Using the washer method, the volume is given by the integral
[tex]\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx[/tex]
where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
[tex]\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}[/tex]
!SUBSTITUTION METHOD!
6y - 5z = -8
3z = -6
4x - 3y - 2z= 21
Answer:
x = 2 y = - 3z = - 2Step-by-step explanation:
6y - 5z = -8 .......... Equation 1
3z = -6 ................... Equation 2
4x - 3y - 2z= 21...... Equation 3
First solve for z in Equation 2
That's
3z = - 6
Divide both sides by 3
z = - 2Next substitute the value of z into Equation 1 in order to find y
We have
6y - 5(-2) = - 8
6y + 10 = - 8
6y = - 8 - 10
6y = - 18
Divide both sides by 6
y = - 3Finally substitute the values of y and z into Equation 3 to find the value of x
That's
4x - 3(-3) - 2(-2) = 21
4x + 9 + 4 = 21
4x + 13 = 21
4x = 21 - 13
4x = 8
Divide both sides by 4
x = 2So the solutions are
x = 2 y = - 3z = - 2Hope this helps you
greatest 2 factors of 90
Answer:
45 & 30
Explanation:
30 x 3 = 90.
45 x 2 = 90.
So the two of these are the answers. Hope it helps!
Answer:
45 and 30
Step-by-step explanation:
here is the question the whole question is in the image
Answer:
The change for the input would be 1, and the change for the output would be 0.35. The rate of change should be 0.35 also.
Step-by-step explanation:
5^(-x)+7=2x+4 This was on plato
Answer:
Below
I hope its not too complicated
[tex]x=\frac{\text{W}_0\left(\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}\right)}{\ln \left(5\right)}+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]5^{\left(-x\right)}+7=2x+4\\\\\mathrm{Prepare}\:5^{\left(-x\right)}+7=2x+4\:\mathrm{for\:Lambert\:form}:\quad 1=\left(2x-3\right)e^{\ln \left(5\right)x}\\\\\mathrm{Rewrite\:the\:equation\:with\:}\\\left(x-\frac{3}{2}\right)\ln \left(5\right)=u\mathrm{\:and\:}x=\frac{u}{\ln \left(5\right)}+\frac{3}{2}\\\\1=\left(2\left(\frac{u}{\ln \left(5\right)}+\frac{3}{2}\right)-3\right)e^{\ln \left(5\right)\left(\frac{u}{\ln \left(5\right)}+\frac{3}{2}\right)}[/tex]
[tex]Simplify\\\\\mathrm{Rewrite}\:1=\frac{2e^{u+\frac{3}{2}\ln \left(5\right)}u}{\ln \left(5\right)}\:\\\\\mathrm{in\:Lambert\:form}:\quad \frac{e^{\frac{2u+3\ln \left(5\right)}{2}}u}{e^{\frac{3\ln \left(5\right)}{2}}}=\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}[/tex]
[tex]\mathrm{Solve\:}\:\frac{e^{\frac{2u+3\ln \left(5\right)}{2}}u}{e^{\frac{3\ln \left(5\right)}{2}}}=\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}:\quad u=\text{W}_0\left(\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}\right)\\\\\mathrm{Substitute\:back}\:u=\left(x-\frac{3}{2}\right)\ln \left(5\right),\:\mathrm{solve\:for}\:x[/tex]
[tex]\mathrm{Solve\:}\:\left(x-\frac{3}{2}\right)\ln \left(5\right)=\text{W}_0\left(\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}\right):\\\quad x=\frac{\text{W}_0\left(\frac{\ln \left(5\right)}{2e^{\frac{3\ln \left(5\right)}{2}}}\right)}{\ln \left(5\right)}+\frac{3}{2}[/tex]
What is the mean of 6,3,2,1,9,9
Answer:
[tex]\boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}[/tex]
Step-by-step explanation:
Given data : 6 , 3 , 2 , 1 , 9 , 9
Σfx = 6 + 3 + 2 + 1 + 9 + 9 = 30
N ( total number of observation ) = 6
Finding the mean
[tex] \boxed{ \sf{mean = \frac{Σfx}{N} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = \frac{30}{6} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = 5}}[/tex]
Hope I helped!
Best regards! :D
pizza house offers 2 different salads, 7 different kinds of pizza, and 5 different desserts. how many different three- course meals can be ordered
Answer:
70
Step-by-step explanation: To get the answer to these types of questions, you multiply all three numbers together.
Explain how rays AB and AC form both a line and an angle.
A line with points C, A, B has arrows for endpoints.
Answer:
An angle is defined as two rays with a common endpoint, so CAB (or BAC) is an angle. A line is described as an infinite set of points that extend forever in either direction, which these rays also do.
Step-by-step explanation:
Angles are rays with a shared endpoint.
Lines extend forever in either direction.
Rays AB and AC extend forever in either direction.
A line with points C, A, and B with arrows at the endpoints can satisfy the fact that the two rays AB and AC form both a line and an angle.
A line with points C, A, and B have arrows on both endpoints.
We need to explain how the line containing the points C, A, and B has two rays AB and AC and how it can form both a line and an angle.
What are a line, ray, and angle?A line has no endpoints, it extends infinitely in both directions and both end point is denoted by an arrow.
A ray has a fixed point on one side and an arrow on the other side which extends infinitely.
An angle is formed by two rays from one common fixed point.
Let us draw the line with points C, A, and B that have arrows at the endpoints.
C A B
<----------------.-------------------->
We can say that AB is a ray since at point A we have a fixed point and at point B there is an arrow.
And AC is also a ray since at point A there is a fixed point and at point C there is an arrow.
The two rays AB and AC together form a line because on both ends sides there are arrows.
An angle can also be formed since AB and AC are two rays from one common fixed point.
Thus a line with points C, A, and B with arrows at the endpoints can satisfy the idea that the two rays AB and AC form both a line and an angle.
Learn more about line, rays, and angle here:
https://brainly.com/question/12040861
#SPJ5
Jorge walks to his friends house he walks 750 m north then realizes he walked too far he turns around and walks 250 m south the entire walk take some 600 seconds what is the speed per second
Answer:
1.67 m/s
Step-by-step explanation:
Speed = Distance/TimeJorge walks in total:
750 m + 250 m = 1000 mI takes him:
600 secondsHis speed is:
1000 m /600 s ≈ 1.67 m/s- 1/3 + 4/5
Minus not negative sign
Answer:
7/15
Step-by-step explanation:
What are the next two terms in this sentence? 5, 10, 20, 40
Answer:
80, 160
Step-by-step explanation:
It's just multiplying the last term by 2.
Answer:
80 and 160
Step-by-step explanation:
5 × 2 = 10
10 × 2 = 20
20 × 2 = 40
40 × 2 = 80
80 × 2 = 160
Hope it helps!
How much work is done when a hoist lifts a 200-kg rock to a height of 3 m?
Answer:
5880 joulesStep-by-step explanation:
Given data
mass of rock, m= 200 kg
height/distance = 3 m
Now we know that the expression for work done is
w= force* distance
and also we need to find the force exerted by mass of rock
F= mg
Substituting our data and solving for force we have (assuming g= 9.81 m/s^2)
Force= 200*9.81
Force= 1962 N
Now we can find the work done
work done= 1962*3
work done= 5880 joules
The work done should be 5880 joules
Calculation of the work done:Since there is the mass of the rock is 200 kg
And, the height is 3 m
Now we know that
work done = force (distance)
Also,
F= mg
= 200(9.81)
= 1962 N
Now the work done is
= 1962(3)
= 5880 joules
Hence, The work done should be 5880 joules
Learn more about work here: https://brainly.com/question/24610764
PLEASE HELP ME I REALLY NEES HELP
Changes of State
Gas
B
Temperature
Solid
Liquid
A
Thermal Energy
4. Suppose the material is being heated.
a. What change of state is represented by line segment A?
b. What is happening to the average kinetic energy of the particles during the
change of state represented by line segment B? Explain.
c. What physical property does the temperature at point B represent? If the
liquid is kept at this temperature what state of matter will be observed?
Explain your answer.
Answer:
Please find the answer in the explanation
Step-by-step explanation:
Suppose the material is being heated.
a. What change of state is represented by line segment A?
The solid changes to liquid state. The change of state is Melting.
b. What is happening to the average kinetic energy of the particles during the change of state represented by line segment B? The average kinetic energy of the particle increases as the heat is applied but remains constant during the change of state.
c. What physical property does the temperature at point B represent?
Vapourisation.
If the liquid is kept at this temperature what state of matter will be observed?
If the temperature persists, the state of matter that will be observed will be gas. Because the liquid must have turned out to vapour.
Four water tanks can hold a total of 432.4 gallons of water. On average, how much water can one tank hold? How much water is in a tank that is half-full? One tank can hold an average of gallons of water. A half-full tank will hold gallons of water.
Answer:
one tank can hold 108.1 gallons. half full is 54.05
Step-by-step explanation:
Answer:
54.05 gallons
Step-by-step explanation:
432.4÷4= 108.1108.1÷2= 54.05I will give brainliest Blue whales eat an average of 5,000 pounds of fish daily, with a standard deviation of 850 pounds. Approximately what percentage of blue whales eat more than 7,550 pounds of fish?
(7,550 - 5,000) / 850 = 3 standard deviations.
The percentage could vary depending on the bell curve diagram your professor uses. I was taught that anything more than 3 standard deviations is 0.15%. So, only about 0.15% of blue whales eat more than 7,550lbs of fish.
Answer:
the answer is 0.15 percent, give the person above me brainlyest for helping!
Step-by-step explanation:
Vincent mows 8 lawns in 2 hours. How many lawns are mowed in 5 hours?
Work Shown:
8 lawns = 2 hours
4 lawns = 1 hour (divide both sides by 2)
20 lawns = 5 hours (multiply both sides by 5)
Answer: 20 Lawns
If he mows 8 lawns in a span of 2 hours that means he mows 4 lawns in 1 hour. 4 * 5 is 20
Mari,Carlos, and Amanda all collect stamps. Carlos has five more stamps then Mari, and Amanda has three times as many stamps as Carlos. Altogether, they have 100 stamps. Find the number of stamps each person has. Write a verbal description of the basic situation.
Which graph shows the solution of the system of equations?
5 numbers that create the mean of 9
Answer:
9,9,9,9,9
Step-by-step explanation:
Let the five unknown numbers be x
= [tex]\frac{x+x+x+x+x}{5} = 9[/tex]
Simplify
[tex]\frac{5x}{5} = \frac{9}{1}[/tex]
Cross-cancel common factor ; 5
[tex]5x\div 5 = x\\\\x = \frac{9}{1} \\\\x = 9[/tex]
Help i dont understand Pls help :(
Answer:
x = 1?
Step-by-step explanation:
I think functions are basically just variables but extra so they both act the same. I'm not 100% sure but I Think
if f(x) = -5x + 1 when f(x) = 6,
replace f(x) with 6 so,
6 = 5x + 1
1 - 6 = 5x + 1 - 1
(subtract one on both sides to isolate the variable)
5 = 5x
5/5 = 5x/5
(to Actually isolate the variable lol
1 = x or x = 1
I believe is the answer? please comment if I'm wrong
*I WAS TOLD MY THOUGHT PROCESS IS WRONG ANYONE WHO SEES THIS PLEASE DISREGARD
Can you simplify this algebraic expression? Type your answer below!
(2x-4) - (6x +6)
Answer:
-4x -10
Step-by-step explanation:
remove paranthese: 2x−4−6x−6
collect like terms: (2x−6x)+(−4−6)
−4x−10
The simplified Algebraic Expression of (2x-4) - (6x +6) is -4x - 10.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
(2x-4) - (6x +6)
Now, solving the above expression
= (2x-4) - (6x +6)
= 2x - 4 - 6x - 6
Combining the like terms
= (2x- 6x) + (-4-6)
= -4x - 10
Hence, the simplified expression is -4x-10.
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ3
a rectangular prism is 5 meters long, 2 meters wide, and 2 meters high. what is the sureface area of this prism in square inches?
Answer:
20 square inches
How do I solve this problem
Answer:
2.9309
Step-by-step explanation:
2.9309 is the answer
(edited) Yo please help its a timed..
Determine whether each function is even, odd, or neither. f(x)= x/ x^2-1
Answer:
it is odd
Step-by-step explanation:
Answer:
Neither I d k just t b h I kinda forgot lol
Step-by-step explanation:
Which of the following scenarios exhibits a function relation? Take the first set listed to be the domain of the relation.
Answer:
-the set of people with Social Security cards and the set of Social Security numbers
Explanation:
There's literally no relation between the height of a tree and the number of trees in a forest that can be clearly seen. Same goes to models and people in a certain town. Birthdays and Students in Class definitely have no correlation as isolated pieces of information. The number of people with social security numbers and the amount of numbers in a SS Card, though, have a direct relation, since the number has to be large so the amount of people that need such a number can have unique numeric representations of their Social Security.
John has 66 socks, all in pairs. He has 1 more pair of white socks than black socks. How many individual socks of each color does he have?
Answer:
Black socks 35
White socks 31
Step-by-step explanation:
What is 45 divided by 8.0
Answer:
answer is 5.625
hope it helps
5.625
40/5=5
5/8=0.625
what is the answer to -5( 8g + -4 )
Answer:
-40g+20
Step-by-step explanation:
-5(8g-4)
-40g+20
3
Liz makes footprints in the snow with her boots that are
foot long. Liz's feet are only
2
3
foot long.
What expression can be used to find out how much longer Liz's boot prints are than her feet?
Answer:
See Explanation
Step-by-step explanation:
The question has missing details; However, the following explanation will guide.
Represent the boots print with y and the Liz's feet with x
To calculate how much the boot is longer than her feet, we simply get the difference between the length of the boot's print and her feet;
i.e.
[tex]Difference = y - x[/tex]
Note that her boot print (y) will always be greater than her feet (x)
Take for instance;
[tex]y = 3\ ft[/tex]
[tex]x = 2\ ft[/tex]
The difference will be
[tex]Difference = 3ft - 2ft[/tex]
[tex]Difference = 1ft[/tex]
PLEASE HELP QUICKLY!!!
Answer:
Option (2)
Step-by-step explanation:
We have to arrange the given numbers in the order from least to greatest.
Numbers are [tex]\sqrt{64},8\frac{1}{7},8.1414..., \frac{15}{2}[/tex]
1). [tex]\sqrt{64}=8[/tex]
2). [tex]8\frac{1}{7}=\frac{57}{7}=8.143[/tex]
3). 8.1414....
4). [tex]\frac{15}{2}=7.5[/tex]
Therefore, increasing order of the numbers will be,
[tex]8.143>8.1414>8>7.5[/tex]
[tex]8\frac{1}{7}>8.1414...>8>7.5[/tex]
Option (2) will be the correct option.
The sum of −4n and 5n is −82
Hey there! I'm happy to help!
The sum of -4n and 5n.
-4n+5n
is
=
-82
-4n+5n=-82
This simplifies to n=-82.
Have a wonderful day! :D