The dimensions of the largest area that can be enclosed is 1590 × 795= 1264050 yd² when no fencing is required along the river.
Given the owner of the Rancho Los Feliz has 3180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river.
We need to find the dimensions of the largest area that can be enclosed.
Therefore, the length of the land is the perimeter of the rectangle minus the river front.
We have; 2x + 3y = 3180 yd
Also, we can rewrite this equation in terms of x;
2x = 3180 - 3yy = (3180 - 2x) / 3
Substituting y in terms of x in the area equation;
Area A = x y= x(3180 - 2x) / 3
Taking the derivative of the area equation to find the maximum value of A;
A' = 1060 - 2x / 3 When A' = 0, x = 1590 / 2 = 795 yd.
Substitute x = 795 into the equation for y;
2(795) + 3y = 3180y = (3180 - 1590) / 3 = 530 yd
Therefore, the dimensions of the largest area that can be enclosed are; Length = 1590 yd Width = 795 yd
Hence, the area is given by; Area = Length × Width= 1590 × 795= 1264050 yd².
To learn more about area of rectangle
https://brainly.com/question/22242374
#SPJ11
if money were valued in terms of how many minutes a person needs to work to buy a dollar, an increase in the number of minutes of work needed would be
If money were valued in terms of how many minutes a person needs to work to buy a dollar, an increase in the number of minutes of work needed would be an increase in the price of money.
A person needs to work for 2 minutes to buy a dollar. If there is an increase in the number of minutes of work needed, say to 3 minutes to buy a dollar, then the price of money (dollar) has increased or it has appreciated.
The time value of money (TVM) is the idea that an amount of cash is worth more now than a similar aggregate and will be sometime not too far off because of its profit possible in the meantime. The time worth of cash is a central guideline of money. A sum of cash in the hand has more prominent worth than a similar aggregate to be paid from here on out. The time worth of cash is likewise alluded to as the present limited esteem.
To learn more about finance and economics,
https://brainly.com/question/10024737
#SPJ4
Find the period and the amplitude of the periodic function. I'm awful with graphs :(
A period is the difference in x over which a sine function returns to its equivalent state and the amplitude is A/5.
Amplitude:
The amplitude of a periodic variable is a measure of its change over a period of time, such as a temporal or spatial period. The amplitude of an aperiodic signal is its magnitude compared to a reference value. There are various definitions (see below) of amplitude, which is any function of the magnitude of the difference between the extreme values of a variable. In the previous text, the phase of a periodic function is called the amplitude.
X = A sin (ω[ t - K]) + b
A is the amplitude (or peak amplitude),
x is the oscillating variable,
ω is angular frequency,
t is time,
K and b are arbitrary constants representing time and displacement respectively.
According to the Question:
An equation does not have an amplitude. This "equation" represents the formula of a vibration, and was better written as:
X= A/5* sin(1000.t + 120)
These oscillations have a certain amplitude. X values can vary from minimum to maximum. Normally, the stop position of the oscillation is X=0. In this case, we can see that the maximum occurs when the sine is +1 and the minimum occurs when the sine is -1.
For theses cases X= A/5 respectively -A/5.
Therefore,
The amplitude is A/5.
For formulas of this type, the term in front of the sinus (or cosine) is equal to the amplitude.
Complete question:
Can I find the amplitude of this equation? A/5 *
(1 point) a standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all. how many 7-card hands will consist of exactly 2 hearts and 2 clubs?
A standard deck of cards consists of four suits with each suit containing 13 cards for a total of 52 cards in all. 6084 consist of exactly 2 hearts and 2 clubs.
We have to find the number of times, when there will be 2 hearts and 2 clubs, when we draw 7 cards, so required number is-
= 13c₂ * 13c₂
= (13!/ 2! * 11!) * (13!/ 2! * 11!)
= 78 * 78
= 6084.
Learn more about probability here:
https://brainly.com/question/13718736
#SPJ4
Lucy reads 450 words in 3 minutes.
This is an equation that can be used to
find w, the number of words Lucy can
read in 20 minutes if she continues to
read at the same rate?
Answer:
3000 words
Step-by-step explanation:
450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.
1 minute = 150 words so 150 words times 20 minutes = 3000 words.
Ina and Lane share a 24-ounce bucket of clay. By the end of the week, Gina has used
3
8
of the bucket, and Lane has used
1
4
of the bucket of clay. How many ounces are left in the bucket?
9 ounces are left in the bucket. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
It is asserted that the four basic operations, usually referred to as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.
We are given that Gina and Lane share a 24-ounce bucket of clay.
Gina has used \(\frac{3}{8}\) of the bucket of clay.
So, we get
\(\frac{3}{8}\) of 24 = 9 ounces
Similarly, Lane has used \(\frac{1}{4}\) of the bucket of clay.
So, we get
\(\frac{1}{4}\) of 24 = 6 ounces
Using the addition operation, we get
Total clay used = 9 + 6 = 15 ounces
Now, using the subtraction operation, we get
Ounces left = 24 - 15 = 9 ounces
Hence, 9 ounces are left in the bucket.
Learn more about arithmetic operations from the given link
https://brainly.com/question/30283549
#SPJ1
Question: Gina and Lane share a 24-ounce bucket of clay. By the end of the week, Gina has used 3/8 of the bucket, and Lane has used 1/4 of the bucket of clay. How many ounces are left in the bucket?
"Your grade must be at least 64 to pass this class"
Answer:
i have 87%
Step-by-step explanation:
Answer:
That mean you need aleast to make C's to pass
how many gallons of gas would it take to drive to the moon and back
Answer:
239 miles per gallon for a round trip.
Step-by-step explanation:
you'd need to achieve 238,900 / 2000 = 119.5 miles per gallon for a one way trip,
Subtract: 22²+8242²+122-16
O22²+122-12
4(x+4)(x-1)
O -x²+12x-12
4x(x+4)(x-1)
-2²+6x-6
о 22(x+4)(x-1)
H
-2x²+12-12
2(x+4)(x-1)
=
6-2(x-1)
6
2x(x+4)= 4(x+4)(x-1) = 2z(x+4)-2(x-1)
x.x
4(x+4)(x-1)-
Answer:
the correct answer is the second one
Step-by-step explanation:
I will add a photo of my solution, because there's a lot to type here
Triangle EFG is dilated by a scale factor of 1/4 to form triangle E'F'G'. Side E'F' measures 12.512.5. What is the measure of side EF?
Answer: 3.125
Step-by-step explanation:
Given
Triangle is dilated by a factor of \(\frac{1}{4}\) i.e. each side multiplies to 0.25.
Side E'F' becomes 0.25 times the original length
\(\Rightarrow E'F'=\dfrac{1}{4}\times 12.5=3.125\)
For the past 16 months, susie has been paying $126.50 each month to her insurance company. after causing an accident last month, her insurance company notified her that her monthly payment will be increased by $21.25. what increase in her annual premium did susie’s insurance company apply as a result of the accident? a. $21.25 b. $125.60 c. $147.75 d. $255.00 please select the best answer from the choices provided a b c d
The annual premium of Susie's insurance company apply as a result of accident is $255 for an year. This is because the monthly insurance payment has been increased by $21.25.
What is Health insurance?
Health insurance or the medical insurance is an insurance which covers the whole or a part of the risk of a person which is incurring the medical expenses. Depending upon the health insurance plan, the risk is shared among many individuals.
Main body:
The increase in monthly insurance payment = $21.25
So, the annual increase in the premium amount paid by Susie will be:
Monthly increase in insurance payment × 12
(As there are 12 months in an year)
Annual increase in premium amount = $21.25 × 12
Annual increase in premium amount = $255
Therefore, the annual increase in the amount of premium paid by Susie for health insurance is $225.
Learn more about Health insurance here:
brainly.com/question/29042328
#SPJ4
the regression r2 is a measure of: part 2 a. the goodness of fit of your regression line. b. whether or not x causes y. c. the square of the determinant of r. d. whether or not ess > tss.
The correct answer to this question is a. The regression \(r_{2}\) is a measure of the goodness of fit of your regression line. This means that it tells you how well the regression line fits the data and how much of the variation in the dependent variable can be explained by the independent variable. In other words, it is a measure of the strength of the relationship between the two variables being analyzed.
The determinant is a mathematical term used in linear algebra that helps determine the properties of a matrix. It is not directly related to the regression \(r_{2}\) value, so option c is incorrect. Option b is also incorrect as the regression \(r_{2}\) value does not determine whether or not x causes y. Finally, option d is also incorrect as ess and tss are not related to the goodness of fit of the regression line.
Overall, the regression \(r_{2}\) value is an important measure in determining the quality of a regression model and how well it can predict outcomes based on the independent variable. It is calculated by dividing the explained variance by the total variance and is expressed as a percentage. A high \(r_{2}\) value indicates a strong relationship between the variables and a good fit of the regression line to the data, while a low \(r_{2}\) value indicates a weak relationship and a poor fit.
Learn more about regression here:
https://brainly.com/question/17731558
#SPJ11
Use identities to find tan, csc, sec, and cot. Where necessary, rationalize denominators
We are given:
\(sin\text{ }\theta=\frac{3}{5},cos\text{ }\theta=\frac{4}{5}\)The tangent is defined as the ratio of the sine and the cosine:
\(tan\text{ }\theta=\frac{sin\text{ }\theta}{cos\text{ }\theta}\)Calculating:
\(\begin{gathered} tan\text{ }\theta=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{5}\cdot\frac{5}{4} \\ \\ tan\text{ \theta}=\frac{3}{4} \end{gathered}\)The cotangent is the reciprocal of the tangent:
\(\begin{gathered} \cot\theta=\frac{1}{\tan\theta} \\ \\ \cot\theta=\frac{1}{\frac{3}{4}}=\frac{4}{3} \end{gathered}\)The secant is the reciprocal of the cosine:
\(\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}} \\ \\ \sec\theta=\frac{5}{4} \end{gathered}\)The cosecant is the reciprocal of the sine:
\(\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{3}{5}} \\ \\ \csc\theta=\frac{5}{3} \end{gathered}\)how many raisins must cookies contain on average for the chance of a cookie containing at least one raisin to be at least 99%?
The number of raisins that must cookies contain on average for the chance of a cookie containing at least one raisin to be at least 99% is λ ≥ − ln(0.01)
Assuming that a Poisson random scatters of raisins.
Let N = the number of raisins per cookie. Then If N is a Poisson random variable with a
parameter λ, then
P(N ≥ 1) = 1 − P(N = 0) = 1 − exp(−λ)
and for this to be at least 0.99, we need
λ ≥ − ln(0.01)
Recall that λ = E[N] is the average number of raisins per cookie.
Learn more about Poisson random variables here: https://brainly.com/question/29148982
#SPJ4
Due by tonight! Urgent need of assistance please help me out <3
Answer:
T: (5, -10)
S: (5, -6)
U: (0, -10)
V: (0, -6)
Step-by-step explanation:
180° clockwise rotation around the origin: all signs must become opposite
for example: (2, -4) after 180 degree clockwise rotation ---> (-2, 4)
T: (-5, 10)
S: (-5, 6)
U: (0, 10)
V: (0, 6)
change all the signs to opposite
T: (5, -10)
S: (5, -6)
U: (0, -10)
V: (0, -6)
attached is the graph after the 180 clockwise rotation around the origin
if I have an 84% which is a B but get a 65 which is a D whats my grade now?
Answer: C
Step-by-step explanation:
0.135 written as a fraction is o 5/37 O 27/200 O 27/100
Answer:
27/200 :)
Step-by-step explanation:
why couldn't Pythagoras use the pythagorean theorem as we know it?
Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.
It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.
He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.
Learn more about theorem here:
brainly.com/question/343682
#SPJ11
The difference of x and y is 14. The value of x is 3 more than
twice the value of y. Write two equations and graph to find
the value of x.
O X = 25
O x = -17
OX= 4
O x = 11
The value of X = 25.
The difference of x and y is 14. The value of x is 3 more thantwice the value of y. Find the value of x and y.Solution:
The two equations are
(i) the first condition is difference of x and y is 14
x - y = 14 ---------equation 1
(ii) the second condition of the given data is value of x is 3 times more than two times of y value.
x - 2y = 3 --------equation 2
From equation 2, we have to separate two variables x and y,
x = 3 + 2y --------equation 3
We have to Substitute equation 3 in equation 1
3 + 2y - y = 14
3 + y = 14
y = 14 - 3
y = 11
Substitute y = 11 in equation 1........
x - 11 = 14
x = 14 + 11
x = 25
So, the value of x is 25 and y is 11.
To learn more about equations refer to:
https://brainly.com/question/2972832
#SPJ1
Answer:
x - y = 14x - 2y = 3x = 25Step-by-step explanation:
Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.
EquationsThe difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...
x - y = 14x - 2y = 3GraphThe attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.
The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.
The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.
Algebraic solutionSince we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:
2(x -y) -(x -2y) = 2(14) -(3)
x = 25 . . . . . . . . . simplify
a. the columns of a matrix a are linearly independent if the equation ax d 0 has the trivial solution. b. if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s. c. the columns of any 4 5 matrix are linearly dependent. d. if x and y are linearly independent, and if
a. Yes, the columns of matrix a are linearly independent if the equation ax = 0 has the trivial solution.
This means that the only solution to the equation is x = 0, which implies that the vectors in the matrix are not linear combinations of each other.
b. No, if s is a linearly dependent set, then each vector is not necessarily a linear combination of the other vectors in s. A linear combination is a combination of two or more vectors where each vector is multiplied by a scalar and then added together.
A linearly dependent set means that one of the vectors can be expressed as a linear combination of the other vectors, but not necessarily all of them.c. No, the columns of any 4 5 matrix are not necessarily linearly dependent.
Linear dependence is determined by the rank of the matrix. If the rank of the matrix is equal to the number of columns, then the columns of the matrix are linearly independent.
However, if the rank of the matrix is less than the number of columns, then the columns of the matrix are linearly dependent.
d. Yes, if x and y are linearly independent, then any linear combination of x and y must equal to zero. This means that the coefficients of x and y must be equal to zero in order for the linear combination to equal zero.
For more questions like Linear click the link below:
https://brainly.com/question/23878734
#SPJ4
Complete question:
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector. D. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.
–5x+2 - 4; Prove: x = 6
Answer:
Step-by-step explanation:
-5x+2-4 if x =6
-5(6)+2-4
-30+2-4
-30-2
-32
help finding coordinates
The coordinates of N by the 270 degree rotation clockwise rule is (-7, 3)
Finding the coordinates of NFrom the question, we have the following parameters that can be used in our computation:
N = (-3, 7)
The transfomation rule is given as
270 degree rotation rule clockwise
Mathematically, this is represented as
(x, y) = (-y, x)
Substitute the known values in the above equation, so, we have the following representation
N' = (-7, 3)
Hence, the coordinates of N after the rotation is (-7, 3)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
Find the volume of the described solid of revolution or state that it does not exist. The region bounded by f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6] is revolved about the x-axis. Set up the integral that should be used to find the volume of the solid. Use increasing limits of integration. (Type exact answers.) Find the volume or state that it does not exist. Select the correct answer and, if necessary, fill in the box to complete your choice. A. The volume is cubic units. (Type an exact answer.) B. The volume does not exist.
The correct option is A. The volume is 6.77 cubic units
The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].
We want to find the volume of the solid of revolution when the region is rotated about the x-axis.
Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}
To set up the integral to find the volume of the solid of revolution, we can use the disk method.
We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.
The area of a disk is given by the formula: A = πr²
where r is the radius of the disk and is equal to f(x) in this case.
Therefore, the area of a disk is: A = πf(x)²
Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.
We have The integral that should be used to find the volume of the solid is given as:
V = ∫₁⁶ πf(x)² dx
We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.
We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx
Let u = x - 1, so that du/dx = 1 and dx = du.
When x = 1, u = 0, and when x = 6, u = 5.
Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.
The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.
Thus, the correct option is A. The volume is 6.77 cubic units.
To know more about disk method visit:
https://brainly.com/question/28184352
#SPJ11
Figure ABCD is a rhombus. Rhombus A B C D is shown. Angle A is (5 x 25) degrees and angle D is (7 x minus 1) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so
\(5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18\)
please help me with this it's a huge test :) i'll mark brainliest!
Answer:
I think A or D
Step-by-step explanation:
What's the slope of the graph
Answer:
1/-2
Step-by-step explanation:
To find the slope:
rise/run
From point to point
So....
From (-1,0)
you go up 2(2)
then left 4(-4)
to get to (-5,2)
so 2/-4 reduced is 1/-2
Let x varies directly as y. If x= 14 when y = 7, then write a linear equation. What is the value of x, when y = 8?
Answer:
x = 16
Step-by-step explanation:
given x varies directly as y then the equation relating them is
x = ky ← k is the constant of variation
to find k use the condition x = 14 when y = 7
14 = 7k ( divide both sides by 7 )
2 = k
x = 2y ← linear equation
when y = 8 , then
x = 2 × 8 = 16
Evaluate this expression for x = 5: 6+ (10 -x2-20
Salut/Hello!
Answer:
Step-by-step explanation:
x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)
I hope it was helpful! :]
Devon has 11 more than twice as many customers as when
he started selling custom baseball hats. He now has 73
customers. How many customers did he have when he
started?
Answer: 6
He started with 6 costumers
a map of the town that hannah lives in can be represented by the cartesian plane. hannah starts off at $(-4, 9)$ and walks $10$ units to the left and $7$ units down to get to her new location. along what line could she have walked to get to the new location directly from her old location? express your answer in the form $ax by
The answer in the form of x,y is -7x + 10y = 118.
A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.
from given conditions, we get,
(-4, 9) and 10 left 7 down puts her at ( -4 - 10 , 9 - 7) = ( -14, 2)
So, the points ( -4, 9) and (-14,2) are on the line
Slope of this line = [ 2 - 9] / [ -14 - -4 ] = [ -7] / [ -10] = 7/10
Equation of the line
y = (7/10)(x - - 4) + 9
y = (7/10) ( x + 4) + 9 multiply through by 10
10y = 7 (x + 4) + 90
10y = 7x + 28 + 90
-7x + 10y = 118
Therefore, the answer in the form of (x , y) is -7x + 10y = 118
To learn more about cartesian plane visit : brainly.com/question/28574364
#SPJ4
b) A men earns Rs.50000 in a month. He spends 30% of his income on foood
2/5 on his child's Education,0.25% on transportation and rest he saves.
i) Find the amount that he spends on each topic.
ii)Find his saving percentage.
Answer:
\(\huge\mathfrak\pink{ here's your solution } \\ \\ im \: soo \: happy \: \)