Answer: d) Not in Col in Nul A
Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:
A.x = b or, in this case, [tex]A.x=u[/tex].
To solve, first write the augmented matrix of the system:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]
Now, find the row-echelon form of matrix A:
1) Multiply 1st row by 2 and add 2nd row;
2) Multiply 1st row by -3 and add 3rd row;
3) MUltiply 1st row by 1 and add 4th row;
4) MUltiply 2nd row by -1;
5) Multiply 2nd row by 3 and add 3rd row;
6) Multiply 2nd row by -3 and add 4th row;
7) Divide 3rd row by -15;
8) Multiply 3rd row by -15 and add 4th row;
The echelon form matrix will be:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]
Which gives a system with impossible solutions.
But if [tex]A.x=0[/tex], there would be a solution.
Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:1. He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice.
Answer:
8 servings
Step-by-step explanation:
Given:Rice-to-spice ratio = 15:1Amount of spice = 40 gramsRice required for one serving = 75 gramsTo find:Number of servingsSolution:Spice required for one serving, using the rice-to-spice ratio to calculate:
75 grams/15 = 5 gramsDavid can make servings according to amount of spice he has:
40 grams / 5 grams = 8Answer: David will be able to make 8 servings
Answer: 8
Step-by-step explanation:
WHY CAN'T ANYONE HELP ME? Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
The daily rate is $33 and the per mile rate is $0.35
Step-by-step explanation:
4x + 440y = 286
3x + 190y = 165.5
We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.
4x + 440y = 286
-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]
[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]
560y = 196
y = 0.35
So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.
[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]
So, the daily rate is $33 and the mile rate is $0.35.
Hope this helped!
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
How can you fit data into a pictogram?
Answer:
Step-by-step explanation:
In a pictogram, data can be arranged as follows:
The organization is given in a Cartesian plane, with a vertical and a horizontal axis, images can be introduced. An independent variable is placed on the horizontal axis, usually small numbers. The dependent variable can be placed on the vertical axis, they are usually larger numbers.
what is the value of this expression when a = 2 and b = -3 ? a^3 - b^3 / 5
Answer:
13 2/5
Step-by-step explanation:
a = 2 and b = -3
so the question asks whats.... a^3 - b^3/5
First we plug in the values of a and b
(2)^3 - (-3)^3 /5
Now we solve the ones in paranthesis first
(2)^3 = 8 because 2×2×2 and
-(-3)^3 forget about the - outside the parenthesis so
(-3)^3 = (-27) because (-3)×(-3)×(-3)
now we put it back together
8 -(-27)/5
the two minus become plus so
8 + 27/5
Now we solve it like fractions
8 and 27/5
simplify
13 and 2/5
Hope that helps!
I _____ some stuff A)'ve done B)'s do C)'s doing D)'s did E) 've
Answer:
A and E
Step-by-step explanation:
If the answer was A, it would translate to:
I have done some stuff.
If the answer was D, it would translate to:
I have some stuff.
Both of the sentences are grammatically correct, so A and E are the answers.
Incorrect:
B. - I's do some stuff - doesn't make sense
C. - I's doing some stuff - doesn't make sense
D. - I's did some stuff - doesn't make sense
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree)
Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)
Answer:
1. [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
2. [tex]cos(60)[/tex]
3. [tex]cos(60) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]cos(\alpha - \beta )[/tex]
[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]
In trigonometry;
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]
By comparison
[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]
Compare expression on the right hand side to the left hand side
[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]
This implies that
[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]
By further comparison
[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]
[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]
[tex]cos(\alpha - \beta ) = cos(60)[/tex]
Hence, the expression is [tex]cos(60)[/tex]
Solving for the exact values;
Express [tex]cos(60)[/tex] as a difference of angles
[tex]cos(60) = cos(90 - 30)[/tex]
Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
So;
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]
------------------------------------------------------------------------------------
In trigonometry;
[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];
---------------------------------------------------------------------------
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes
[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = \frac{1}{2}[/tex]
Hence;
[tex]cos(60) = \frac{1}{2}[/tex]
An infinite population has a standard deviation of 10. A random sample of 100 items from this population is selected. The sample mean is determined to be 60. At 80% confidence, the margin of error is
Answer:
1.28
Step-by-step explanation:
Margin of error is also called confidence interval, and it shows how much the results from sample reflects the characteristics of the larger population.
The following steps are used to calculate margin of error.
- obtain population standard deviation (σ) and sample size (n)
- divide standard deviation by square root of sample size
- multiply result by z score consistent with the given confidence. In this case confidence is 80% and z score for it is 1.28
Margin of error= z * (σ ÷ √n)
Margin of error = 1.28 * (10 ÷ √100)
Margin of error= 1.28 * (10 ÷ 10) = 1.28
think about whether the diagram represents a function.
Step-by-step explanation:
im sorry but i need more info or a picture or something to actually anwser the question...
Determine the value of X....... Please
Answer:
x is approximately 53°
Answer:52.64°
Step-by-step explanation:
opp=31
hyp=39
sin x° =[tex]\frac{opp}{hyp}[/tex]
sin x°=31/39
sin x°=0.7949
x=[tex]sin^{-1} (0.7949)\\[/tex]
x=52.64
The simple interest on a sum of money invested at 5% per annum for 3 years was $90. The sum of money invested was
Answer:
Sum of money = $600
Step-by-step explanation:
X = sum of money
Simple interest means that its the same percentage of interest for a given number of years.
The interest per annum is 5% for 3 years, so 5% x 3 = 15%
15% = 0.15 (as a decimal)
Now, we can put this into an equation:
0.15x = 90
x = 90 / 0.15
x = 600.
sum of money invested = $600
PLEASE HELP ASAP!! Write a polynomial f(x) that satisfies the following conditions. Polynomial of lowest degree with zeros of -4 (multiplicity of 1), 2 (multiplicity of 3), and with f(0)=64
Answer:
See below.
Step-by-step explanation:
So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.
Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.
Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.
Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:
In other words, we will have:
[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.
Let's determine n first. We know that f(0)=64, thus:
[tex]f(0)=64=4(-2)^3\cdot n[/tex]
[tex]64=-32n, n=-2[/tex]
Now, let's expand:
Expand:
[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]
[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]
[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]
[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]
This is the simplest it can get.
The population of fruit flies in a laboratory grows geometrically and is checked everyday at noon. If the population began with 80 fruit flies and reached 125 in two days, what is the population after 4 days?
Answer:
[tex]\boxed{195}[/tex]
Step-by-step explanation:
The fruit flies grows geometrically.
[tex]125=80k^2[/tex]
Find the value of k.
[tex]\sqrt{\frac{125}{80} } =k[/tex]
[tex]1.25=k[/tex]
[tex]P=80(1.25)^t[/tex]
[tex]t[/tex] is number of days.
[tex]P=80(1.25)^4[/tex]
[tex]P=195[/tex]
What does 1/6 of 1272 equal?
Answer:
212
Step-by-step explanation:
Answer:
212
Step-by-step explanation:
you have to first divide 1272 by 6 or you can find a number that you can multiply it by so what times 6 equals 1272 so it is guess and check meathodso 200x6 = 1200, and 12x6= 721200+72=1272 and 200+12=212solve for x in the diagram below
Answer:
45
Step-by-step explanation:
Both angles (2x+45) and x together form a straight angle which measures 180 degrees.
Together should make you think of adding the angle measurements.
So we have that (2x+45)+x should be 180 degrees.
The equation we want to solve is:
(2x+45)+x=180
2x+45+x=180
(2x+x)+45=180
3x+45=180
3x=180-45
3x=135
x=135/3
x=45
Let's confirm that x is 45.
(2x+45) with x=45:
(2*45+45)
(3*45)
135
So (2x+45)+x at x=45 gives us:
135+45
180
Answer has been confirmed.
Answer:
[tex]\boxed{x = 45}[/tex]
Step-by-step explanation:
=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)
=> [tex]3x+45 = 180[/tex]
Subtracting 45 to both sides
=> 3x = 180-45
=> 3x = 135
Dividing both sides by 3
=> x = 45
Determine the amount of paint required to cover a wall that is 11feet high and 15feet wide, if the wall has two rectangular windows (which are not to be painted), each measuring 3feet by 7feet.
Answer:
123 Square Feet. Of Paint. Probably gonna take a little more than a sample-size quart, let me know how it turns out.
Step-by-step explanation:
You would need 11*15=165 square feet of paint. BUT
You need 42 less square feet, because there are 2, 7*3=21 square-foot windows.
165-42
explain square roots
Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)
The parabola y= x2 - 4 opens:
O up
O down
O right
O left
Answer:
it opens up
goes up 4 but doesn't move left or right
A random sample of 144 observations produced a sample proportion of 0.4. An approximate 90% confidence interval for the population proportion p is between:_______
a) 0.320 and 0.480
b) 0.333 and 0.480
c) 0.333 and 0.467
d) 0.359 and 0.441
e) 0.313 and 0.487
Answer:
CI =(0.333, 0.480)
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = p±Z * √p(1-p)/n±0.5/n
Z is the z-score at 90% confidence
p is the sample proportion
n is the sample size
Given n = 144, p = 0.4 and z-score at 90% CI = 1.645 (from z table)
Substituting this values;
CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n
CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144
CI = 0.4 ±1.645 * √0.24/144 ± 0.00347
CI = 0.4 ±1.645 * 0.04087± 0.00347
CI = 0.4±0.06723±0.00347
CI =(0.333, 0.480)
If the payment is not made on the credit card by the end of the grace period,
which of the following will occur?
Answer: C. Interest will be charged
Step-by-step explanation:
Answer:
Step-by-step explanation:
Interest will be charged is your answer!
how many solutions if both slopes are the same but the y-intercepts are different
Answer:
No solutions.
Step-by-step explanation:
You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.
Hope this helps!
Answer: no solution
Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.
Let's look at an example.
Below, you will see two equations.
Both of the lines have a slope of 1.
So, they must be parallel which means they don't cross.
So there is no solution.
what is that is the derivative of
x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
Answer:
see explanation
Step-by-step explanation:
differentiate using the power rule.
[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus
[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1
x = 5 → 2(5) - 1 = 10 - 1 = 9
To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero
2x - 1 = 0 , then
2x = 1 and
x = [tex]\frac{1}{2}[/tex]
Suppose a car depreciates linearly the second you drive it off the lot. If you purchased the car for $31,500 and after 5 years the car is worth $20,500, find the slope of the depreciation line.
Answer: m = - 2200
Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.
The year a car is bought and its price means:
f(0) = 31,500
Five years later, the price is $20,500, i.e.:
f(5) = 20,500
With these two pairs of value, slope is calculated as:
[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]
[tex]m = \frac{20500-31500}{5-0}[/tex]
[tex]m = \frac{- 1100}{5}[/tex]
m = - 2200
The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.
A fisherman uses a spring scale to weigh a tilapia fish. He records the fish weight as a kilograms and notices that the spring stretches b centimeters. Which expression represents the spring constant (1 =9.8 )? A). 980ab B). 9.8ab C). 9.8ab D). 980ab
Answer:
k = [tex]\frac{980a}{b}[/tex]
Step-by-step explanation:
Fisherman noticed a stretch in the spring = 'b' centimetres
Weight of the fish = a kilograms
If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,
F = kΔx
Where k = spring constant
Δx = stretch in the spring
F = weight applied
F = mg
Here 'm' = mass of the fish
g = gravitational constant
F = a(9.8)
= 9.8a
Δx = b centimetres = 0.01b meters
Therefore, 9.8a = k(0.01b)
k = [tex]\frac{9.8a}{0.01b}[/tex]
k = [tex]\frac{980a}{b}[/tex]
Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]
Trigonometry Dilemma
Answer:
17.1
Step-by-step explanation:
The missing side is x
tan 25° = [tex]\frac{opposite }{adjacent }[/tex] tan 25° = [tex]\frac{8}{x}[/tex]switch tan 25° and x
x = [tex]\frac{8}{tan 25}[/tex] x= 17.15≈17.1Find y................
Answer:
[tex] y = 3 [/tex]
Step-by-step explanation:
Given the above right angled triangle, we would use a trigonometric ratio formula to find y.
Given angle = 30°
Hypotenuse = 6
Opposite side = y
Solve for y using the trigonometric ratio formula as follows:
[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]
[tex] sin(30) = \frac{y}{6} [/tex]
Multiply both sides by 6
[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]
[tex] 0.5*6 = y [/tex]
[tex] 3 = y [/tex]
[tex] y = 3 [/tex]
Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay rate of 22% per hour. They start with 500 viruses that they want to check on in the next 8 hours. How many viruses will they find in 8 hours? Round your answer to the nearest whole number.
Answer:
They will find 69 viruses in 8 hours.
Step-by-step explanation:
The number of viruses after t hours is given by the following equation:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.
They start with 500 viruses
This means that [tex]V(0) = 500[/tex]
Decay rate of 22% per hour.
This means that [tex]r = 0.22[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 500(1-0.22)^{t}[/tex]
[tex]V(t) = 500(0.78)^{t}[/tex]
How many viruses will they find in 8 hours?
This is V(8).
[tex]V(t) = 500(0.78)^{t}[/tex]
[tex]V(8) = 500(0.78)^{8}[/tex]
[tex]V(8) = 68.51[/tex]
Rounding to the nearest whole number
They will find 69 viruses in 8 hours.
Answer:
The researchers will find 86 viruses.
Step-by-step explanation:
Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.
A =?
A0 = 500
R= -0.22/hour
t= 8 hours
Substitute the values in the formula.
A= A0e^rt
A= 500e^-0.22x8
Compute the amount.
A ≈ 86.02
Round to the nearest whole number.
A ≈ 86
12. A veterinarian will prescribe an antibiotic to a dog based on its weight. The effective dosage of the antibiotic is given by d ≤ 1∕5w2, where d is dosage in milligrams and w is the dog's weight in pounds. Which of the following graphs displays the effective dosage of the antibiotic?
Answer:
Graph C. See explanations below.
Step-by-step explanation:
Looking for graph corresponding to d <= (w^2)/5
Take the third graph, which has a solid line (to correspond to the inequality <=, or less than or equal to).
For a dog's weight of 10 lb, the corresponding dose is 20 mg = 10^2/5
for 20 lb, dose = 80 mg (=20^2/5)
...
For 40 lb, dose = 320 mg (=40^2/5).
So this is the correct graph.
The fourth (d) is similar. But the dotted line eliminates the equality in
d <= w^2/5
so not correct.
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.
16 sin4x
16sin4x = _____
Answer:
[tex]6-8cos2x+2cos4x[/tex]
Step-by-step explanation:
We are given that
[tex]16sin^4 x[/tex]
We can write the given expression as
[tex]16(sin^2x \times sin^2 x)[/tex]
[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]
By using the formula
[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]
[tex]4(1-cos2x)^2[/tex]
[tex]4(1-2cos2x+cos^2(2x)[/tex]
Using the identity
[tex](a-b)^2=a^2+b^2-2ab[/tex]
[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]
[tex]4-8cos2x+2+2cos4x[/tex]
[tex]6-8cos2x+2cos4x[/tex]
This is required expression.
HELP ASAP PLEASEEEEE C is the center of the circle. Find the length of DGE A. s= 161 over 18 pie B. s= 343 over 35 pie C. s= 343 over 18 pie D. s= 343 over 9 pie
Answer:
C. [tex] \frac{343}{18} pie [/tex]
Step-by-step explanation:
Given a circle of:
Radius (r) = 14
Measure of minor arc = 115°
We are required to find the length of DGE = length of major arc.
Length of arc is given as 2πr(θ/360)
Measure of the major arc DGE (θ) = 360 - 115 = 245°
Length of major arc DGE = [tex] 2*pie*14*\frac{245}{360} [/tex]
[tex] = 28*pie*\frac{49}{72} [/tex]
[tex] = \frac{28*49}{72} pie [/tex]
[tex] = \frac{7*49}{18} pie [/tex]
[tex] = \frac{343}{18} pie [/tex]
Length of arc DGE =
[tex] \frac{343}{18} pie [/tex]
Three of the sides will require fencing and the fourth wall already exists. If the farmer has 116 feet of fencing, what are the dimensions of the region with the largest area
Answer:
29 ft x 58 ft
Step-by-step explanation:
Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.
The amount of wire available is:
[tex]116 = 2x+y\\y=116-2x[/tex]
The area of the region is:
[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]
The value of 'x' for which the derivate of the area function is zero will yield the maximum area:
[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]
The value of y is:
[tex]y=116-2*29\\y=58\ ft[/tex]
The dimensions of the region with the largest area are 29 ft x 58 ft.