tickets and 4 children tickets for the total 130. This can be written as:
8a + 4c = 130 ....... equation ii
6a + 5c = 112.50 ...... equation i
8a + 4c = 130 ....... equation ii
Multiply equation i by 4
Multiply equation ii by 5
24a + 20c = 450 ........ equation iii
40a + 20c = 650 ......... equation iv
Subtract iii from iv
16a = 200
a = 200/16
a = 12.50
Adult tickets cost 12.50
From equation ii,
8a + 4c = 130
8(12.50) + 4c = 130
100 + 4c = 130
4c = 130 - 100
4c = 30
c = 30/4
c = 7.50
Children tickets cost 7.50
Using the concept of elimination, the cost of adult and children tickets are $12.5 and $7.5 respectively
Let :
Number of adult tickets = a Number of children's tickets = cCreating a system of equation thus :
6a + 5c = 112.50 - - - (1)
8a + 4c = 130 - - - - (2)
Multiply (1) by 4 and (2) by 5
24a + 20c = 450 - - - - (3)
40a + 20c = 650 - - - - (4)
Subtract
-16a = - 200
Divide both sides by - 16
a = 12.5
From (2) :
8(12.5) + 4c = 130
100 + 4c = 130
4c = 130 - 100
4c = 30
c = 7.5
Hence, the cost of adult and children tickets are $12.5 and $7.5
Learn more : https://brainly.com/question/17802216
PLZ HURRY IT'S URGENT!!!
Petrucio has $50 to spend on entertainment. Music downloads are $2.00 each and movie downloads are $5.00 each. What possible combinations can Petrucio buy? SELECT ALL THAT APPLY
options:
8 songs and 6 movies
20 songs and 2 movies
4 songs and 10 movies
7 songs and 8 movies
Answer:
*20 Songs and 2 Movies
*8 Songs and 6 movies
Step-by-step explanation:
will give brainlest plz help!!!Which relation is a function?
The correct answer is the graph in the top right corner because it is a constant function. The bottom left graph is also considered a function but is an absolute function. So both are technically correct.
Multiply and simplify the product. (3 – 5i)(–2 + 4i) Select the product.
Answer:
-20i^2 + 22i - 6
Step-by-step explanation:
(3 - 5i)(-2 + 4i) = -6 + 10i + 12i - 20i^2 = -20i^2 + 22i - 6
if you want to go further,
-20i^2 + 22i - 6 = -2(10i^2 - 11i + 3)
Answer:
14+22i
Step-by-step explanation:
Edge Verified
What is 40/4.
From this_guy
Answer:
10
Step-by-step explanation:
40/4= 10
what is downpayment?
Answer:
Down payment is when you are trying to by something that is expensive up front like a house or a car. It is usually paid in cash or equivalent at the time of finalizing the transaction. A loan of some sort is then required to finance the remainder of the payment.
Step-by-step explanation:
Miguel is designing shipping boxes that are rectangular prisms. One shape of the box with height h in feet, has a volume defined by the function V(h)=h(h-10(h-8). What is the height that would produce the maximum volume for the domain 0
Answer: 105ft^3
Step-by-step explanation:
Answer:
[tex]105ft^{3}[/tex]
Step-by-step explanation:
V(h) = h(–h + 10)(–h + 8)
Apply the distributive property to the right side and simplify.
V(h) = h(–h + 10)(–h + 8)
V(h) = {h(-h) + h(10)}(-h+8)
V(h) = (-h²+10h)(-h+8)
V(h) = (-h²)(-h) + (-h²)(8) + (10h)(-h) + (10h)(8)
V(h) = -8h² -10h² + 80h
V(h) = -18h² + 80h
Plug in the value of h from 1 to 9 (since 0<h<10) into the function V(h) = -18h² + 80h and create a table
h | V(h)
1 | 63
2 | 96
3 | 105 <------maximum volume is the highest y-value
4 | 96
5 | 75
6 | 48
7 | 21
8 | 0
9 | -9
The maximum volume for the domain 0<h<10 is 105 cubic feet.
A paddle boat company charges $15 rental fee plus $12.75 per hour for rentals. If Jimmy has $45, which inequality can he use to determine if he has enough money to rent a paddle boat for 4 hours?
a. 15 + 12.75x ≤ 45
b. 15 + 12.75x ≥ 45
c. 15x + 12.75 ≤ 45
d. 15x + 12.75 ≥ 45
Answer:
A.
Step-by-step explanation:
$15 rental fee added to the 12.75 per hour. you have to multiply the 12.75 times the amount of hours rented, which we don't know yet so that's variable x. then he has only $45 to spend so it has to be equal to or less than that.