The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
what is perimeter ?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.
calculation
In order to construct a hog pen, I have 800 feet of fencing.
Assume that "l" represents the rectangle's length and "w" its width.
One of your properties borders a river that I own.
I can secure my property with fencing on its three sides.
because of this, the fencing's necessary perimeter p = l + 2w
The fencing's perimeter is now equal to
⇒ l + 2w = 800
= l = 800 - 2w
now the rectangle's area = A = lw
Therefore, A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]
By diffusing the area equation, we can figure out the rectangle's greatest area.
Therefore, A' = 800 - 4w
Again, A" = -4
The rectangle has the largest area since the second order differentiation is constant negative.
Put simply, we obtain: A' = 0 , A' = 800- 4w
⇒800- 4w = 0
⇒ 4 w = 800
⇒ w = 200
So the rectangle has a 200-foot width.
The rectangle's length is currently:
l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
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A Question 8 (2 points) Retake question
Which equation would reflect the function over the Y-AXIS
f(x)= |x-31+2
Og(x) =
-x +31-2
g(x) = -x - 3| +2
) g(x) = |-x + 3| + 2
g(x) = -x - 3| + 2
A Question 9 (2 points) Retake question
The equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.
The required value of f(3) is 10.
What is a reflection across the y-axis?Reflection across the y-axis is defined as reflecting a point across they = x, the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).
So reflected across the y-axis: f(x) → f(-x),
⇒ (x,y) → (-x , y)
As per the given question,
f(x) = |x-3| + 2
f(-x) = |-x-3| + 2 = g(x)
Thus, the equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.
The function f(x) is given in the question,
f(x) = 4x - 2,
To determine the value of f(3)
Substitute the value of x = 3 in the given function,
f(3) = 4(3) - 2
f(3) = 12 - 2
f(3) = 10
Thus, the required value of f(3) is 10.
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liters/minute, where t is in minutes since the pump is started. if the holding tank contains 1000 liters of water when the pump is started, approximately how much water does it hold two hours later?
Approximately, water does it hold two hours later is = 248.72 liters
Given that,
The holding tank contains 1000 liters of water
Water does it hold two hours later,
Then,
1) Integrate the function, from t =0 to t = 120 minutes to obtain the number of liters pumped out in the entire interval, and
2) Substract the result from the initial content of the tank (1000 liters).
So
We can write,
Let us assume,
Integral of (6 - 6 [tex]e^{-0.13t}[/tex] ) dt ]from t =0 to t = 120 min
= 6t + 6 [tex]e^{-0.13t}[/tex] / 0.13
= 6t + 46.1538 6 [tex]e^{-0.13t}[/tex] ] from t =0 to t = 120 min
= 6*120 + 46.1538 e^(-0.13*120) - 0 - 46.1538
= 720 + 46.1538 (1.678) - 46.1538
= 720 + 77.44 - 46.1538 liters
= 751.28 liters
2) If the holding tank contains 1000 liters of water,
1000 liters - 751.28 liters = 248.72 liters
Therefore,
Approximately, water does it hold two hours later is = 248.72 liters
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f(x) = x3 – 7x + 6 (a) Show that (x – 2) is a factor of f (x). (b) Hence, or otherwise, factorise f(x) completely.
Answer:
see explanation
Step-by-step explanation:
if (x - h) is a factor of f(x) then f(h) = 0
(a)
if (x - 2) is a factor of f(x) then f(2) = 0
f(2) = 2³ - 7(2) + 6
= 8 - 14 + 6
= - 6 + 6
= 0
since f(2) = 0 then (x - 2) is a factor of f(x)
(b)
using synthetic division to factor f(x)
insert a zero in the x² position on the table
2 | 1 0 - 7 6
↓ 2 4 - 6
-----------------------
1 2 - 3 0
quotient is
x² + 2x - 3 = (x + 3)(x - 1)
Then
f(x) = (x - 2)(x + 3)(x - 1)
9. Sales: $50,000
Returns: $4,680
Net Sales: (a)
Cost of goods sold: $22,950
Gross profit: (b)
The gross profit of the Blog Inc would be $22,370.
What is gross profit?Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Sales: $50,000
Returns: $4,680
Cost of goods sold: $22,950
Therefore,
Net Sales: 50,000 - 4,680
= 45,320
We can calculate the Gross Profit;
Gross Profit = (Net Sales – Cost of Goods Sold)
= ($45,320- $22,950)
= $22,370
Hence, the gross profit would be $22,370.
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PLS HELP
Assume that all grade-point averages are to be standardized on a scale between 0 and 5. How many grade-point averages must be obtained so that the sample mean is within 0.009 of the population mean? Assume that a 98% confidence level is desired. If using the range rule of thumb, o can be estimated as
Range/4 = 5-0/4 = 1.25. Does the sample size seem practical?
No, the sample size is not practical.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find grade-point averages.
The sample mean is within 0.009 of the population mean.
98% confidence level is desired
The formula for sample size is n = (z alpha/2× S/E)²
where n = sample size
z alpha/2 = critical value for 98% confidence = 2.58
S = 1.25 and
E = 0.009
n = (2.58 × 1.25 / 0.009)² = 128401.5 ~ 128402
Sample size does not seem practical.
Hence, the sample size is not practical.
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how do you divide 9.51 by 6
Answer: 1.00585 or 1.585. Both are correct
Step-by-step explanation:
What is the answer to this problem?
Answer:
450x-9000
Step-by-step explanation:
You will be 9,000 dollars in debt, and it costs 300 dollars to make but sells for 750.
750-300 = 450 (profit per desk)
If a segment is drawn perpendicular to a line, the point of intersection is called the ____ of the perpendicular.
Answer: Foot
Step-by-step explanation:
The point of intersection is called the foot of the perpendicular. I remember learning this in my Math class!
PLEASE HELP!!! i'm terrible at graphing.
The graph of the given function, g(x) = -5^x + 5, is shown below
Graphing a functionFrom the question, we are to graph the given function.
From the given information,
The given function is
g(x) = -5^x + 5
To graph the function, we will determine some of the points on the line
When x = -2
g(2) = -5^(-2) + 5
g(2) = -1/25 + 5
g(2) = 4 24/25 = 4.96
When x = -1
g(1) = -5^(-1) + 5
g(1) = -1/5 + 5
g(1) = 4 4/5 = 4.8
When x = 0
g(0) = -5^(0) + 5
g(0) = -1 + 5
g(0) = 4
When x = 1
g(1) = -5^(1) + 5
g(1) = -5 + 5
g(1) = 0
When x = 2
g(2) = -5^(2) + 5
g(2) = -25 + 5
g(2) = -20
Using the above points, the graph of the function is shown below.
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Write y+3=5(x+4) in slope intercept form
Answer:
Below
Step-by-step explanation:
y+3=5(x+4) Expand R side, then subtract 3 from both sides of equation
y = 5x+ 17 Done .
Answer:
y = 5x+17
Step-by-step explanation:
To get this equation to slope intercept form, get the y variable by itself on one side of the equal sign.
y+3=5(x+4)
[Distribute the 5 to x and 4]
y+3 = 5x+20
[Subtract 3 from both sides]
y = 5x+17
[Done!]
PLEASE HELP much appreciated!
y>-2x+4 is the inequality of the given graph.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given line passes through (2,0) and (0,4)
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
m=4/-2=-2
4=-2(0)+b
b=4
Hence equation of line y=-2x+4
The shaded region is the above the line and line is dotted. so we have to use greater than symbol.
Hence, y>-2x+4 is the inequality of the given graph.
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Write an equation in standard form of the line that passes through the given points.
X -4 -1 2 5
y 5 1 -3-7
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{-8}{2 +4} \implies \cfrac{ -8 }{ 6 } \implies - \cfrac{ 4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-4)}) \implies y -5 = - \cfrac{ 4 }{ 3 } ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-5)=3\left( - \cfrac{ 4 }{ 3 } ( x +4) \right)}\implies 3y-15=-4(x+4) \\\\\\ 3y-15=-4x-16\implies 3y=-4x-1\implies {\Large \begin{array}{llll} 4x+3y=-1 \end{array}}[/tex]
What is the answer i need them now pls I'm going to fail
Answer:
C
Step-by-step explanation:
its 19735 hope it helps
Rewrite using a single exponent.
Answer:[tex]5^{18}[/tex]
Step-by-step explanation:
5^18
...... i need help past due
Answer:
Step-by-step explanation:
The given is the number of years she drives for and how much she drives in a year.
We can use this to figure out how many miles she drives in 3, 4, and 6 years.
To do that, just multiply the number of years by the number of miles she drives in a year
[tex]\frac{9000}{1} =\frac{miles}{x years}[/tex]
[tex]9000 * x years = 1 * miles[/tex]
[tex]3 * 9000 = 27,000\\4 * 9000 = 36,000\\6 * 9000 = 54,000[/tex]
Put points at (3,27000) , (4,36000) , (6,54000)
Draw a straight line through them (not like mine)
Let theta be an angle such that cos(theta) = -1/9 and 0 <=theta<=2pi
Assume that cos(theta/2) < 0. Then if
Terminal point of theta/2 = (a1, a2), enter a1 and a2 in that order.
In this case, the terminal point of theta/2 can be determined using the following steps:
Since cos(theta/2) < 0 and the cosine function has a range of [-1, 1], it follows that theta/2 must be in the second or third quadrant (90 degrees to 180 degrees or 180 degrees to 270 degrees).
To find the terminal point of theta/2, we can use the formula for converting from polar to Cartesian coordinates: x = rcos(theta) and y = rsin(theta), where (x,y) is the Cartesian coordinates of the terminal point, r is the radius, and theta is the angle in radians.
In this case, the radius is 1 (since the terminal point is on the unit circle) and the angle is theta/2. Substituting these values into the formulas above, we get:
x = 1 * cos(theta/2)
y = 1 * sin(theta/2)
To find the values of cos(theta/2) and sin(theta/2), we can use the identity cos(theta/2) = sqrt((1 + cos(theta))/2) and sin(theta/2) = sqrt((1 - cos(theta))/2).
Substituting the given value of cos(theta) (-1/9) and the identities above into the formulas for x and y, we get:
x = sqrt((1 + (-1/9))/2) = -sqrt(2)/3
y = sqrt((1 - (-1/9))/2) = sqrt(8)/3
Thus, the coordinates of the terminal point of theta/2 are (-sqrt(2)/3, sqrt(8)/3).
The terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).
How to find terminal point?To find the terminal point (a₁, a₂) of theta/2, use the half-angle identity for cosine:
cos(theta/2) = ± √((1 + cos(theta)) / 2)
Given that cos(theta) = -1/9 and cos(theta/2) < 0, the negative sign should be used in the half-angle identity.
Calculate cos(theta/2):
cos(theta/2) = - √((1 + cos(theta)) / 2)
cos(theta/2) = - √((1 - 1/9) / 2)
cos(theta/2) = - √((8/9) / 2)
cos(theta/2) = - √(8/18)
cos(theta/2) = - √(4/9)
cos(theta/2) = - 2/3
Cos(theta/2) = -2/3. To find the terminal point (a₁, a₂), determine the values of a₁ and a₂.
Since cos(theta/2) is negative, a₁ is negative. To find the value of a₂, use the Pythagorean identity:
cos²(theta/2) + sin²(theta/2) = 1
Since cos(theta/2) = -2/3, calculate sin(theta/2):
sin²(theta/2) = 1 - cos²(theta/2)
sin²(theta/2) = 1 - (-2/3)²
sin²(theta/2) = 1 - 4/9
sin²(theta/2) = 5/9
sin(theta/2) = ± √(5/9)
sin(theta/2) = ± √(5) / 3
Since theta is in the second quadrant (cos(theta) = -1/9), sin(theta) is positive in the second quadrant. Therefore, sin(theta/2) = √(5) / 3.
Now, sin(theta/2) = √(5) / 3.
So, the terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).
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Find all numbers whose absolute value is 3 .
Answer:
-3 and 3
Step-by-step explanation:
Absolute value makes a negative number positive and allows a positive number to stay the same. |-3| becomes 3, and |3| stays as 3, so the correct answers are -3 and 3.
Neeeeeeeeed help please please
Answer:
Step-by-step explanation:
Derive the expected mean squares for a balanced three-stage nested design assuming that A is fixed and that B and C are random. Obtain formulas for estimating the variance components. Assume the restricted form of the mixed model
The expected mean square can be generated in minitab as shown below :
What is expected mean square ?
Expected mean squares in statistics are the predicted values of certain statistics emerging in sums of squares partitions in the analysis of variance. They can be used to determine which statistic belongs in the denominator of an F-test that is being used to test the null hypothesis that a given effect is not there.
Not often, although in some circumstances, perhaps. The average squared departure of observed data values from the sample or population mean is known as variation. The average squared difference between actual and anticipated values is known as MSE (mean squared error).
Te expected mean squares for a balanced three-stage nested design assuming that A is fixed and that B and C are random.
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what's 2+2?
a. fish
b.3
c.4
d.6,472
Im just giving away points to anyone who needs some.
Answer:
what's 2+2?
a. fish
b.3
c.4
d.6,472
Im just giving away points to anyone who needs some.
c.4
Answer: 4
Step-by-step explanation:
2+2=4
Find the slope of the line.
Answer:
ez 2/1
Step-by-step explanation:
i need help Which of the points E , F , G , or H is the center of dilation?
Responses
E
F
G
H
segment EH and segment E'H' both pass through the center of dilation.
Which statement is true about the dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).
In the figure attached, triangle EFG is shown.
H is located at (0, 1)
The center of dilation is located at (0, 2)
Then, H' is located at (0, 0), so that the distance between the center of dilation and H' is twice the distance between the center of dilation and H.
E is located at (0, 5)
Then, E' is located at (0, 8), so that the distance between the center of dilation and E' is twice the distance between the center of dilation and E.
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Chandler buys a pair of tennis shoes for $89.99. If the shoes are discounted 35% and there
is 7.5% sales tax, how much will he pay in total for the shoes?
Total amount he will pay is equal to 62.880 after giving discount of 35% and adding the sales tax of 7.5%.
What is Discount ?Discount is the total price which is deducted from the original terms so as we have to pay less.
Discount is always given on the marked price of the article.
Marked price is the cost at which article is marked.
Chandler buy shoes of $89.99.
Total discount on shoes = 35%
Price after getting Discount = 58.4935
Sales Tax = 7.5 %
Price after sales tax = 58.4935 + 7.5% of 58.4935
= 62.880
So total amount he will pay is equal to 62.880.
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A cone and it’s dimensions are shown in the diagram.Which measurement is closest to the volume of the cone in cubic inches?
Answer:
the volume of the cone is approximately 28.26 cubic inches.
Step-by-step explanation:
To find the volume of a cone, you can use the formula:
V = (1/3) * π * r^2 * h
where V is the volume of the cone, r is the radius of the base of the cone, and h is the height of the cone.
Using the dimensions provided in the diagram, the radius of the base of the cone is 3 inches and the height of the cone is 8 inches. Plugging these values into the formula, we get:
V = (1/3) * π * 3^2 * 8
= (1/3) * 3.14 * 9 * 8
= 28.26 cubic inches
So, the volume of the cone is approximately 28.26 cubic inches.
What is the value of x in the equation
8(x - 3) - 4x = 20?
A
x=−11
B
x=11
C
x=1
D
x=−1
Answer:
x = 11
Step-by-step explanation:
8(x-3) - 4x = 20
8x - 24 - 4x = 20
4x = 44
x = 11
Answer:
x=11
Step-by-step explanation:
8(x-3)-4x=20
8(x)+8(-3)-4x=20
8x-24-4x=20
4x-24=20
+24. +24
4x=44
/x. /x
x=11
Hopes this helps
Decide whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem. Explain.
Answer:
No
Step-by-step explanation:
You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.
HL theoremThe HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.
Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.
__
Additional comment
There is not enough information here to permit the triangles to be declared congruent.
For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.
Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.
When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.
Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t
p
0
4
1
7
2
10
3
13
Show your work here
Enter your answer
Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t. P
0. 4
1 7
2 10
3 13
Show your work here
Enter your answer
The required linear equation that defines the dependent variable, p, in terms of the independent variable, t is p = 3t + 4.
Explain linear equation?A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the slant and b is the y-catch. Sometimes, the above is known as a "straight condition of two factors," where y and x are the factors.
According to question:Let linear equation be p = at + b
Where a and b are constant.
On putting the values from the table,
4 = 0×a + b
b = 4
and,
7 = 1×a + b ⇒ a + b = 7
a + 4 = 7
a = 3
Then,
p = 3t + 4
Thus, required equation is p = 3t + 4.
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19. find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. what is the maximum volume?
A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
Here,
radius=10 cm
r²+h²/4=10²
r²=10²-h²/4
volume=πr²h
=π(10²-h²/4).h
V=π(10²h-h³/4)
dV/dh=π(10²-3h²/4)
dV/dh=0
10²=3h²/4
10²*2²/3=h²
20/√3=h
h=11.55 cm
r²=10²-h²/4
=10²-(10²*2²/3)/4
r²=(100-400/12)
r²=100-33.33
r²=66.67
r=√66.67
r=8.165 cm
volume=πr²h
=3.14*8.165*8.165*11.55
volume=2417.82 cm³
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.
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What is the value of the expression 32.4 ÷ 6?
Group of answer choices
4.4
5.4
6.4
7.4
Answer:
If you divide 32.4 by 6, then you get 5.4 as an answer
how would 5,608,,912,013 be written in word form
Answer:five thousand six hundred eight