The perimeter of the area of the pen the farmer intends to build for his
ship includes the length of the permanent stone wall.
Response:
i) The length and width of the rectangular pen are; x, and [tex]\dfrac{100 - x}{2}[/tex], therefore;
The area is; [tex]A = \dfrac{1}{2} \cdot x \cdot (100 - x)[/tex][tex]ii) \hspace{0.5 cm}\dfrac{dA}{dx} = 50 - x[/tex]
[tex]\dfrac{d^2A}{dx^2} = -1[/tex]
iii) The value of x that makes the area as large as possible is x = 50
How is the function for the area and the maximum area obtained?Given:
The length of fencing the farmer has = 100 m
Part of the area of the pen is a permanent stone wall.
Let x represent the length of the stone wall, we have;
2 × Width = 100 m - x
Therefore;
Width, w, of the rectangular pen, [tex]w = \mathbf{\dfrac{100 - x}{2}}[/tex]
Area of a rectangle = Length × Width
Area of the rectangular pen, is therefore;
[tex]A = x \times \dfrac{100 - x}{2} = \underline{\dfrac{1}{2} \cdot x \cdot (100 - x)}[/tex][tex]ii) \hspace{0.5 cm} \mathbf{\dfrac{dA}{dx}}[/tex], and [tex]\mathbf{\dfrac{d^2A}{dx^2} }[/tex] are found as follows;
[tex]\dfrac{dA}{dx} = \mathbf{\dfrac{d}{dx} \left( \dfrac{1}{2} \cdot x \cdot (100 - x) \right)} = \underline{50 - x}[/tex]
[tex]\dfrac{d^2A}{dx^2} = \mathbf{ \dfrac{d}{dx} \left( 50 - x\right)} = \underline{-1}[/tex]
iii) The value of x that makes the area as large as possible is given as follows;
Given that the second derivative, [tex]\dfrac{d^2A}{dx^2} =-1[/tex], is negative, we have;
At the maximum area, [tex]\dfrac{dA}{dx} = \mathbf{0}[/tex], which gives;
[tex]\dfrac{dA}{dx} = 50 - x = 0[/tex]
x = 50
The value of x that makes the area as large as possible is x = 50Learn more about the maximum value of a function here:
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Determine if the set of numbers is in order from least to greatest. Explain. -5,3,-3,1,0
Answer:
-5, -3, 0, 1, 3
Step-by-step explanation:
This is the order these numbers would be in on a number line. Hope this helps!
Mrs.Dawson spent 28 dollars for 8 notebooks
Answer:
I need more info but if your wondering how much each notebook cost the answer is
Step-by-step explanation:
So first we have to divide 28/8 beacuse thats how many over how much.
When we do it it becomes 3.5. Now this is our number but we must add a zero to the end, so now it $3.50. $3.50 for each notebook!
Hope this helps you, :3
Please consiter <3 me it helps me out a lot!
math answer plz need help with this plz answer
Answer:
31.4 m , 37.68m , 43,96in , 3.14 ,175.84 ft , 3.14 , 25 ft
Step-by-step explanation:
Circumference of circle(c)= 2πr or πd
a.
Given,
d=10m
Now,
C=πd
3.14*10
31.4 m
b.
Given,
r=6
Now,
C=2πr
2*3.14*6
37.68m
2.
Given,
d=14in
Now,
C=πd
3.14*14
43.96 in
I used 3.14 for value of π.
4. Given,
r=28ft
Now,
C=2πr
2*3.14*28
175.84 ft
I used 3.14 for the value of π.
5.
Given,
C=78.5 ft
Now,
C=πd
78.5/π=d
d=78.5/3.14
d=25 ft
Please help, deadline is midnight
Answer:
x=-21.25
Step-by-step explanation:
One half of the number of roses julia planted in her garden is 2/5 the number of tulips she planted, what was the ratio of the number of tulips to roses in the garden
The ratio of the number of tulips to roses in Julia's garden is 5:4.
A ratio is a quantitative comparison between two or more quantities or values.
Let the number of roses Julia planted is denoted by 'R',
and the number of tulips she planted is denoted by 'T'.
According to the given information,
"One half of the number of roses Julia planted is 2/5 the number of tulips she planted."
So, the mathematical expression is
(1/2)R = (2/5)T
T = (5/2)(1/2)R
T = (5/4)R
As, the ratio of the number of tulips to roses is T:R, which can be expressed as (5/4):1 or simply 5:4.
Therefore, the ratio is 5:4.
Learn more about Ratio here:
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Please answer these questions (3,4,5)
Answer
3. 6.4 - 2.218=5.182
4. 51.04 - 23.21=27.83
5. 125.50Php - 78.25Php= 47.25Php
Answer:5.182, 27.73, and 47.25
Step-by-step explanation:
Hope this helps!:)
what is the greatest common factor of 48r^3s^5 and 64rs^4
Answer:
16rs⁴
Step-by-step explanation:
prime factorization of 48r³s⁵ is: 2·2·2·2·3·r·r·r·s·s·s·s·s
prime factorization of 64rs⁴ is: 2·2·2·2·2·2·r·s·s·s·s
if you were to circle factors common to each you would have:
2·2·2·2·r·s·s·s·s which equals 16rs⁴ which is the GCF
12÷12
Cmon pelase help me I need help pelase help me I really need help plsssss
f
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p
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Answer:
1
Step-by-step explanation:
Divide 12 in to 12 separate groups and you get 1 group of 12.
Answer:
1
Step-by-step explanation:
7 a) The table shows the masses of the planets in our solar system.
Planet Mass (kg)
Mercury 3.30 × 1023
Venus 4.87 × 1024
Earth 5.97 × 1024
Mars 6.42 × 1023
Jupiter 1.90 × 1027
Saturn 5.68 × 1026
Uranus 8.68 × 1025
Neptune 1.02 × 1026
List the planets in order of their mass, starting with the lightest
Find the midpoint between (-3,5) and (4, -1)
Answer:
Midpoint=(12,2)
As a decimal: Midpoint=(0.5,2)
How do you write 652% as a fraction, mixed number, or whole number?
HELP PLEASE
Steve bought a car for seven thousand five hundred Euros. He was given a ten percent discount on the full price. How much did he pay for the car?
Seven hundred fifty thousand Euros
(1/2)^3 X 1/2
Please answer this..•
Answer:
[tex]{ \tt{ {( \frac{1}{2} )}^{3} \times \frac{1}{2} }} \\ \\ = { \tt{ \frac{1}{6} \times \frac{1}{2} }} \\ \\ = { \tt{ \frac{1}{12} }} \\ \\ = { \tt{ {12}^{ - 1} }}[/tex]
(111²) how to solve it
Answer:
12,321
Step-by-step explanation:
111 to the second power (basically 111 x 111) is 12,321. Multiply 111 by 111 since the exponent is 2. I hope this helps!
Match the expression is equivalent to 5(2x+3) when using the distributive property?
(5*2x)+3
5(3+2x)
10x + 15
25x
Answer:
10x + 15
Step-by-step explanation:
5(2x + 3) ← multiply each term in the parenthesis by 5
= 10x + 15
A= 63 m2
b=?
h= 12 m2
Answer:
51m2 this is the answer thank u
The measure of an angle is 75°.
What is the measure of its supplement?
Answer:
105°
Step-by-step explanation:
180-75=105
Answer:
105 degrees
Step-by-step explanation:
What is the solution of each system of equations? Show your work-6x-5y=64x+y=3
Answer:
-6y = 70x = 3
Step-by-step explanation:
-6x - 5y= 64x+ y=3
---------------------------
-y - y
---------------------------------
-6x -6y = 64x = 3
------------------------------------
+6x +6x
-------------------------------------
-6y = 70x = 3
Answer:
[tex]x=\frac{9}{157} \\y=-\frac{105}{157}[/tex]
Step-by-step explanation:
-6x-5y=64x+y=3
-6x-5y=64x+y
-6x-64x=y+5y
-70x=6y
divide by 2
-35x=3y
y=-(35/3)x
y+64x=3
-(35/3)x+64x=3
-35x+192x=9
157x=9
x=9/157
y=-35/3x
[tex]y=-\frac{35}{3} \times\frac{9}{157} \\y=-\frac{105}{157}[/tex]
rewrite the equation below so that it does not have fractions. do not use decimals in your answers 2+7/9x=5/6
Answer:
-3/2
Step-by-step explanation:
2+7\9x=5/6
2+7/9=5/6
9⋅2/9+7/9=5/6
9⋅2+7/9=5/6
Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.
What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.
Answer 60?
Step-by-step explanation:
edmentum
The approximate angle of elevation if Brendan looks up at the tower is 20.03°
How to find the angle of elevation?The angle of elevation if Brendan looks up is as follows;
using trigonometric ratios,
sin x° = opposite / hypotenuse
sin x° = 50 / 146
sin x° = 0.34246575342
x = sin⁻¹ 0.34246575342
x = 20.0271724581
x = 20.03°
Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°
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Find the value of cos G rounded to the nearest hundredth if necessary
Answer:
cos G = 0.5
Step-by-step explanation:
cos G = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{FG}{EG}[/tex] = [tex]\frac{2}{4}[/tex] = 0.5
help pls solve the problems that have the check mark and show ur work
Answer:
1) x/2 + 1
2) x/2 + 1
3) x/2 + 1
Step-by-step explanation:
1) (2x * 1/4) = (2 * 1/4 * x) = (1/2 * x) = (x/2)
(4 * 1/4) = (4/4) = (1)
(x/2) + (1) = (x/2 + 1)
2) (1/6 * 3 * x) = (3/6 * x) = (1/2 * x) = (x/2)
(1/6 * 6) = (6/6) = (1)
(x/2) + (1) = (x/2 + 1)
3) (1/4 * x) = (3/12 * x) = (3x/12)
(3x/12) + (3x/12) = (6x/12) = (1/2 * x) = (x/2)
(9 - 8) = 1
(x/2) + (1) = (x/2 + 1)
The expanded form of the expressions is 2x + 1 and x/2 + 1
Expression and expansionGiven the expression 1/4(2x + 4)
Expand the expression
1/4(2x + 4) = 1/4(2x) + 1/4(4)
1/4(2x + 4) = 2x + 1
For the expression 1/6(3x + 6)
1/6(3x + 6) = 1/6(3x) + 1/6(6)
1/6(3x + 6) = x/2 + 1
For the expression 1/4 x + 9 + 3/12 x - 8
Simplify the expression
1/4 x + 1/4x + 9 - 8
2/4 x + 1
1/2 x + 1
Learn more on expression and expansion here: https://brainly.com/question/29114
Determine x, y, and z.
Answer:
y = 35 degrees; x = 10 degrees; z = 135 degrees
Step-by-step explanation:
We can find the measure of y using 180 - (85 + 60) = 35
We can find the measure of x using 180 - (105 + 65) = 10
We can find the measure of z using 180 - (35 + 10) = 135
Write an equation in slope intercept form for the cost at each store
Answer:
See attachment
Step-by-step explanation:
On attachment
Find the value of x. Round to the nearest tenth.
Answer:
19.7
Step-by-step explanation:
37-17.3=19.7 which would be the value of x
write 4:20 in the simplest form
Answer:
[tex]1:5[/tex] is the answer
Step-by-step explanation:
→[tex]4:20\\\\\frac{4}{20}\\\\\frac{1}{5} \\\\1:5[/tex]
Answer:
1/5
Step-by-step explanation:
Please help !!!!!!!!!
Answer:
9^2= 81, √25= 5, 21^2= 441, √4= 2, √144= 12, 16^2= 256, √625= 25, (-11)^2=121
A boy rides his bike at a speed of 28 miles per hour. How
many hours will it take him to complete a trip of 120 miles?
Round your answer to the nearest whole number.
hours
Answer:
About 4 hours.
Step-by-step explanation:
Let's set up a proportion and cross multiply.
[tex]\frac{28 miles}{1 hour} = \frac{120 miles}{x}[/tex]
Cross multiply.
120 = 28x
Divide by 28 on both sides.
= 4.28571428571
Round this to the nearest whole number, which is just 4. The answer is about 4 hours.
pls help its urgent!!!
Answer:
and below
Step-by-step explanation:
33a+21c = 228
a+b = 8
solving the equation b= 3 a =5
-16 -12 -8 -4
Common difference of the arithmetic sequence
