The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
Let's assume that the length of the pen would be x.
We have been given the perimeter as 480 meters.
Let w be the width of the rectangle and l be the length of the rectangle
The perimeter of a rectangle = 2(l+w)
So, 480= 2(x + w)
240 = x + w
w = 240 - x
Length = x and width = (240 – x)
Area = x(240 - x) = 240x - x²
To get the maximum area, we equate the first derivative of the area to zero.
A = 240x - x²dA/dx = 240 - 2x = 0
2x = 240
x = 120
So, width = 240 – x = 240 – 120 = 120.
Maximum area = length × width
Maximum area = 120 × 120 = 14400 meters²
Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².
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help please quick question
[tex]f=\frac{x}{x-1}[/tex]
the domain is 1
composite f of f is: f(f(x))
finding the domain of the composite through [tex]\frac{x}{x-1} =1\\x=x-1\\0=-1\\[/tex]
using a graphing calculator, I know that a hole is at (1,1), but can I figure that out without using a graphing calculator and through the domain, say 1=0. Can somebody please just quickly explain this to me.
Step-by-step explanation:
What you are trying to do, it solve for the zeros of the rational function. To find the domain of composite function,
[tex] \frac{x}{x - 1} [/tex]
Substitute x/(x-1) for every x you see.
[tex] \frac{ \frac{x}{x - 1} }{ \frac{x}{x - 1} - 1} = \frac{x(x \\ - 1)}{1} = x(x - 1)[/tex]
We know that the function domain can not be 1, this functions works for all reals, so our domain is
All reals except 1.
Stephen was thinking of a number. Stephen doubles it, then adds 11 to get an answer of 47.7. What was the original number?
The original number in the statement is 18.5
How to determine the original number?The statements in the question are given as:
A number. Doubles the numberAdds 11 to the numberResult = 47.7Let the number be x
So, we have the following equation
2x + 11 = 47.7
Subtract 11 from both sides
2x = 36.7
Divide by 2
x = 18.35
Hence, the number is 18.35
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Square MNOP with vertices M(-7,-4),
N(-4,-3), O(-3, -6), and P(-6, -7): k = 2
The image of the scaled copy of the square is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the image of the scaled copy of the square?From the question, we have the following parameters that can be used in our computation:
Square MNOP with vertices M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7): Scale factor of dilation, k = 2This means that
Scaled copy = Scale factor * Vertices of MNOP
So, we have
M'N'O'P' =M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7)* 2
Evaluate
M'N'O'P' =M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
Hence, the image of the dilation is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
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Complete question
Given that Square MNOP with vertices M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7): k = 2
Calculate the image of the scaled copy
Manita installs a program on her computer. After 3 minutes, the window shows that the installation is 15% complete. Humi installs the same program on a different computer. After her computer showed that the installation was 15% complete, it took Humi’s computer 68 minutes to complete the installation. Which computer installs the program faster and how many minutes faster did it install this program?
Manita's computer installed the software 48 minutes before than Humi's computer.
What is unit rate?A unit rate means a rate for one of something.
Given that, Manita's computer takes 3 minutes to download a program 15% and Humi's computer install it in 68 minutes 100%.
Manita's computer;-
15% in 3 min
1% in 1/5 minutes
100% in 1/5x100 = 20 minutes.
Whereas, Humi's computer took 68 minutes to install the same program.
This mean, Manita's computer was faster than Humi's.
68-20 = 48
Hence, Manita's computer installed the software 48 minutes before than Humi's computer.
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Help please asap!!
A- z=15
B- z= 20
C- z=23
D- z=41
Answer:
z = 15
Step-by-step explanation:
The sum S of the interior angles of a regular polygon is given by the formula
S = (n-2) x 180 where n is the number sides
Here n = 9
So S = (9-2) x 180 = 7 x 180 = 1,260
There are 9 interior angles and each angle is (5z + 65)
So the sum of all 9 interior angles = 9 (5z + 65)
= 45z + 585
Set these equal to each other and solve for z
45z + 585 = 1260
45z = 675
z = 675/45 = 15
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
a. Your income on the 31st day is given as follows: $10,737,418.24
b. Your total income for working 31 days is of: $21,474,836.47
What is a geometric sequence?The definition of a geometric sequence is given as follows:
[tex]a_n = a_1(r)^{n - 1}[/tex]
In which the terms are given as follows:
[tex]a_1[/tex] is the first term.r is the common ratio of the sequence.In a geometric sequence, each term is the multiplication of the previous term by the common ratio.
The sequence in this problem is given as follows:
(0.01, 0.02, 0.04, ...).
Hence the first term and the common ratio of the sequence are given as follows:
[tex]a_1 = 0.01, q = 2[/tex]
Thus the definition is of:
[tex]a_n = 0.01(2)^{n - 1}[/tex]
The income on the 31st day is of:
[tex]a_{31} = 0.01(2)^{30} = 10,737,418.24[/tex]
The sum of the first n terms of a geometric sequence is given as follows:
[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]
Then the sum of the first 31 terms is of:
[tex]S_{31} = 0.01\frac{1 - (2)^{31}}{1 - 2} = 21,474,836.47[/tex]
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Will give brainliest
Answer:
The first one is B
The second one is The y intercept is 8
Step-by-step explanation:
Can someone help me with this?
What is the range of the function shown ???
Answer:
option number 2
Step-by-step explanation:
you can see inital and final co ordinate
Answer:
y > -2
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
The y-value of the lowest point of the curve is just above y = -2.The y-value of the highest point of the curve is more than y = 3.Therefore, the most appropriate range from the given answer options is:
y > -2Note: The graph appears to be the exponential function [tex]y=2^x-2[/tex] with a horizontal asymptote at y = -2. This means that the curve will get closer and closer to y = -2 as x approaches negative infinity, but it will never touch it. The function approaches infinity as x approaches infinity. Therefore, the range for this function is y > -2
An orchard has 468 pear trees. The number of rows exceeds the number of trees per row by 8. How many trees are there in each row
If an orchard has 468 pear trees and The number of rows exceeds the number of trees per row by 8. the number of trees that are in each row would be 18
How to solve for the number of treesWe have to define T as the number of trees that are in a row.
Then we have to define t + 8 as the number of rows that we have
This would give us the equation that is written as
t(t + 8) = 468
then we would have
t² + 8t -468 = 0
We would have to find the factors of 468 which when inputted in the equation would give us the value 468
t(t + 8) = 468
This factor would be 18
such that
18 ( 18 + 8) = 468
18 * 26 = 468
468 = 468
Hence the number of trees that are in each row would be 18
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If using the method of completing the square to solve the quadratic equation x^2-16x+37=0 which number would have to be added to "complete the square"?
Answer:
-27
(negative number)
Step-by-step explanation:
-b/2a = -(-16)/2(1) = 16/2 = 8
x + 8
x x^2 8x
+
8 8x 64
So we got 64, but 64 is not 37 so we need to change that by subtracting 27 from it.
64 - 27 = 37
So the final answer (in vertex form) is:
(x+8)^2 - 27
(-27) is the number being added
cos \theta =-(5)/(13) ∅and sin θ > 0. Identify the quadrant of θ and find sin θ.
Answer: D. Qufdrant: II
sinΘ=12/13
Step-by-step explanation:
[tex]\displaystyle\\cos\theta=-\frac{5}{13} \ \ \ \ sin\theta > 0\\\\sin^2\theta+cos^2\theta=1\\\\sin^2\theta=1-cos^2\theta\\\\sin\theta=б\sqrt{1-cos^2\theta} \\\\sin\theta > 0, \ \ hence\\\\sin\theta=\sqrt{1-cos^2\theta} \\\\sin\theta=\sqrt{1-(-\frac{5}{13})^2 } \\\\sin\theta=\sqrt{1-\frac{25}{169} } \\\\sin\theta=\sqrt{\frac{169-25}{169} } \\\\sin\theta=\sqrt{\frac{144}{169} } \\\\sin\theta=\frac{12}{13}[/tex]
[tex]\displaystyle\\\left \{ {{cos\theta < 0} \atop {sin\theta > 0}} \right. \ \ \ \ \Rightarrow\ \ \ \ quadrant\ II[/tex]
Which expression is equivalent to 27 + 63 ? 3(9 + 18) 9(3 + 7) 21(7 + 3) 7(21 + 9)
Which expression is equivalent to 27 + 63 ?
3(9 + 18)
9(3 + 7)
21(7 + 3)
7(21 + 9)
PLEASE SHOW ALL STEPS AND EXPLAIN
The greatest common factor will be 8.
What is common factor? What is a mathematical equation? What is Probability?A common factor is a whole number which is a factor of two or more numbers. The highest common factor (HCF) is the greatest factor that will divide into two or more numbers. The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have three numbers 24, 56 and 72.
The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24
The factors of 56 are : 1, 2, 4, 7, 8, 14, 28, 56
The factors of 72 are : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the greatest common factor will be 8.
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Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:
Water pressure can be measured in atmospheres (atm). Use the infomation in the graph to write an equation that models the pressure (y) at depth (x).
The linear function for the given graph is y = x + 0.1
What is a linear function?
The graph of a linear function is a straight line. The following is the form of a linear function. y = mx + b. One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.
The coordinates of the given graph are (0,1) and (10,2)
Then, slope (m) = (2-1)/(10-0) = 1/10 = 0.1
y-intercept (b) = 1
Then, y = 1x + 0.1
Hence, the linear function for the given graph is y = x + 0.1
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Find the circumference of this circle.
Use 3.14 to approximate ™.
C = 2πr
14 ft
C = [?] ft
Entered
Answer:
43.9823
Step-by-step explanation:
14 / 2 = 7
7 = r
2π(7)
= 43.9823
If an arrow is shot straight upward on the surface of the moon with initial velocity 60m/s, its height after t seconds is given by h(t) = 60t - 0.8t². (a) What is the velocity of the arrow after 1 second? (b) At what time t > 0 will the arrow hit the moon? (c) What is the velocity of the arrow when it hits the moon? (d) At what time does the arrow reach its maximal height? Show your working out!
The motion of the arrow, described by the kinematic equation for the height, h(t) = 60·t - 0.8·t² are as follows;
(a) The velocity after 1 second is 58.4 m/s
(b) The arrow hits the moon after 75 seconds
(c) The velocity of the arrow when it hits the moon is 60 m/s
(d) The arrow reaches the maximum height in37.5 seconds.
What is a kinematic equation?A kinematic equation is an equation that describes the motion of an object moving under constant acceleration.
The kinematic (equation) function for the height of the arrow is; h(t) = 60·t - 0.8·t²
The initial velocity of the arrow = 60 m/s
(a) The velocity of the arrow = The rate of change of the height, therefore;
v = h'(t) = 60 - 2 × 0.8·t = 60 - 1.6·t
The velocity after 1 second = h'(1) = 60 - 1.6 × 1 = 58.4
The velocity of the arrow after 1 second is 58.4 m/s
(b) When the arrow hits the moon, we get;
h(t) = 0, therefore;
h(t) = 60·t - 0.8·t² = 0
( 60 - 0.8·t)·t = 0
t = 0 or 60 - 0.8·t = 0
t = 60/0.8 = 75
The time the arrow hit the moon is 75 seconds after being shot
(c) The velocity of the arrow when it hits the moon is found using the equation;
h'(37.5) = 1.6 × 37.5 = 60
The velocity when it hits the moon, the velocity is 60 m/s
(d) The motion of the arrow is symmetrical, therefore, the time it takes the arrow to reach the the maximal height is the time it takes the arrow to reach back to the moon surface, which indicates;
The time it takes the arrow to reach maximum height is half the time it takes the arrow to hit the moon after being shot = 75/2 seconds = 37.5 seconds
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$12,800 a year, about 15% is taken out for taxes. How much is taken out for taxes?
Answer: 1920
Step-by-step explanation:
Find the slope of the line that passes through all of the points
on the table.
x
3
4
5
6
7
8
y
1
10
19
28
37
46
Answer:
this is what I got and hope this helps sorry if it's wrong
You withdraw $375 from your bank account. You receive a stack of 24 bills consisting of $5, $10, and $20 bills. The number of $5 bills is one-half the number of $10 bills. How many of each type of bill do you receive?
The number of $ 5 bills = 3
The number of $ 10 bills = 6
The number of $ 20 bills = 15
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount be = $ 375
Let the total number of bills = 24
Let the number of $ 5 bills be = x
Let the number of $ 10 bills be = y
Let the number of $ 20 bills be = z
The total number of $ 5 bills x = ( 1/2 ) x number of $ 10 bills
So , x = y/2
Now , the equation will be
The total number of bills = x + y + z
So , x + y + z = 24 be equation (1)
And ,
The total amount = 5x + 10y + 20z
So , 5x + 10y + 20z = 375
Divide by 5 on both sides , we get
x + 2y + 4z = 75 be equation (2)
On simplifying equation (1) and equation (2) , we get
x + y + z = 24
Substituting the value of y , we get
x + 2x + z = 24
3x + z = 24 be equation (3)
And ,
x + 2y + 4z = 75
x + 4x + 4z = 75
5x + 4z = 75 be equation (4)
Multiply equation (3) with 4 , we get
12x + 4z = 96 be equation (5)
Subtract equation (4) from equation (5) , we get
7x = 21
Divide by 7 on both sides , we get
x = 3
Therefore , the number of $ 5 bills is 3
Substitute the value of x , we get
y = 2x
y = 6
Therefore , the number of $ 10 bills is 6
Substitute the value for x and y in equation (1) , we get
x + y + z = 24
3 + 6 + z = 24
z + 9 = 24
Subtract 9 on both sides , we get
z = 15
Therefore , the number of $ 20 bills is 15
Hence ,
The number of $ 5 bills = 3
The number of $ 10 bills = 6
The number of $ 20 bills = 15
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8 times the difference of 10 and b
Answer:
8(10-b)
Step-by-step explanation:
8(10-b)
open the bracket
80-8b
hope it helps.. please mark brainliest
You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase.
You missed the second payment. What is the amount of interest of the bill you will receive?
The interest on the bill will be calculated as follows:
Amount of Loan = $550
Sales Tax = 6% of $550 = $33
Total Loan = $550 + $33 = $583
Interest = 13.25% APR x $583 = $77.13
Late fee = $29
Total Interest = $77.13 + $29 = $106.13
Find the total surface area of this cuboid.
Answer:
148cm
Step-by-step explanation:
can you help me with this
The result of the definite double integral over the interval is given as follows:
[tex]\int\int_D f(x,y)dxdy = -120[/tex]
How to solve the double integral?The double integral is solved in two steps, first the inner integral is solved, and then the result of the inner integral is used to calculate the outer integral.
Considering the function and the region, the complete integral in this problem is given as follows:
[tex]\int_{-4}^{2}\int_{-4}^{2} (3x + y)dxdy[/tex]
Then the inner integral in this problem is given as follows:
[tex]I = \int_{-4}^{2} (3x + y)dx[/tex]
We are integrating the variable x, then the variable y is a constant, as thus the result is given as follows:
I = 1.5x² + xy, from x = -4 to x = 2.
Then, applying the Fundamental Theorem of Calculus, the result is given as follows:
I = 1.5(2)² + 2y - 1.5(-4)² + 4y = 6y - 18.
Then the outer integral is calculated as follows:
[tex]O = \int_{-4}^{2} 6y - 18[/tex]
Then the result is given as follows:
O = y² - 18y, from y = -4 to y = 2.
O = (2)² - 18(2) - (-4)² + 18(-4)
O = -120.
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why did the chicken cross the rode
Answer: y did the chicken cross the road
Step-by-step explanation: ??????
The function of X equals 2X is transformed to G X equals 2X -3 what type of transformation has occurred
The transformation that has occurred is a vertical shift by 3 units down when the function of X = 2X is transformed to X = 2X -3
What is meant by linear equations?Function that have the form ax + b = 0—where a and b are constants and x is a variable—are known as linear equations. Because they plot as a single direction, these equations are referred to as "linear which is equals to The slope of this line is dictated by the value of a, and the y-intercept (where the line crosses the y-axis) is determined by the value of b. Solving a linear equation entails determining the value of x that makes the equation true. Algebraic strategies like graphing, substitution, or elimination can be used for this. In a number of disciplines, such as engineering, physics, and finance, linear equations are often utilized.
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Given f(x)=-x-5, find f(0)
PLEASE HELP ME!!!!!!
replace x with 0
f(x) = -x - 5
find f(0)
f(0) = 0-5
f(0) = -5
emma ray and norman shared 4/5 of a pizza. Do you think thet had 1/3 each? yes or no?
No, because 4/5 divided by 2 is 2/5 which does not equal 1/3 :)
Convert 8 weeks into days.
*Note: you must use these exact conversion factors to get this question right.
Answer:56 days
Step-by-step explanation:8 weeks*7 days= 56 days total
Give the linear homogeneous DE with constant coefficients that has solution y =
(c1)e^(−2x) + (c2)e^(x).
y''+y-2=0 is the linear homogeneous DE with constant coefficients that has solution y=c₁e⁻²ˣ+ c₂eˣ
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given the general solution y=c₁e⁻²ˣ+ c₂eˣ
the set of fundamental solutions becomes eˣ and e⁻²ˣ
This set is corresponding to the distinct roots m= 1, -2of the corresponding auxiliary equation. Hence, the auxiliary equation so formed is
(m-1)(m-(-2))
(m-1)(m+2)
m²+2m-m-2
m²+m-2
The corresponding linear homogeneous DE with constant coefficients is
y''+y-2=0
Hence, y''+y-2=0 is the linear homogeneous DE with constant coefficients that has solution y=c₁e⁻²ˣ+ c₂eˣ
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