Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.
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Find the volume of a cone with a radius of 11.5 inches and a height of 15 inches. Enter the answer in terms of pie
The volume of a cone with diameter 11.5 inches and a height of 15 inches is 519 in³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, A cone with a radius of 11.5 inches and a height of 15 inches.
Now, The diameter is 11.5 inches, hence radius is 11.5/2 = 5.75 inches.
We know the volume of a cone is (1/3)πr²h.
∴ The volume of a cone is = (1/3)×π×(5.75)²×15 inch³.
= 519 in³.
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What is the sum of the series sum from n equals 1 to infinity of negative 3 times three eighths to the n power question mark
Answer:
[tex]\textsf{A)} \quad -\dfrac{9}{5}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given sum:
[tex]\displaystyle \sum^{\infty}_{n=1} -3\left(\dfrac{3}{8}\right)^n[/tex]
Therefore, the first term in the series is:
[tex]a_1=-3\left(\dfrac{3}{8}\right)^1=-\dfrac{9}{8}[/tex]
The common ratio, r, is:
[tex]r=\dfrac{3}{8}[/tex]
Substitute the first term, a, and common ratio, r, into the formula:
[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{1-\frac{3}{8}}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{\frac{5}{8}}[/tex]
[tex]\implies S_{\infty}=-\dfrac{9}{5}[/tex]
Therefore, the sum of the given series is:
[tex]-\dfrac{9}{5}[/tex]The lengths of footlong sub sandwiches at a local sub shop follow an approximately normal distribution with unknown mean
and standard deviation 0.2 inch. If 20% of these sandwiches are shorter than 11.7 inches, find the mean length u.
Mean
inches
(Round to 2 decimal
Answer:
Step-by-step explanation:
18. a. If ΔA B C is rotated 180° about the origin, what are the coordinates of B'
If Δ A B C is to be translated to ΔA'B'C' by the following motion rule:
(x,y)⇒(x-2,y+4)
What will be the coordinates of vertex A'?
a. The coordinates of vertex B is (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
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If ΔA B C is rotated 180° about the origin, the coordinates of B' (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
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The two figures are congruent. Find the measure of the requested side or angle
angle A = 63.7°, B= 26.3°, D= 49° , then angle C = 221
What are congruent shapes?Two shapes that are the same size and the same shape are congruent.Congruent shapes are shapes that are exactly the same.
The corresponding sides are the same and the corresponding angles are the same.
This means the corresponding angles of the two shapes are equal.
With this, angle A = 63.7°, angle B= 26.3° , angle D =49°
The sum of angles in a quadrilateral is 360°
therefore angle C = 360-(63.7+49+26.3)
C = 360-139
C = 221°
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Knowledge Check
The graph below shows the numbers of orders received by a company for five months.
Number of orders
3400
3300-
3200-
3100-
3000-
2900+
2800-
March
April
May
Month
une
(a) What was the greatest number of orders in a month?
orders
(b) When did the number of orders have the greatest
decrease?
July
X
Ś
The Greatest Number of orders were in the month = September
The Numbers of orders increased in month = August to September
What is a graph ?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
According to the given information
From graph
We got to know
In may , orders = 3150
In June , orders = 3050
In July , orders = 2900
In August , orders = 3200
In September , orders = 3250
a) The Greatest Number of orders were in the month = September
b) The Numbers of orders increased in month = August to September
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What is the mean of this data 678,592,652,800,502,396,502,301
Hello,
I hope you and your family are doing well!
To find the mean of a set of numbers, you need to add up all of the numbers and divide the sum by the total number of numbers in the set.
In this case, the mean would be calculated as follows:
(678 + 592 + 652 + 800 + 502 + 396 + 502 + 301) / 8 = 515.25
So the mean of this data set is 515.25.
The mean is a measure of the central tendency of a data set and can be used to represent the entire set of numbers by giving a single value that is representative of the set as a whole. It is also known as the average.
---
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You have one type of candy that sells for $2.00/lb and another type of candy that sells for $8.90/lb. You would like to have 55.2 lbs of a candy mixture that sells for $2.50/lb. How much of each candy will you need to obtain the desired mixture?
You will need ___ lbs of the cheaper candy
and ____ lbs of the expensive candy.
You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.
What is equation of two variables?A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors
According to given information:Let x be number of pounds of cheaper candy and y represent that of expensive candy.
Then, x + y = 55.2----(1)
And
2x + 8.9y = 55.2(2.5) = 138
2x + 8.9y = 138---------(2)
On solving above two equation, we get
x = 51.2
y = 4
Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib
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Which equation best represents a line perpendicular to a line passing through points (–1, 2) and (1, –8)?
Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0
The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be
y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)
y + 8 = -5x + 5
y = - 5x - 3
The equation that best represents a line perpendicular will be y = - 5x - 3.
Here is a system of equations: (3x - y = 17 x+4y =10 .Solve the system by graphing the equations (by hand or using technology).
how do you solve it step by step ?
The graph of the system of equations is shown below, and the solution is: (6, 1).
What is the Solution of a System by Graphing?When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.
In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.
The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.
Both lines intersect at point (6, 1).
Therefore, the solution is (6, 1)
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A rectangle’s width w, height h, and area A are all functions of time t. At the instant when the rectangle’s area is 20 square inches and the width is 4 inches, the height is decreasing at a rate of 3 inches per second while the area is increasing at a rate of 7 square inches per second. Determine the rate of change of the width of the rectangle at that instant.
The rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
What is meant by a rectangle?Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).
A crossed rectangle is a crossed quadrilateral made up of two opposing sides and the two diagonals of a rectangle. It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic, with opposite sides of equal length and equal angles that are not right angles.
We have,
W=width of the rectangle
H=height of the rectangle
A=Area of the rectangle
We know that,
A=W×H
A=20, W=4
20=4×H
H=5 inches
dA/dt=7 (inches)²/sec
dH/dt= -3 inches/sec
dA/dt=W.(dH/dt)+H×dW/dt
dA/dt=4(-3)+5(dW/dt)
7=-12+5(dW/dt)
dW/dt=19/5
dW/dt=3.8 inches/sec
Therefore, the rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
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Given g(x) = 3x + 6, identify the domain, range, and x-intercept of the function. Domain: 3 < x < 6; Range: −6 < y < ∞; x-intercept (2, 0) Domain: 3 < x < 6; Range: −∞ < y < 6; x-intercept (−2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
The linear function g(x) = 3 · x + 6 has the following features:
Domain: - ∞ < x < + ∞
Range: - ∞ < y < + ∞
x-Intercept: (- 2, 0)
How to find the domain, range and x-intercept of a linear function
In this problem we must determine the domain, the range and the x-intercept of a linear function, that is, a polynomial of the form y = m · x + b, where m is the slope and b is the x-intercept. We must find the information by understanding the following features:
The domain of a linear function is all real numbers.The range of a linear function is all real numbers. The y-intercept of the function is the point of the linear function where x = 0.If we know that the function is g(x) = 3 · x + 6, then its domain and range are - ∞ < x < ∞ and - ∞ < y < ∞ and its x-intercept is:
0 = 3 · x + 6
- 3 · x = 6
x = - 2
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Step-by-step explanation:
The given function is g(x) = 3x + 6.
Domain: The domain of a function is the set of all possible input values (x) for which the function is defined. Since the function is a linear equation, it is defined for all real values of x. Therefore, the domain of the function is: Domain: -∞ < x < ∞ Range: The range of a function is the set of all possible output values (y) that the function can produce. The slope of the given function is positive (3), so the function increases without bound as x increases.
Therefore, the range of the function is: Range: -∞ < y < ∞ x-intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. 0 = 3x + 6 -6 = 3x -2 = x Therefore, the x-intercept is (-2, 0).
So, the correct option is: Domain: -∞ < x < ∞; Range: -∞ < y < ∞; x-intercept (-2, 0).
A manufacturing company finds that they can sell 250 items at $3.50 per item and 350 items at $2.50 per item.
If the relationship between the number of items sold a and the price per item p is a linear one:
Find a formula that gives a in terms of p: x =
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell…
items if the price is $1.50.
Answer:
a = 600 -100pa = 450 for p = 1.50Step-by-step explanation:
You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.
SlopeWe can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...
m = ∆a/∆p = 100/(-1) = -100
InterceptThe y-intercept (b) can be found by solving the slope-intercept equation for b:
y = mx +b
b = y - mx
For (x, y) = (3.50, 250), the value of 'b' is ...
b = 250 -(-100)(3.50) = 600
EquationThe slope-intercept equation for 'a' in terms of p is ...
a = -100p +600
Evaluation
The value of 'a' for p = 1.50 is ...
a = -100(1.50) +600
a = 450
They will sell 450 items if the price per item is $1.50.
Determine the probability: There is a 40% chance of rain this weekend.
a. 0.60
b. 0.40
c. 40
d. 4
Answer:
Step-by-step explanation:
help. plsss i dont understand so gimme a answer or something
Hello can someone please help me out? Thank you i will give brainly
Answer:
Area = 28.27 in²
Step-by-step explanation:
Now we have to,
→ find the area of the circle.
Formula we use,
→ π × r²
Now the required area will be,
→ π × r²
→ 3.14 × 3²
→ 3.14 × 9
→ 28.27 in²
Hence, the area is 28.27 in².
how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
We might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.
What are equations?An equation is a claim that shows the equality of two mathematical expressions.
For instance, the equal sign separates the two equations that make up the equation 3x + 5 = 14: 3x + 5 and 14.
So, we need a total of x pounds of mixed nuts.
Peanuts weigh 0.70 pounds in this combo.
Three pounds of peanuts are used to create the 20% mixture, or 0.20*15.
The equation we got: 0.70 x + 3 = 0.40(x + 15)
Now, solve as follows:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, we might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.
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The radius of a cylindrical construction pipe is 2.5. If the pipe is 28ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:V = 550 ft^3
Step-by-step explanation:
The volume of a cylinder is
V = pi r^2 h
We know the radius is 2.5 and the height is 28
V = 3.14 * (2.5)^2 * 28
V =549.5 ft^3
Rounding to the nearest whole number
V = 550 ft^3
solve 6(z-1) + 14 = -40
Answer:
z = -8
Step-by-step explanation:
6(z-1) + 14 = -40
6z - 6 + 14 = -40 Distribute the 6
6z + 8 = -40 Combine Like Terms
6z = -48 Subtract 8 on Both Sides
z = -8 Divide by 6 on Both Sides
Find the values of x and y.
Answer:
x = 30y = 5Step-by-step explanation:
You want to know the values of x and y in the given figure.
Equilateral triangleThe left-side triangle has angles marked as congruent. Hence it is an equilateral triangle, which also has congruent sides.
8y = 40
y = 40/8 = 5
Isosceles triangleThe angle at the middle of the longest line is supplementary to the adjacent angle in the equilateral triangle, hence is 120°.
The marked side length of 40 and the equilateral triangle side length of 40 mean the triangle on the right is an isosceles triangle with an a.pex angle of 120°. Its congruent base angles (x°) must be (180° -120°)/2 = 30°.
x° = 30°
The values of x and y are 30 and 5, respectively.
PLEASE HURRY I NEED TO FINISH MY TEST!!
Determine which integer in the solution set will make the equation true.
8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
A.−4
B.12
C.0
D.3
Answer: x=3
Step-by-step explanation:
When you plug in each number only 3 is the right answer.
A. 8(-4)-4=2(2(-4)+4)
-36=8 False
B. 8(12)-4=2(2(12)+4)
92=56 False
C. 8(0)-4=2(2(0)+4)
-4=8 False
D. 8(3)-4=2(2(3)+4)
20=20 True
A figure was rotated 270° clockwise about the origin.
Which is most likely the new figure?
Answer:
Step-by-step explanation:
It will lie in quadrant 3
Step-by-step explanation:
Here, we want to know where the resulting image will lie after the rotation
After the rotation, it is expected that the resulting image will lie in quadrant 3
First 90 to quadrant 1
second 90 to quadrant 2
Third 90 to quadrant 3
Answer:
B is the correct answer
Step-by-step explanation:
i think:)
If cos (0) = -3.29, what is cos (+0)?
A. -3.29
B. 3.29
C. 73.1°
D. -73.1°
Answer:
A
Step-by-step explanation:
There is no difference between -0 and +0.
So the ans is -3.29 itself.
Describe how the given function can be obtained by transforming the graph of the reciprocal function f(x)=x/1
(Just do letter A ty)
Translate the graph [tex]5[/tex] units right, reflect over the [tex]x[/tex]-axis, and then perform a vertical stretch with a factor of [tex]3[/tex].
simplify 3/7 + 1/7 please answer
Answer:
2/7 ≈0.285714286
Step-by-step explanation: 3/7−1/7
Since 3/7 and 1/7 have the same denominator, subtract them by subtracting their numerators.
3−1 over 7
Subtract 1 from 3 to get 2.
2/7
the Factor
so 2/7 ≈0.285714286
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The maximun value (63) is located at point (1, 2).
Step-by-step explanation:Used method: Graph method from operations research.1. Graph the restrictions.Check attached image 1.
The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.
2. Find all extreme values.In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.
Check attached image 2 to see the extreme values.
Point A is located at: (-3, -2)
Point B is located at: (-3, -4)
Point C is located at: (3, -4)
Point D is located at: (1, 2)
3. Evaluate all extreme points using the given function.Given function: [tex]P=10x+6y+41[/tex]
Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.
Evaluating the points:
[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]
4. Conclude.The maximun value (63) is located at point (1, 2).
Note:There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.
An executive committee consists of 9 members: 5 men and 4 women. 3 members are selected at random to attend a
meeting in Hawaii. The names are drawn from a hat. What is the probability that all 3 selected are men?
Answer:P(3 men) =
Step-by-step explanation:
9. RWS congruent to TUV. Find the values of x and y.
The value of x would be 11° and the value of y would be 6.
What are congruent triangles?
Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.
ΔRWS ≅ ΔTUV
As both triangles are congruent then we can say that
∠S ≅ ∠V
so ∠S = 29°
Now in ΔRWS,
By using the sum of all angles of the triangle property, we can write
∠R +∠W + ∠S = 180°
(8x - 27)° + 90° + 29° = 180°
8x = 180° - 92°
8x = 88°
x = 88/8
x = 11°
Now Side RS ≅ Side TV
3y + 7 = 25
3y = 25 - 7
3y = 18
y = 18/3
y = 6
Hence, the value of x would be 11° and the value of y would be 6.
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Which system of linear inequalities is graphed?
y ≤3x-2
x+ 2y≥4
y≥3x-2
x+2y ≤4
y< 3x-2
x+2y>4
y>3x-2
x+2y <4
The system of linear inequalities is graphed is y≥3x-2; x+2y ≤4. Hence option b is the correct.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The graph consists of two inequalities.
Since the graph lines are solid, thus the inequality sign either "less than or equal" or "greater than or equal".
First find the equation of line.
One line passes through the points (0,2) and (4,0).
The equation of line that passes through the point (a,0) and (0,b) is
x/a + y/b = 1
The equation of the line is x/4 + y/2 =1
(x + 2y)/4 = 1
x + 2y = 4
The equation of the inequality will be either x + 2y ≤ 4 or x + 2y ≥ 4.
Putting x =0 and y = 0 in x + 2y ≤ 4
0 + 0 ≤ 4
0≤ 4 (true)
In the graph (0,0) includes in the shaded region. Therefore the inequality is x + 2y ≤ 4.
The second line passes through the points (0,-2) and (3,7).
If a line passes through the points (x₁, y₁) and (x₂, y₂), then the equation of line is y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
The equation of the line is
y - 7 = (7 + 2)/(3 - 0)(x - 3)
y - 7 = 3x -9
y = 3x - 2
The equation of the inequality will be either y ≥ 3x-2 and y ≤ 3x-2:
Putting x =0 and y = 0 in y ≥ 3x-2
0 ≥ 0-2
0 ≥ -2 true
In the graph (0,0) includes in the shaded region. Therefore the inequality is y ≥ 3x-2.
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download short story a vacation trip roger paré pdf free
To find a book it is necessary to write the name "a vacation trip" in the search engine and add the word PDF to obtain better results.
¿How to download a book from the internet?To download a book from the Internet it is necessary to review various pages since some do not contain the complete book and others may have some type of virus that can damage the device.
In the same way, there are some platforms or applications that require a subscription payment to be able to access the content in an unlimited way.
¡Hope this helped!