Answer:
the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
[tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
Step-by-step explanation:
Given the data in the question;
y = [tex]y = e^{(x - 1 )[/tex], y = 0, x = 1, x = 2.
Now, using the integration capabilities of a graphing utility
y = [tex]y = e_2}^{(x - 1 )_[/tex], y = 0
Volume = [tex]\pi \int\limits^2_1 ( e^{x-1)^2} - (0)^2 dx[/tex]
Volume = [tex]\pi \int\limits^2_1 ( e^{x-1)^2 dx[/tex]
Volume = [tex]\pi \int\limits^2_1 e^{2x-2}dx[/tex]
Volume = [tex]\frac{\pi }{e^2} \int\limits^2_1 e^{2x}dx[/tex]
Volume = [tex]\frac{\pi }{e^2} [\frac{e^{2x}}{2}]^2_1[/tex]
Volume = [tex]\frac{\pi }{2e^2} [e^4 - e^2 ][/tex]
Volume = [tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
[tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
what is the equation of a line that passes through 2,-3 with a slope of 2/3
Answer:
y=2/3x-13/3
Step-by-step explanation:
this is the equation
GIVING 50 POINTS IF YOU ANSWER!!!!
Answer:
MAD would be more similar than mean
Step-by-step explanation:
Without doing any calculations, I assumed that the average value for each neighbor is different since their dot plots surround different areas. The MAD is the mean absolute deviation where it shows how distributed are the dot plots compared to the average value. In this case, I can tell that both neighborhoods having a very similar distribution of dot plots relative to their average/mean. Hope this helps!
The sum of two angle measures is supplementary. The measure of the first angle is
123∘.
What is the measure of the second angle?
Select one:
57∘
67∘
47∘
37∘
The volume of wood in a tree varies jointly as the height of the tree and the
square of the distance around the tree trunk. If the volume of wood is 15.84 cubic
feet when the height is 22 feet and the distance around the trunk is 3 feet, what is
the volume of wood obtained from a tree that is 32 feet tall having a measurement
of 4 feet around the trunk?
please help :))
Answer:
The volume is 40.96 cubic feet
Step-by-step explanation:
Given
[tex]V\ \alpha\ h * d^2[/tex]
Where
[tex]V = Volume\\ h = height\\ d = distance[/tex]
[tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]
Required
The volume when h = 32 and d = 4
[tex]V\ \alpha\ h * d^2[/tex]
Express as an equation
[tex]V = khd^2[/tex]
Where k is the constant of variation.
Make k the subject
[tex]k = \frac{V}{hd^2}[/tex]
Substitute [tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]
[tex]k = \frac{15.84}{22 * 3^2}[/tex]
[tex]k = \frac{15.84}{22 * 9}[/tex]
[tex]k = \frac{15.84}{198}[/tex]
[tex]k = 0.08[/tex]
To solve for V when h = 32 and d = 4, we have:
[tex]V = khd^2[/tex]
[tex]V = 0.08 * 32 * 4^2[/tex]
[tex]V = 0.08 * 32 * 16[/tex]
[tex]V = 40.96[/tex]
The volume is 40.96 cubic feet
The volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, we have:
V = volume of the wood varying jointly as height of the tree and square of the distance around the trunk.
Let we take:
r = distance of the wood around the trunk (in feet)h = height of the tree ( in feet)V will of course increase as r or h increases, and as it varies jointly, thus:
[tex]V \propto h r^2[/tex]
Let the constant of proportionality be 'k', then:
[tex]V = kr^2h[/tex] (in cubic foot)
For case 1, it was specified that V = 15.84 cubic foot when r = 3 ft and h = 22 ft,
Putting these values gives us:
[tex]15.84 = k(3)^2(22)\\\\k = \dfrac{15.84}{198} = 0.08[/tex]
Thus, we have:
[tex]\rm V = 0.08r^2 h \: \rm ft^3[/tex]
Assuming second wood was also obtained from same kind of tree, we get the volume of the wood for h = 32 and r = 4 feet as:
[tex]V = 0.08 (4)^2 (32) = 40.96 \: \rm ft^3[/tex]
Thus, the volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]
Learn more about proportionality here:
https://brainly.com/question/13082482
If I went to the store and purchased a
T-shirt for $10 and jeans for $25, what
was my total expense at the store? Explain
how you got your total.
A cube has an A on 3 sides and a B on 3 sides. Rolling it 50 times results in 17 A's and 33 B's.
Using this observed probability, how many A's would be rolled in 750 tries?
what is the square root of 377.68
Answer:
19.4339908408
answer pls i will give brainliest!
Answer:
surface tension
Step-by-step explanation:
It seems to defy the laws of physics, but a paper clip made of steel can indeed float on the water surface. The high surface tension helps the paper clip - with much higher density - float on the water.
The cohesive forces between liquid molecules are responsible for the phenomenon known as surface tension. The molecules at the surface of a glass of water do not have other water molecules on all sides of them and consequently they cohere more strongly to those directly associated with them (in this case, next to and below them, but not above). It is not really true that a "skin" forms on the water surface; the stronger cohesion between the water molecules as opposed to the attraction of the water molecules to the air makes it more difficult to move an object through the surface than to move it when it is completely submersed.
Find the measures of the interior angles of the triangle.
∠A = 30°
∠B = °
∠C= °
I uploaded the file. Please help this is due in 10 min! I will also give brainiest! PLEASE NO DROP FILES OR I WILL REPORT!
Answer:
∠A = 30°
∠B = 60°
∠C= 90°
Step-by-step explanation:
This is a right triangle, you can see it mainly by the red square in C, and it is always used to mark 90 degrees.
Knowing that, you now know ∠C is 90°
Now, to find ∠B, you should use the following equation:
A+B+C = 180°This means that the sum of the three angles of a triangle gives 180. ALWAYS. So to find the missing angle, ∠B, do the following:
Fill the values of the equation with the angles you now know:
30° + B + 90° = 180Solve the equation, passing the 30° and 90° to the other side of the equal sing with Inverse Operation:
B = 180° - 30° - 90°B = 60
Hope it helps!!
At West High School, 10% of the student population is taking a calculus course, 8% is taking a physics course, and 6% is taking both. Find the probability that a student chosen at random is taking a physics course, given that the student is taking a calculus course. A. 0.06 B. 0.60 C. 0.70 D. 0.75
Answer:
the closest answer I got was A
Step-by-step explanation:
hope this helped at all
Answer:
It's B
Step-by-step explanation:
Round 3.28 to the nearest thousandth
Answer:
3.280
Step-by-step explanation:
You just add a 0
Which of the following represents the distance between -8 and 4 on a number line?
Answer:
You would put an open dot on both ends from -8 to 4 or just a distance of 12
Step-by-step explanation:
The following article was presented as supplemental reading in Unit 7:
Joshanloo, M., Rastegar, P., Bakhshi, A. (2012). The big five personality domains as predictors of social wellbeing in Iranian university students. Journal of Social and Personal Relationships. 29(5), 639-660.
The researchers presented this correlation matrix:
Which of their alternative hypotheses were supported by the evidence at a minimum of alpha .05 (choose one or more)?
-Neurotism was negatively associated with total social wellbeing
-Openness is positively associated with total social wellbeing
-Agreeableness is positively associated with total social wellbeing
-Conscientiousness is positively associated with total social wellbeing
-Extraversion is positively associated with total social wellbeing
Answer:
Candice
Step-by-step explanation:
Circuit boards from two assembly lines set up to produce identical boards are mixed in one storage tray. As inspectors examine the boards, they find that it is difficult to determine whether a board comes from line A or line B. A probabilistic assessment of this question is often helpful. Suppose that the storage tray contains 10 circuit boards of which six came from line A and four from line B. An inspector selects two of these identical-looking boards for inspection. He is interested in X, the number of inspected boards from line A.
a. Find the probability function for X .
b. Graph the probability function of X .
c. Find the distribution function of X .
d. Graph the distribution function of X .
Answer:
a) X = 2/15 , 8/15, 1/3
b) attached below ( probability plot )
C) F(x ) attached below
d) cumulative probability plot
Step-by-step explanation:
a) Determine the probability of Function X
P( x = 0 ) = 6 / 45 = 2 /15 = 0.1333
P( x = 1 ) = 8/15 = 0.5333
P( x = 2 ) = 1/3 = 0.3333
Hence the probability of Function X = 2/15 , 8/15, 1/3
b) Graph of the probability Function of X
x 0 1 2
p(x) 0.1333 0.5333 0.3333
attached below is the plot ( probability plot )
c) Determine the Distribution function of CX
using the results achieved in part ( a )
attached below is the solution
d) Graph of distribution function of X
x 0 1 2
p(x) 0.1333 0.6667 1
attached below is the plot ( cumulative probability plot )
Please help! 4th grade math. (See below)
*Use an equation to write each fraction or product as a multiple of a unit fraction*
3/5
Find the 9th term of the geometric sequence show below
Answer:
40x^20
Step-by-step explanation:
Each sequence the x value doubles.
Each sequence the x exponent goes up by 5
In the figure TU is tangent to the circle at the U point. See below
Answer: 6
Explanation: 8 + 4 divided by 2 = 6
I know this is definitely the correct answer but I forgot which theorem it is. If you need any further explanation I will gladly try and find some more.
Whoever will answer the second question will be marked brainliest.
answer faaaast
Please help me 7th grade math
Answer: 1/8
Step-by-step explanation: hoped this helped :))
If
Find the missing side of each right triangle (((((Pythagorean’s Theorem))))))))
Answer:
3
Step-by-step explanation:
36-27 = 9
[tex]\sqrt{9} = 3[/tex]
Mrs. Garcia wants to paint her patio floor. She needs to determine the area so she will know how much paint to buy. What is the area of the patio floor shown?
Answer: 375 ft
Step-by-step explanation:
break the shape into three parts in order to find the area of each of them look at the picture. I broke the parts into numbers 1 ,2 ,and 3. You can take the area for number one bye using the length given which is 20 and the width which is 5. Multiply the length times width and you'll receive the area. Box 2 : subtract 5 - 15 in order to get the width which is 10 and use the lengths given at the top which is 20. multiply them in order to get the area. box 3 : in order to get the width you can subtract 30 by 20 + 5 which leaves you with 5, which is the width. The length is already given to you on the side which is 15. Multiply 5 by 15 in order to get the area.once you get all of the areas for the boxes which should be 100, 200, 75. add them all up to obtain the area of the shape which should equal 375 ft.
1) If you roll two dice, one red and one blue, what is the probability that the red die shows 5 and
the product of both numbers shown is less than 20?
Answer:
3 combinations
Step-by-step explanation:
when did the alec meet the stallion ?
Answer:
The Black Stallion, known as the Black or Shêtân, is the title character from author Walter Farley's bestselling series about the Arab stallion and his young owner, Alec Ramsay. The series chronicles the story of a sheikh's prized stallion after he comes into Alec's possession, although later books furnish the Black's backstory. Shaytan (under various transliterations) is the Arabic word for "devil".
what is x²=16?
2
3
4
8
Answer: 4
Step-by-step explanation:
4^2=16
Answer:
4
Step-by-step explanation:
When we square something we just multiply it by itself.
2 x 2 = 4 so not 2
3 x 3 = 9 so not 3 either
4 x 4 = 16 this one is correct!
8 x 8 = 64 not this one either
So the answer is 4 BOOM
The wholesale price of a basketball was $10.00. The store marked it up an additional 120%. What was the sale price?
Answer:
The sale price was 54.55 but if you round it up its 55 hope i helped!
Step-by-step explanation:
For each pair of functions F and G below, find f(g(x)) and g(f(x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
Answer:
FG
Step-by-step explanation:
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The function f(x) = x - 4 and g(x) = x + 4 and the function f(x) = -3/x and g(x) = 3/x are not inverse of each other.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
For each pair of functions F and G below, find f(g(x)) and g(f(x)).
a) f(x) = x - 4 and g(x) = x + 4
Then f(g(x)) will be
[tex]\rm f(g(x)) = x[/tex]
Then g(f(x)) will be
[tex]\rm g(f(x)) = x[/tex]
The functions f and g are not inverse of each other.
b) f(x) = -3/x and g(x) = 3/x
Then f(g(x)) will be
[tex]\rm f(g(x)) =- x[/tex]
Then g(f(x)) will be
[tex]\rm g(f(x)) = -x[/tex]
The functions f and g are not inverse of each other.
More about the function link is given below.
https://brainly.com/question/5245372
An object has a weight of 6.4 N.
Calculate the mass of the object.
Use the equation
mass = weight = gravitational field strength (g)
gravitational field strength = 9.8 N/kg
Answer:
Step-by-step explanation:
We can do this quite simply by using Newton's equation: forcegravity = G × M × mseparation2 .
Suppose: your mass, m, is 60 kilogram; the mass of your colleague, M, is 70 kg; your centre-to-centre separation, r, is 1 m; and G is 6.67 × 10 -11 newton square metre kilogram-2.
If you place a 28-foot ladder against the top of a 22 foot building
Answer:
17.3 ft
Step-by-step explanation:
To find the second leg, use the following: √c² - a². Substitute c for 28, and a for 22.
b = √28² - 22² {Square 28 to get 784, and square 22 to get 484.}
b = √784 - 484 {Subtract 484 from 784 to get 300.}
b = √300 {Find the square root of 300.}
b = 17.32051 {Round to the nearest tenth.}
b = 17.3 ft.
The bottom of the ladder will be 17.3 ft from the bottom of the building.
I hope this helps! ^w^
Mathematics Grade 5 Sample Items
Tral
Question 26
Line
Guide
Enter a value for b that makes this statement true; 5* b is less than 5 but greater than 0.
?
Answer:
The answer is within the range of 0.1 - 0.9.
Step-by-step explanation:
For example, 0.5 could be the answer.