Answers
Answer:
Dimensions: 150 m x 150 m
Area: 22,500m²
Step-by-step explanation:
Given information:
Rectangular fieldTotal amount of fencing = 600mAll 4 sides of the field need to be fencedLet [tex]x[/tex] = width of the field
Let [tex]y[/tex] = length of the field
Create two equations from the given information:
Area of field: [tex]A= xy[/tex]
Perimeter of fence: [tex]2(x + y) = 600[/tex]
Rearrange the equation for the perimeter of the fence to make y the subject:
[tex]\begin{aligned} \implies 2(x + y) & = 600\\ x+y & = 300\\y & = 300-x\end{aligned}[/tex]
Substitute this into the equation for Area:
[tex]\begin{aligned}\implies A & = xy\\& = x(300-x)\\& = 300x-x^2 \end{aligned}[/tex]
To find the value of x that will make the area a maximum, differentiate A with respect to x:
[tex]\begin{aligned}A & =300x-x^2\\\implies \dfrac{dA}{dx}& =300-2x\end{aligned}[/tex]
Set it to zero and solve for x:
[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 300-2x & =0 \\ x & = 150 \end{aligned}[/tex]
Substitute the found value of x into the original equation for the perimeter and solve for y:
[tex]\begin{aligned}2(x + y) & = 600\\\implies 2(150)+2y & = 600\\2y & = 300\\y & = 150\end{aligned}[/tex]
Therefore, the dimensions that will give Tanya the maximum area are:
150 m x 150 m
The maximum area is:
[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 150 \cdot 150\\& = 22500\: \sf m^2 \end{aligned}[/tex]
Related Questions
unit rate for typing 34 words in a minute in a half
Answers
Answer:
Rate is 1.1333 words per second
Step-by-step explanation:
We understand rating as frequency or speed of doing something per time (seconds mainly)
[tex]{ \green{ \tt{rate = \frac{item \: quantity}{time} }}} \\ [/tex]
Let's find rate in terms of seconds (words per second)
[tex]{ \rm{rate = \frac{34 \: words}{ (\frac{1}{2} \times 60) \: seconds} }} \\ \\ { \rm{rate = \frac{34}{30} }} \\ \\ { \rm{rate = 1.133 \: \: words \: per \: second}}[/tex]
Are the two triangles similar? How do you know? (image attached)
Answers
Answer:
no
Step-by-step explanation:
they're not same because no angles are mentioned and sides are diff too
i been asking for help since yesterday
Use the graph above to complete problems 1 - 5.
Mary is planning a costume party. She spent $375.00 as shown on the graph. How much of the money was spent, to the nearest dollar, on the following items?
1) On decorations?
2) On food?
3) On party hall rental?
4) On prizes?
5) On invitations?
Answers
For the first, decorations, Mary spent $?? as shown by the blue triangle on the pie chart. Let’s get the other ones first to total the money left over.
For the second, she spent $65 on food, as shown by the green triangle on the pie chart.
For the third, she spent $80 on party hall rental, as shown by the blue triangle on the pie chart.
For the fourth, she spent $30 on prizes, as shown by the dark blue triangle.
And for the fifth one, she spent $45 on invitations. A bit too expensive if you ask me.
Then we add all the costs together, and get 220. After adding the extra costs such as candy, costumes, and music, we get a total of $345. We would subtract this from $375 to get a total of $30 left over, which was spent on decorations. The ??? value of the light blue triangle is $30.
Hope this helps!
Blank + -5 = -63................................
Answers
Answer:
-58
Step-by-step explanation:
x + -5 = -63
x = -63+(-5)
x =- 58
In a a computer game positive numbers represent earning points and negatiive numbers represents.wich number represents losing more than 500 points
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that represents losing more than 500 points is x<-500.
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given In a computer game positive numbers represent earning points and negative numbers represent losing points. Therefore, the loss of more than 500 points is given by the inequality,
x< -500
Hence, the expression that represents losing more than 500 points is x<-500.
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You need to invest $1000 in a bank account and are give two options. The first option is to earn $50 every month you leave the money in the account. The second one is to earn 3% interest each month. Describe each of these two functions and make a table of values for each for several months. Which account would you choose?
Answers
Answer:
Option 1Earn $50 every month.
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 50x + 1000[/tex]
This is a linear function.
Option 2Earn 3% interest each month.
(Assuming the interest earned each month is compounding interest.)
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 1000(1.03)^x[/tex]
This is an exponential function.
Table of values[tex]\large \begin{array}{| c | l | l |}\cline{1-3} & \multicolumn{2}{|c|}{\sf Account\:Balance} \\ \cline{1-3} & \sf Option\:1 & \sf Option\:2 \\\sf Month & \sf \$50\:per\:mth & \sf 3\%\:per\:mth \\\cline{1-3} 0 & \$1000 & \$1000 \\\cline{1-3} 1 & \$1050 & \$1030 \\\cline{1-3} 2 & \$1100 & \$1060.90 \\\cline{1-3} 3 & \$1150 & \$1092.73 \\\cline{1-3} 4 & \$1200 & \$1125.51 \\\cline{1-3} 5 & \$1250 & \$1159.27 \\\cline{1-3} 6 & \$1300 & \$1194.05 \\\cline{1-3} 7 & \$1350 & \$1229.87 \\\cline{1-3}\end{array}[/tex]
From the table of values, it appears that Account Option 1 is the best choice, as the accumulative growth of this account is higher than the other account option.
However, there will be a point in time when Account Option 2 starts accruing more than Account Option 2 each month. To find this, graph the two functions and find the point of intersection.
From the attached graph, Account Option 1 accrues more until month 32. From month 33, Account Option 2 accrues more in the account.
ConclusionIf the money is going to be invested for less than 33 months then Account Option 1 is the better choice. However, if the money is going to be invested for 33 months or more, then Account Option 2 is the better choice.
How many solutions are there to the equation?
2x + 3 = 2x + 7
Answers
Answer:
this equation has no solutions.
Step-by-step explanation:
2x+3 = 2x+7
3=7
Answer this for 28 points
Answers
Answer: I think B
Step-by-step explanation:
This Week's High Temperatures (°F)
29, 38, 45, 31, 50, 58, 62
Last Week's High Temperatures (°F)
44, 31, 66, 32, 26, 58, 78
Which measures of center and variability for the
temperatures were lower this week than last week?
Check all that apply.
mean
median
mode
range
mean absolute deviation
Done
Answers
The measures of center and variability for the
temperatures that were lower this week than last week include mean, range, mean absolute deviation.
What is a mean?It should be noted that a mean simply means the average set if numbers given.
Also, the range is the difference between the highest number and the lowest number in the data.
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Answer:
mean,range,mean absolute deviation
Step-by-step explanation:
just took it on edge
After years of successful existence, a company producing Smart TV formulated an equation for the cost P of manufacturing n number of television sets. The equation is P(n)=1200n+700. Find the cost of 50 television set.
a. Php 59,300
b. Php 60,000
c. Php 60,700
d. Php 61,200
Answers
Put n=50
P(50)
1200(50)+70060000+70060700Option C
Answer:
C
Step-by-step explanation:
To find the cost for 50 televisions:
We put the value of n=50
P(50)
1200(50)+700
60000+700
60, 700
Option C
what is the polar coordinate of (0, pie)
Answers
Answer:
The angle's beginning and ending points are referred to as the initial and terminal sides, respectively. Distance from the origin and two angles are the three parameters of 3D polar coordinates or spherical coordinates. is a three-dimensional polar coordinate.
Step-by-step explanation:
Read above.
Choose the function whose graph is given by
Answers
Answer:
cos(x)+1 or cos x + 1
Step-by-step explanation:
The wave starts at y=2 this means it is a cosine function, then the first positive x-intercept is at about (pi, 0) which is about 3, this leads to cos x + 1 as the answer.
does someone mind helping me with this question? Thank you!
Answers
Answer:
60
Step-by-step explanation:
Use PEMDAS (parentheses, exponent, multiply, divide, addition, subtraction)
First, substitute 5 for x:
3(3(5) + 5)
Multipliy inside the parentheses:
3(15 + 5)
Add inside the parentheses:
3(20)
Multiply:
60
There's your answer! Hope I helped.
53, 13, 34, 41, 26,61, 34, 13,69 mean median mode and range
Answers
Answer:
mean 38.22
median 34
mode 13 & 34
range 56
Step-by-step explanation:
mean- add all values together and divide by number of values
median- order from least to greatest find the middle value
mode- the value that appears most often, can be more than one value
range- smallest value subtracted from the largest
A certain planet has a day length of 24 hours. the planet is totally covered in water,
except for one small island. at hour 0, the island has 100% light with the planet's star
in the top of the sky. at hour 12, the island has 0% light and is in total darkness.
write an equation that models the amount of light in the sky on the island in terms
of hours passed.
Answers
Answer:
above
Step-by-step explanation:
the entire method for the question is linked above :)
1. How many solutions does the equation have?
8x −6(2x − 2) = -12 + 2x + 15
-
No Solutions
One Solution
OTwo Solutions
An infinite number of solutions
Answers
solve x - 23 = 57 ⅔ x = 7
Answers
Step-by-step explanation:
[tex]x - 23 = 57 \\ x = 57 + 23 \\ x =80 \\ \\ \frac{2}{3}x = 7 \\ ( \frac{3}{2}) \frac{2}{3}x = 7( \frac{3}{2}) \\ x = \frac{21}{2} [/tex]
somebody pls help me with this question pls
Answers
3x6x10=180 because I’ve split the shape in half
7x4x4=112
180+112=292
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−3/4x, through (4, -1)
Answers
Answer:
y = -3/4x + 2
Step-by-step explanation:
The line is parallel to y = -3/4x and passes through the point (4, -1)
=============================================================
Solving :
⇒ As they are parallel, the slope remains the same (-3/4)
Now apply into the point slope formula :
⇒ y + 1 = -3/4 (x - 4)
⇒ y + 1 = -3/4x + 3
⇒ y = -3/4x + 2 [in slope-intercept form]
Triangle ABC is an isosceles right triangle. What is the measure of one base angle?
Answers
Answer:
45°
Step-by-step explanation:
ΔABC is an isosceles right triangle. So, one angle is 90°
In an isosceles triangle, base angles are congruent.
Let the base angles be x ,x
x + x +90 = 180 {Angle sum property}
2x + 90 = 180
2x = 180 - 90
2x = 90
x = 90/2
x = 45
Base angle = 45°
If f(x)=(4x-3) / 2 and g(x) =(2x+3) / 4, which of the following is true?
A f(g(x)) =1
B f(g (x)) = 0
C f(g(x))=-1
D f(g(x)) = x
Answers
Answer:
f(g(x))= x
Step-by-step explanation:
f(x)=(4x-3)/2
g(x) =(2x+3)/4
f(g(x)) means use the value obtained from g(x) in the equation defined by f(x). Since g(x) =(2x+3)/4, we can substitute (2x+3)/4 in place of the x in f(x).
If f(x)=(4x-3)/2 then use the expression (2x+3)/4 in place of "x" in (4x-3)/2
f(x) = (4x-3)/2
g(x) = (2x+3)/4
f(g(x))=(4((2x+3)/4)-3)/2
f(g(x))=(((8x+12)/4)-3)/2
f(g(x))= (2x+3-3)/2
f(g(x))= 2x/2
f(g(x))= x
How would you solve this problem step by step ?
4√15(2√2 + √5)
Answers
[tex]~~4\sqrt{15} \left( 2\sqrt 2 + \sqrt 5 \right)\\\\=8\sqrt{15} \sqrt 2 + 4\sqrt{15} \sqrt 5\\\\=8\sqrt{15\times 2}+4 \sqrt{15 \times 5}\\\\=8\sqrt{30}+4\sqrt{3 \times 5 \times 5}\\\\=8\sqrt{30} + 4 \sqrt{3\times 5^2}\\\\=8\sqrt{30} + 4\cdot 5 \sqrt 3\\\\=8\sqrt{30} +20\sqrt{3}[/tex]
Kyle recorded his height, in inches, from age 6 to age 18. The graph below shows the data that he recorded as a function of his height over time. Kyle plotted many of the points from memory, but has some accurate data from old medical records. His two most accurately plotted points occurred at age 6 with a height of 45 inches and at age 18 with a height of 75 inches. Use these two data points to determine the equation for the line of best fit for Kyle's data.
Answers
Answer:
you probably moved on, but for everyone else:
y= 5/2x + 30
Step-by-step explanation:
True or False? A circle could be circumscribed about the quadrilateral below.
O A. True
B. False
Answers
A circle could be circumscribed about the quadrilateral is true.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points
If opposite angles of a quadrilateral add to 180 then it is called a cyclic quadrilateral and a circle can be inscribed in it.
Here, the opposite sides are 115 and 65
115+65=180
The other opposite sides have 90 and 90
90+90=180, which means that it is true that a circle can be circumscribed about the quadrilateral above.
Hence, A circle could be circumscribed about the quadrilateral is true.
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Decide whether the data in the table represent a linear function or an
exponential function. Explain how you know.
y
1
16
2
8
3
0
4
-8
5
-16
A. The data represent an exponential function because there is a
common ratio of 2.
B. The data represent a linear function because there is a common
difference of 8.
OC. The data represent a linear function because there is a common
difference of -8.
D. The data represent an exponential function because there is a
common ratio of 1
Answers
Answer:
A data represent an exponential function because there is a common ratio of 1
Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answers
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
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Which expression is equivalent to (4mn/m^-2n^6)^-2
Answers
The expression that is equivalent to (4mn/m^-2n^6)^-2 is [tex]\frac{n^{10}}{16m^{6}}[/tex]
How to determine the equivalent expression?The expression is given as:
(4mn/m^-2n^6)^-2
Apply the law of indices
[tex](4m^{1 + 2}n^{1-6})^{-2[/tex]
Evaluate the sum and the differences
[tex](4m^{3}n^{-5})^{-2[/tex]
Apply the negative exponent
[tex]\frac{1}{16m^{2*3}}}n^{5*2}[/tex]
Evaluate
[tex]\frac{1}{16m^{6}}n^{10}[/tex]
Rewrite as:
[tex]\frac{n^{10}}{16m^{6}}[/tex]
Hence, the expression that is equivalent to (4mn/m^-2n^6)^-2 is [tex]\frac{n^{10}}{16m^{6}}[/tex]
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PLEASE HELP!!! find the area of the shaded triangle
Answers
Area of unshaded region= 4ft
8-4= 4 square feet
Answer:
4 ft squared
Step-by-step explanation:
2 add 2 is 4
4 multiplied by 4 is 16
16 divided by 2 is 8
8 divided by 2 is 4
can someone do this for me please?! Just the answer pls
Answers
Answer:
see the attachment photo!
Let R be the region in the first quadrant enclosed by the graph y=(square root(6x+4)), the line y=2x, and the y-axis. . . .Set up but do not integrate an integral,expression in terms of a single variable for the volume of the solid generated when R is revolved about the y axis
Answers
The two boundary curves y = √(6x + 4) and y = 2x meet at
√(6x + 4) = 2x
6x + 4 = 4x²
2x² - 3x - 2 = 0
(x - 2) (2x + 1) = 0
⇒ x = -1/2 and x = 2
R is bounded to the left by the y-axis (x = 0), so R is the set
R = {(x, y) : 0 ≤ x ≤ 2 and 2x ≤ y ≤ √(6x + 4)}
Using the shell method, the volume is made up of cylindrical shells of radius x and height √(6x + 4) - 2x. So each shell of thickness ∆x contributes a volume of
2π (radius) (height) ∆x = 2π x (√(6x + 4) - 2x) ∆x
and as we let ∆x approach zero, the total volume of the solid is given by the definite integral
[tex]\displaystyle \boxed{2\pi \int_0^2 x \left(\sqrt{6x + 4} - 2x\right) \, dx}[/tex]