Find the area of the surface generated by revolving the given curve about the y-axis. x= V25 - y2, -3 Sy S3 - Surface Area =
Answers
The area of the surface generated by revolving the curve about the y-axis is 60π sq. units.
What is the area of the surface generated?The area of the surface generated is calculated by applying the following formula as shown below;
S = 2π ∫[a,b] x(y) √(1 + (dx/dy)²) dy,
The equation of the curve is given as;
x = √(25 - y²)
The boundary is -3 ≤ y ≤ 3.
The derivative of the function;
dx/dy = (d/dy) √(25 - y²)
dx/dy = (-1/2)(25 - y²)^(-1/2)(-2y)
dx/dy = y / √(25 - y²).
The surface area is calculated as follows;
\(S = 2\pi \int\limits^3_{-3} {\sqrt{(25 - y^2)}\sqrt{1+\frac{y}{25 - y^2} } }\ dy\)
\(S = 2\pi \int\limits^3_{-3} {\sqrt{(25 - y^2)}\sqrt{\frac{25 - y^2 + y^2}{25 - y^2} } }\ dy\\\\S = 2\pi \int\limits^3_{-3} {\sqrt{(25 - y^2)}\sqrt{\frac{25}{25 - y^2} } }\ dy\\\\S = 2\pi \int\limits^3_{-3} {\sqrt{25 }\ dy\)
The integral is determined as;
\(S = 2\pi (5) \int\limits^3_{-3} \ dy\\\\S = 2\pi (5) [ y]^3_{-3} \\\\S = 10\pi [ y]^3_{-3}\)
Simplify further and the area becomes;
S = 10π [y] from -3 to 3
S = 10π (3 - (-3))
S = 10π (6)
S = 60π.
Learn more about area of curve here: https://brainly.com/question/15122151
#SPJ4
Related Questions
does anyone mind helpin me with this issue
Answers
Answer:
5
Step-by-step explanation:
QR / PS = QP / SR
2x + 3 / 4x - 7 = 7 / 7
2x + 3 / 4x - 7 = 1
2x + 3 = 4x - 7
4x - 2x = 3 + 7
2x = 10
x = 10 / 2
x = 5
Which equation best represents c, the total amount Mr. Thomas should be charged
for driving m miles?
Answers
Answer:
c = 0.15m + 45
Step-by-step explanation:
Generally, we have the equation of a straight line as;
y = mx + b
where m is the slope and b is the y-intercept
To get the value of m, we can use the slope equation
m = (y2-y1)/(x2-x1)
Let us select two points to use from the table
we have;
(40,51) and (20,48)
So substituting these values;
m = (48-51)/(20-40) = 0.15
So we have the partially completed equation as;
y = 0.15x + b
To get the value of b, we use any of the points
Using the last, we have
51 = 0.15(40) + b
b = 45
So we have the complete equation as;
y = 0.15x + 45
using the terms in the question, we have;
c = 0.15m + 45
In which interval does a root exist for this equation? tan(x) = 3x^2
PLEASE HELP
Answers
To determine the interval for which a root exists, you can use the intermediate value theorem.
First, observe that the left-hand side of the equation, tan(x), is undefined for x = (n + 1/2) π, where n is an integer. Thus, we can restrict our attention to the interval (-π/2, π/2) where the tangent function is continuous and strictly increasing.
Next, note that tan(0) = 0 and tan(π/6) = 1/√3 < 3/36 = 1/12. Also, as x approaches π/2 from the left, tan(x) approaches infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (0, π/6).
Similarly, tan(-π/6) = -1/√3 > -1/12, and as x approaches -π/2 from the right, tan(x) approaches negative infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (-π/6, 0).
Therefore, the equation tan(x) = 3x^2 has at least one root in the interval (-π/6, π/6).
Name the property of real numbers illustrated by each equation.
21+19.7-19.7=21
Answers
The property of real numbers illustrated by the equation 21 + 19.7 - 19.7 = 21 is the additive identity property.
The additive identity property states that the sum of any number and zero is equal to the original number. In the given equation, the number 21 is added to 19.7 and then subtracted by 19.7. The result is equal to 21, which is the original number.
In this case, the number 0 acts as the additive identity. When we add or subtract zero to any number, it doesn't change the value of the original number. So, in the equation, the subtraction of 19.7 and addition of 19.7 cancel each other out, leaving the original number 21.
Thus, the equation 21 + 19.7 - 19.7 = 21 illustrates the additive identity property, showing that adding or subtracting zero does not change the value of a number.
Learn more about additive identity property here:
https://brainly.com/question/23172909
#SPJ11
Aship leaves port on a bearing of 34 0 and travels 13,5 mi. The ship then turns due east and travels 3.7 mi. How tar is the ship from port, and what is its bearing from port?
Answers
The ship is approximately 14.879 miles away from the port, and its bearing from the port is approximately 26.35°.
To find the exact values of the ship's distance from the port and its bearing from the port, we can perform the necessary calculations.
Ship's movement on a bearing of 34.0°:
Horizontal component = 13.5 mi * cos(34.0°) ≈ 11.1764 mi
Vertical component = 13.5 mi * sin(34.0°) ≈ 7.3564 mi
Ship's movement due east:
Horizontal component = 3.7 mi
Vertical component = 0
Vector addition:
Horizontal displacement = 11.1764 mi + 3.7 mi ≈ 14.8764 mi
Vertical displacement = 7.3564 mi + 0 ≈ 7.3564 mi
Distance from the port:
Distance = √(Horizontal displacement² + Vertical displacement²)
= √(14.8764 mi² + 7.3564 mi²)
≈ √(221.142 m²)
≈ 14.879 mi
Bearing from the port:
Bearing = arctan(Vertical displacement / Horizontal displacement)
= arctan(7.3564 mi / 14.8764 mi)
≈ 0.4601 rad (in radians)
≈ 26.35° (in degrees)
The ship is approximately 14.879 miles away from the port. The ship's bearing from the port is approximately 26.35°.
To know more about distance:
https://brainly.com/question/15256256
#SPJ4
--The given question is incomplete, the complete question is given below " Aship leaves port on a bearing of 34.0° and travels 13.5 mi. The ship then turns due east and travels 3.7 mi. How tar is the ship from port, and what is its bearing from port?"--
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
Answers
Answer: I hope it helps :)
x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13Step-by-step explanation:
1.
\(Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}\)
2.
\(Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23\)
3.
\(Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6\)
4.
\(Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}\)
5.
\(Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y\)
The 4-It wall shown here slands 28 ft from the building. Find the length of the shortest straight bearn that will reach to the side of the building from the ground outside the wall. Bcom 2 Building 1'
Answers
The length of the shortest straight is approximately 28.01 ft.
What is the right triangle?
A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".
To find the length of the shortest straight beam,we can use the Pythagorean theorem.
Let's denote the length of the beam as L and a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.
Using the Pythagorean theorem,
\(L^2 = (28 ft)^2 + (1 ft)^2\)
Simplifying the equation:
\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)
\(L = \sqrt{785}ft\)
Calculating the value of L:
L ≈ 28.01 ft
Therefore, the length of the shortest straight beam is approximately 28.01 ft.
To learn more about the right trianglefrom the given link
brainly.com/question/29869536
#SPJ4
A compressive load of 80,000 lb is applied to a bar with
circular section0.75indiameter and a length of 10 in. if the
modulus of elasticity of the bar material is10,000 ksi and the
Poisson’s ratio i
Answers
The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.
A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.
if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.
We have to determine the decrease in diameter of the bar due to the applied load.
Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.
Length of the bar, L = 10 in
Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²
Stress produced by the applied load,σ = P/A
= 80,000/0.4418
= 181163.5 psi
Young's modulus of elasticity, E = 10,000 ksi
Poisson's ratio, ν = 0.3
The longitudinal strain produced in the bar, ɛ = σ/E
= 181163.5/10,000,000
= 0.01811635
The lateral strain produced in the bar, υ = νɛ
= 0.3 × 0.01811635
= 0.005434905'
The decrease in diameter of the bar due to the applied load, ∆d/d = -υ
= -0.005434905∆d
= -0.005434905d
The final diameter of the bar,
d - ∆d = d + 0.005434905d
= 1.005434905d
To know more about ratio visit:
https://brainly.com/question/13419413
#SPJ11
find the quotient 5/6 divided by 2
Answers
Answer:
0.41666666666
Step-by-step explanation:
I used a calculator.
= 5/6 x 1/2
= 5/12
GAMES Darius is playing a bowling game where he rolls balls into a 10-point hole or a 25-point hole. He rolls a total of 11 balls, and his score is 215 points. Write a system of equations to represent the information and use substitution to determine how many balls Darius rolled into each hole.
Answers
By solving the system of equations, we found that the number of balls rolled in 10 point hole is 4 and the number of balls rolled in 25 point hole is 7.
What is meant by the system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions of systems of equations.
Given,
Total number of balls rolled = 11
Total points scored = 215
Let the number of 10-point balls rolled by Darius be x and the number of 25-point balls rolled be y.
We can now write a system of equations, using the given information.
x + y = 11
10x + 25y = 215
On solving this system of equations, we can find the values of x and y.
Multiply the first equation by 10.
10x + 10y = 110
10x + 25y = 215
Now subtract the equations.
-15y = -105
y = 7
Now find x by substituting y in any equation.
x + y = 11
x + 7 = 11
x = 4
Therefore by solving the system of equations, we found that the number of balls rolled in 10 point hole is 4 and the number of balls rolled in 25 point hole is 7.
To learn more about the system of equations, follow the link.
brainly.com/question/13729904
#SPJ1
In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 48. 2 feet away from the base of the tower. The angle of elevation of the zip line is 33°. Estimate the length of the zip line to the nearest tenth of a foot
Answers
The estimated length of the zip line is 62.8 feet.
The length of a zip line can be estimated using the formula for the length of a side of a right triangle, which is the square root of the sum of the squares of the two shorter sides. In the case of the obstacle course, the two shorter sides are the height of the tower and the horizontal distance from the base of the tower to the point on the ground.
To calculate the length of the zip line, we first need to calculate the height of the tower. The angle of elevation of the zip line is 33°, so we can use trigonometry and the Law of Sines to calculate the height of the tower. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of the triangle. Since we know the angle of elevation (33°) and the horizontal distance (48.2 feet), we can calculate the height of the tower using the formula:
h = (48.2 * sin(33°)) / sin(90°)
h = 42.7 feet
Now we can calculate the length of the zip line using the formula for the length of a side of a right triangle:
\(L = sqrt(h^2 + d^2)L = sqrt(42.7^2 + 48.2^2)L = 62.8 feet\)
Rounding to the nearest tenth of a foot, the length of the zip line is 62.8 feet.
Learn more about trigonometry here:
https://brainly.com/question/22986150
#SPJ4
How many hours is a 7am to 3pm shift?
Answers
Answer:
8 hours shift because you count from 7 am to 3pm
The total number of hours between the 7 am and 3 pm shift is 8 hours.
What is meant by the hour?
Depending on the speed of the Earth's rotation, an hour is a measure of time that is traditionally calculated as 1/24 of a day and scientifically estimated to last between 3,599 and 3,601 seconds. There are 24 hours in a day and 60 minutes in an hour.
The 24-hour day is divided into two sections, a.m. and p.m., according to the 12-hour clock time convention. Latin terminology for the hours of the day, AM and PM, are commonly employed. The abbreviations AM and PM stand for Ante meridiem and Post meridiem, respectively, which indicate before noon or midday and afternoon or midday. AM is used to denote the first 12-hour period, which runs from midnight to noon, and PM is used to denote the following 12-hour period, which runs from noon to midnight.
From 7 am to 12 pm, the number of hours = 5
From 12 pm to 3 pm, the number of hours = 3
Therefore the total number of hours between the 7 am and 3 pm shift is (3+5) = 8 hours.
To learn more about hours, follow the link.
https://brainly.com/question/291457
#SPJ4
geometry it's about relations within triangles. need help solving for variables
Answers
Answer:
`18. x=9
19. x=4
20. x=25,5
21. x=3
22. x=3,5
23. x=10
Step-by-step explanation:
Decorative pots for flowers in the shape of a regular four-sided prism with external dimensions a = 18 cm. h = 16 cm are made of concrete. The thickness of the walls is 3 cm. How many m³ of concrete is needed to make 80 of such pots, if 5% more concrete should be counted due to waste?
Answers
The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.
Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³
for more such question on cubic meters
https://brainly.com/question/30106291
#SPJ8
please HELP!!! GUYS
the homework is due tom
Answers
Answer:
A(-4.5;2) B(0;-3.5).......
help me please urgent
Answers
Answer:
3+ x • {2x} + 5 = 858
Step-by-step explanation:
<33 hoped this helped !!!
In isosceles ABC, AC is the base, Points D. Band
Fare the midpoints of AB. A and BC
respectively. The length of BD is 13 inches and
ZBFD 65. Find each measure
a. A
b. DE
G. AD
d. M EDF
Answers
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
The measure of each of the following are as follows :
the measure of A = 115 degree.
the measure of DE = √338/4.
the measure of AD = √338/2.
the measure of DEF = 57.5 degrees.
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
To know more about the triangles on brainly : brainly.com/question/9265928
#SPJ4
b) Write 36 as a product of its prime factors.
Write the factors in order, from smallest to largest.
Answers
Answer:2*2*3*3
Step-by-step explanation:
Marco needs to buy some cat food At the nearest store, 3 bags of cat food cost $16.50. How muc
would Marco spend on 5 bags of cat food?
Answers
what is 76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 eqaul to
Answers
Answer:
76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 is a very large number and its exact value is not possible to calculate by hand or with common calculators. However, it can be calculated using a computer with advanced mathematical software.
Step-by-step explanation:
Now you're going to imagine that you invested $1,000 in a company one year ago, and you want to see how well your investment would be doing today.
To begin, choose a company that you're familiar with and that seems as if it might be a good investment - that is, a company that you think will have rising stock prices. Think about companies that you use or know are popular Remember, not all companies are public companies. You'll need to check the New York Stock Exchange to find out if you can actually buy shares in this company Once you've settled on a company, find its stock price from one year ago and for today Write a journal entry about your imagined investment Answer the following questions as you write
1.) What stock did you buy?
2.) Why did you think buying this stock would be a good idea?
3.) How much would you have made or lost on an investment of $1,000?
(Hint First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today Compare that to your initial investment of $1,000)
4.) Could you have made more money by selling sooner?
Answers
Answer:
Step-by-step explanation:
1. What stock did you buy?
Apple Inc.
2. Why did you think buying this stock would be a good idea?
Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.
3. How much would you have made or lost on an investment of $1,000?
I would have made $105.
Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.
4. Could you have made more money by selling sooner?
Yes, on October 3, 2018 it was at its peak for the year.
your investment would be doing great today. you would make $115 from the given investment.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Given, you're going to imagine that you invested $1,000 in a company one year ago
I will buy the stocks of amazon.The popularity of Amazon products is rising daily. The business frequently introduces cutting-edge technology. I was confident that it would be a secure investment.I would have made $115.Hint: To start, divide $1,000 by the stock's current price, one year ago, to see how many shares you might have purchased. It can be necessary to infer the stock price from the graph. The number of shares should be rounded up to the next whole number. Then, multiply the number of shares you purchased by the stock's current price to determine the share's current worth. Contrast that with your $1,000 original investment.on September 5, 2022, it was at its peak for the year.Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.
Learn more about stocks here:
https://brainly.com/question/3210355
#SPJ1
Find the volume of the prism
Answers
The first prisms volume is 2.4 and the second prisms volume is 200
Step-by-step explanation:
Volume is length x width x height so it’d be
2 x 1 x 1.2 which equals 2.4
And the second one is
10 x 4 x 5 which equals 200
What is the volume of this figure?
12 m
3 m
4 m
3 m
2 m
9 m
Help pls
Answers
The volume of the cube is 144 cubic units.
To calculate the volume of a cube, we need to know the length of one side, as all sides of a cube are equal. In this case, the given length of the cube is 12 units.
The formula for finding the volume of a cube is:
Volume = side × side × side
or
Volume = length × width × height
Since all sides of a cube are equal, we can use any of the given dimensions (length, width, or height) as the side length. Let's use the length as the side length.
Volume = 12 × 4 × 3
Simplifying the calculation, we have:
Volume = 144 cubic units
Therefore, the volume of the given cube, with a length of 12 units, a width of 4 units, and a height of 3 units, is 144 cubic units.
To know more about volume here
https://brainly.com/question/11168779
#SPJ4
please help due todayyy://
Answers
Answer:
B. product graph
Step-by-step explanation:
Hope it helps
CarryOnLearning
38. connect these ordered pairs: (1,5), (0,4), (1,3), (2,3), (3,4), and (2,5). what shape do you end up with?
Answers
By plotting the ordered pairs and joining them, the figure obtained is a hexagon.
We are given the ordered pairs as:
(1, 5), (0, 4), (1, 3), (2, 3), (3, 4), and (2, 5).
Ordered pairs are the pairs that are written in the form:
(x, y)
where x is the abscissa and y is the ordinate of the points.
We will first plot these ordered pairs on a graph.
Now we will join the points.
We can see that the figure that is being obtained is a hexagon as it has six sides.
Therefore, we get that, by plotting the ordered pairs and joining them, the figure obtained is a hexagon.
Learn more about ordered pairs here:
https://brainly.com/question/1528681
#SPJ4
find the volume of the solid generated in the following situation. the region r bounded by the graphs of x=0, y=2x, and y=2 is revolved about the line
Answers
The final equation would be: ∫[0,2] π(y²/4) dyπ/4 ∫[0,2] y² dyπ/4 × [y³/3] [0,2]π/4 × (8/3)π/6π/2
The volume of the solid generated in the given situation is π/2 cubic units.
The situation states that the region r bounded by the graphs of x=0, y=2x, and y=2 is revolved around the line.
We need to determine the volume of the solid generated.
We can find the volume by using the disk method.
The equation of the line is x=0. We will have to integrate concerning y. It can be observed that the region r is bound between the lines y = 0 and
y = 2.
We will integrate the area of the disks along the line of revolution (x = 0). The area of each disk is given by A=πr² where "r" is the radius of the disk. For the given situation,
the radius is x = y/2.
Substituting the value of the radius, the equation becomes (y/2)²A=π(y²/4)
The limits of integration are y = 0 and
y = 2.
We will substitute these limits in the above equation and integrate them. The final equation would be:
∫[0,2] π(y²/4) dyπ/4 ∫[0,2] y² dyπ/4 × [y³/3] [0,2]π/4 × (8/3)π/6π/2
The volume of the solid generated in the given situation is π/2 cubic units.
Given that, the region r bounded by the graphs of x=0,
y=2x, and
y=2 revolved around the line.
The given region r is shown below: graph{y=2x [-5, 5, -2.5, 2.5]}graph{y=2 [-5, 5, -2.5, 2.5]}graph{x=0 [-5, 5, -2.5, 2.5]}
The axis of revolution is x=0. For the given situation, we use the disk method to determine the volume of the solid generated. The equation of the line is x=0. We will have to integrate concerning y. It can be observed that the region r is bound between the lines y = 0 and
y = 2.
We will integrate the area of the disks along the line of revolution (x = 0).
The area of each disk is given by A=πr² where "r" is the radius of the disk.
For the given situation, the radius is x = y/2.
The limits of integration are y = 0 and
y = 2.
We will substitute these limits in the above equation and integrate them.
To know more about volume visit:
https://brainly.com/question/13338592
#SPJ11
The Second Statement is the ____ of the first.
Answers
Answer:
inverse because if your switching the order up it would be inverse
Step-by-step explanation:
Ben bowled 151 and 183 in his first two games. What must he bowl in his third game to have an average of at least 1702
Answers
Answer:
1368
Step-by-step explanation:
let 3rd game be x
151+183+x=1702
334+x=1702
x=1702-334
x=1368
Q1: Use simple exponential smoothing with a = 0.75 to forecast the water pumps sales for February through May. Assume that the forecast for January was for 25 units. [4 marks) Month January February March April Air-condition sales 28 72 98 126
Answers
Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units, March: 37.63 units, April: 72.66 units.
To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month Actual Sales Forecast
-------------------------------------
January 28 25
February 72 26.5
March 98 37.63
April 126 72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.
To know more about the function visit :
https://brainly.com/question/11624077
#SPJ11
Apply the distributive property to create an equivalent expression. ( 1 -2g +4h)\cdot 5 =(1−2g+4h)⋅5=left parenthesis, 1, minus, 2, g, plus, 4, h, right parenthesis, dot, 5, equals
Answers
Answer:
5 - 10g + 20hStep-by-step explanation:
Given three elements A, B and C related together according to the expression A(B+C), according to distributive property, the element A will be distributed to the rest of the element as shown;
A(B+C) = A(B)+A(C)
A(B+C) = AB + AC (Law of distributivity)
Given the expression according to the question (1−2g+4h)⋅5, in order to use the distributive law to find the equivalent expression, we will use the concept above as shown;
= (1−2g+4h)⋅5
= 5.(1−2g+4h)
= 5(1)-5(2g)+5(4h)
= 5 - 10g + 20h
Hence the equivalent expression using the distributive property is 5 - 10g + 20h
Answer:
5 - 10g + 20h