The area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)` is `50π√2`.
The radius of the sphere as 10, that is `r = 10`.
The equation of the cone is given by `z > √(x²+y²)` which represents the top half of the cone.
The cone is centered at the origin, which means the vertex is at the origin.
Here, the equation of the sphere is `x² + y² + z² = 10²`
`We need to find the area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)`Since the cone is symmetric about the xy-plane and centered at the origin, we can work in the upper half of the cone and multiply by 2 at the end.
Let the projection of the point P on the xy-plane be Q. This means that `z = PQ = sqrt(x² + y²)`.The equation of the sphere is `x² + y² + z² = 10²`
Substituting `z = sqrt(x² + y²)` to get `x² + y² + (sqrt(x² + y²))² = 10²`Simplifying and rearranging to get
`z = sqrt(100 - x² - y²)`
This is the equation of the sphere in the first octant. The portion of the sphere in the cone `z > sqrt(x² + y²)` is the part of the sphere that is above the cone, i.e., `z > sqrt(100 - x² - y²) > sqrt(x² + y²)`
Since the sphere is centered at the origin, we can integrate in cylindrical coordinates.Let `r` be the distance from the origin, and let `θ` be the angle made with the positive x-axis.
Then `x = r cos θ` and `y = r sin θ`.Since we are working in the first octant, `0 ≤ θ ≤ π/2`.The limits of integration for `r` can be found by considering the intersection of the two surfaces.`z = sqrt(100 - x² - y²)` and `z = sqrt(x² + y²)` gives `sqrt(100 - x² - y²) = sqrt(x² + y²)` or `100 - x² - y² = x² + y²`.
This simplifies to `x² + y² = 50`.Thus the limits of integration for `r` are `0 ≤ r ≤ sqrt(50)`
Substitute `z = sqrt(100 - x² - y²)` into the inequality `
z > sqrt(x² + y²)` to get `sqrt(100 - x² - y²) > sqrt(x² + y²)`.
This simplifies to `100 - x² - y² > x² + y²`. This simplifies to `2y² + 2x² < 100`.
Thus the limits of integration for `θ` are `0 ≤ θ ≤ π/2`.
The area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)` is given by the integral:
`A = 2 ∫₀^(π/2) ∫₀^sqrt(50 - r²) sqrt(100 - r²) r dr dθ`
To evaluate this integral lets make the substitution `u = 100 - r²`.
Then `du/dx = -2x` and `du = -2x dr`. Thus, `x dr = -1/2 du`.
Substituting to get:
`A = 2 ∫₀^(π/2) ∫₀^sqrt(50) √u * (-1/2) du dθ`
This simplifies to:`
A = -∫₀^(π/2) u^(3/2) |₀^100/√2 dθ`
Evaluating
:`A = 2 ∫₀^(π/2) 100^(3/2)/2 - 0 dθ`
Simplifying:`
A = ∫₀^(π/2) 100√2 dθ`Evaluating:`
A = 100√2 * π/2`
Simplifing:`A = 50π√2`
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Write an absolute value inequality for the graph
Step-by-step explanation:
sooooo hard
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I'll be friend
PO
What is the slope of a line that goes through the following 2 points?
(-12,-5) (0, -8)
Answer:
-1/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-8-(-5))/(0-(-12))
m=(-8+5)/(0+12)
m=-3/12
simplify
m=-1/4
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Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 4 / 5;
The value of x as an int variable is 0
What is a int variable?An int(integer) variable is a variable containing only whole numbers.
Given the expression;
x = - 3 + 4 % 6/ 5
Let's make into proper fraction, we have
x = - 3 + {}4/ 100 × 6/ 5
Multiply through
x = -3 + 6/ 5/ 4/ 100
x = -3 + {6/ 5 ÷ 0. 4}
x = -3 + {3}
expand the bracket
x = -3 + 3
Add like terms
x = 0
Thus, the value of x as an int variable is 0
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Complete question;
Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;
need help with 3&4 pls
Lloyd's account has a balance of −$53.50. If he owes the bank more than $40, his account gets closed. Which of the following is true about Lloyd's account?
It stays open, because |−53.50| > 40
It gets closed, because |−53.50| < 40
It stays open, because |−53.50| < 40
It gets closed, because |−53.50| > 40
Answer:
It stays open,because |−53.50| > 40
Step-by-step explanation:
His account has 53.50 dollars, so he can still pay it off. Don't get confused about the fact that he has 53.50 dollars, not owes.
Hope this helps!
Have a great day!
the ratio of two supplementary angles is 3:9 what is the measure of the larger angle
Answer:
135
Step-by-step explanation:
Ratio = 3 : 9
Angles are : 3x , 9x
3x + 9x = 180 {supplementary angles}
12x = 180 {divide both side by 12}
x = 180/12
x = 15
Larger angle = 9x = 9*15 = 135
Complete the table to show the coordinates of the vertices of A’B’C’
The coordinates of the vertices of A’B’C’ are A' = (1, 3), B' = (3, 4) and C' = (4, 1)
From the question, we have the following parameters that can be used in our computation:
The graph
The coordinates of the vertices of A’B’C’ are the coordinates of the locations of the the vertices A', B' and C'
Using the above as a guide, we have the following:
From the graph, we have the coordinates of the vertices of A’B’C’ to be
A' = (1, 3)
B' = (3, 4)
C' = (4, 1)
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One vertex of an equilateral triangle is at the origin and the other vertex is at (3,4)
1)Find the sides?
Answer:
5 units
Step-by-step explanation:
Points:
(0, 0) and (3, 4)The distance:
d= √(4-0)²+(3-0)² = √16+9= √25 = 5Sides of the triangle are 5
Answer:
(5 , 0)
Step-by-step explanation:
Quadrilateral FGHI is dilated by a scale factor of to form quadrilateral F'G'H'I.
What is the measure of side I'F'?
H
62.6
I
56
28
56
Answer:
I’F’ = 21
Step-by-step explanation:
To find the length of I’F’
We perform the dilation on IF using the given dilation factor
All we have to do here is to multiply the length of IF by the dilation factor
We have this as ;
28 * 3/4 = 21
the measure of an angle is 166 degrees. what is the measure of of its supplementary angle?
Answer:
14°
Step-by-step explanation:
Supplementary angles add up to 180° so subtract 166 from 180.
In a survey given by camp counselors, campers were
asked if they like to swim and if they like to have a
cookout. The Venn diagram displays the campers'
preferences.
Camp Preferences
S
0.06
0.89
C
0.04
0.01
A camper is selected at random. Let S be the event that
the camper likes to swim and let C be the event that the
camper likes to have a cookout. What is the probability
that a randomly selected camper does not like to have a
cookout?
O 0.01
O 0.04
O 0.06
O 0.07
The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.
To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).
Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.
1 - 0.04 = 0.96
Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.
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algorithm depth-first search : find the order of visit: 2. algorithm breadth first search : find the order of visit
The order of visit for DFS and BFS will differ based on the structure of the graph or tree and the starting node. DFS will typically visit nodes in a deeper order, while BFS will visit nodes in a breadth-first order.
Both algorithm depth-first search and algorithm breadth-first search are used to traverse or search a graph or tree data structure. The difference between them lies in their traversal strategy.
Depth-first search (DFS) starts at a root node and explores as far as possible along each branch before backtracking. It follows a content-loaded algorithm, meaning that it prioritizes exploring deeper into the structure before considering other branches. In terms of visit order, DFS starts at the root node, then moves to its first child node, and continues to explore its descendants until it reaches a leaf node. Once it has visited all descendants of the current node, it backtracks to the previous node and repeats the process until it has visited all nodes.
On the other hand, breadth-first search (BFS) starts at the root node and explores all the neighboring nodes at the current depth level before moving on to the next depth level. It follows a breadth-first algorithm, meaning that it prioritizes exploring all nodes at a given depth level before moving on to deeper levels. In terms of visit order, BFS visits all nodes at a given depth level before moving on to the next level.
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Determine the decision rule. Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places to the right of the decimal point as needed.) A. Reject H 0 if Z N B. Reject H 0 if Z gTAT <− or Z STA C. Reject H 0 if Z star D. Reject H 0
< State your conclusion. Choose the correct answer below
. A. Since Z wrar falls into the rejection region, reject H 0
. B. Since Z Z star does not fall into the rejection region, do not reject H 0
. C. Since Zertar does not fall into the rejection region, reject H 0
. D. Since Z gray falls into the rojection region, do not reject H O ∗
.
The given question is incomplete, please provide the complete question so that I can help you with it. If the decision rule for a hypothesis test is to reject the null hypothesis if the p-value is less than or equal to a level of significance α.
The decision rule can be written Reject H0 if p-value ≤ αOtherwise, do not reject H0.In this decision rule, the level of significance is the maximum probability of rejecting the null hypothesis when it is true. It is usually set at 0.05 or 0.01.
The p-value is the probability of obtaining a sample statistic as extreme as the one observed or more extreme, given that the null hypothesis is true. If the p-value is small, it indicates strong evidence against the null hypothesis, and we reject the null hypothesis. If the p-value is large, it indicates weak evidence against the null hypothesis, and we fail to reject the null hypothesis.
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2 (4 + n) - 5 for n = 0 = ??
Answer:
3
Step-by-step explanation:
2 (4 + n) - 5
Let n = 0
2(4+0) -5
Parentheses first
2(4)-5
Multiply
8-5
Subtract
3
Answer:
put n= 0
2 ( 4 + 0 ) - 5
2 (4)-5
8-5
3
done
what is perpendicular?
What is parallel?
And what are the differences between the two?
Which of the following is run on sentence
Answer:
d
Step-by-step explanation:
because it needs a period to complete the thought?
Write the equation in standard form for the circle with center (-4, 0) and radius 6./3.
Step-by-step explanation:
center -4,0
(x- - 4)^2 + (y-0)^2
(x+4)^2 + y ^2
with radius 6/3
(x+4)^2 + y^2 = ( 6/3)^2
(x+4)^2 + y^2 = 4
20 points will give out award :)
Answer:
the answer is (25-π) there was no figure drawn
4. Which of the following is the correct formula for the area of a triangle?
O
O
A = =acco
cos B
a² = sin² b + cos² c
1
A = -bcsin A
2
a² + b² = c²
Option c. A = 1/2 bcSin A is the area of a traingle
What is the area of a triangle using the sine ruleThe sine rule is a mathematical equation that links the side lengths of a triangle to the sines of its respective angles. The formula for determining the area in such a triangle is represented as follows:
A = (1/2) ab sin C
= (1/2) bc sin A
= (1/2) ac sin B
where a, b, and c symbolize the lengths of the triangle's sides while A, B, and C stand for the measures of their opposite angles.
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Draw the graph of f(x)=[[x - 4]] - 2
Answer:
See attachment.
Step-by-step explanation:
Given absolute value function:
\(f(x)=|x-4|-2\)
The parent absolute value function is f(x) = |x|.
Graph of the parent absolute value function:
Vertex at (0, 0)|y| = -x if x ≤ 0|y| = x if x ≥ 0Translations
\(\textsf{For $a > 0$}:\)
\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.\)
\(f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.\)
\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.\)
\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.\)
The graph of the given function is a transformation of the parent function by:
Translation of 4 units right.Translation of 2 units down.Therefore, the vertex of the given function is (4, -2).
Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:
\(\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}\)
\(\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}\)
To draw the graph of the given function:
Plot the vertex (4, -2).Draw a straight line from the vertex through point (8, 2).Draw a straight line from the vertex through point (0, 2).PLEASE HELP! 25 POINTS
Answer:
D
Step-by-step explanation:
OUTCASTS OF POKER FLAT QUESTIONS: ENGLISH
PUT THIS IN THE WRONG CATEGORY.
1. Explain three details from the story that establishes its regionalism. You must write at least three complete sentences--no sentence fragments or phrases.
2. What culture about the West does the author, Harte, convey?
3. If you were living in the East in the late 1800s, what would you find interesting about this story?
4. Although the characters in the story have little in common, they band together. Why do you think this is?
5. The circumstances these characters find themselves in seems to bring out their true characters. Which one surprised you the most? Why?
1. One detail that establishes the story's regionalism is the setting, which takes place in a small mining town in the West called Poker Flat.
2. The author, Harte, conveys a culture about the West that emphasizes the harsh and unforgiving nature of the land and its people. The characters in the story struggle against the harshness of the environment and the moral ambiguity of the mining town.
3. If you were living in the East in the late 1800s, you would find interesting the story's depiction of the West as a land of opportunity and adventure, but also one of danger and hardship. The story would also provide a glimpse into the everyday lives of people living in the West, which would likely be quite different from what they were familiar with in the East.
4. The characters band together because they are all outcasts, each in their own way, and they find comfort in each other's company. They are all looking for a sense of community and belonging that they have been denied in Poker Flat.
5. The character that surprised me the most was Mother Shipton. I was surprised by her sudden change of character when she revealed her past and her true identity as a former prostitute, which was quite different from the religious and moral woman she had pretended to be. I think this was surprising because it shows how people can hide their past and their true selves in order to fit in and be accepted by society.
What is the regionalism about?Another detail is the use of Western colloquialism and dialect in the dialogue of the characters.
Lastly, the story also includes a description of the harsh winter conditions and rugged terrain of the Sierra Nevada mountains, which is specific to that region.
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the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring. T/F
False, the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
The probability of any event can never exceed 1. An event with probability 1 is absolutely certain to occur, and no higher likelihood is possible. Even if two events' probability are both 1, the highest possible value of the union is only 1.
The probability of an event is a numerical measure of the likelihood of the event occurring. Values of this probability can be assigned based on theoretical, empirical, or subjective reasons, so long as the values are in accord with certain fundamental rules of probability theory.
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A box is shaped like an octagonal prism. Here is what the base of the prism looks like. I already got question one solved, but question two is If the volume of the box is 123in cubed, what is the height of the box?
Answer:
287(inches)³
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Compute each of these double sums. (a) ∑
i=1
3
∑
j=1
2
(i−j) (b) ∑
i=0
3
∑
j=0
2
(3i+2j) (c) ∑
i=1
3
∑
j=0
2
j (d) ∑
i=0
2
∑
j=0
3
i
2
j
3
The required double sums are as follows:a) 3b) 18c) 9d) 2214.
a) We have to find out the double sum, given below:∑
i=1
3
∑
j=1
2
(i−j)The formula is given below for the above expression= ∑
i=1
m
∑
j=1
n
(a i−b j)= a 1+ a 2+ … + a m
n b − b 1+ b 2+ … + b n
m a)∑
i=1
3
∑
j=1
2
(i−j) is the sum of i−j where i runs from 1 to 3 and j runs from 1 to 2. Using the formula, we have the following result
∑
i=1
3
∑
j=1
2
(i−j)= [3.2.(3−1−0+1)]/2= 3
b) We have to find out the double sum, given below:∑
i=0
3
∑
j=0
2
(3i+2j)
The formula is given below for the above expression= ∑
i=0
m
∑
j=0
n
(a i+b j)= a 1+ a 2+ … + a m+1
n+1 b 1+ b 2+ … + b n+1
m+1a)∑
i=0
3
∑
j=0
2
(3i+2j) is the sum of 3i+2j where i runs from 0 to 3 and j runs from 0 to 2. Using the formula, we have the following result∑
i=0
3
∑
j=0
2
(3i+2j)= [(3.4.2)+(2.3.3)]/2= 18c) We have to find out the double sum, given below:∑
i=1
3
∑
j=0
2
jThe formula is given below for the above expression= ∑
i=1
m
∑
j=0
n
(a i+b j)= a 1+ a 2+ … + a m
n b+ b + … + b n a)∑
i=1
3
∑
j=0
2
j is the sum of j where i runs from 1 to 3 and j runs from 0 to 2. Using the formula, we have the following result∑
i=1
3
∑
j=0
2
j= 0+ 1+ 2+ 0+ 1+ 2+ 0+ 1+ 2= 9d) We have to find out the double sum, given below:∑
i=0
2
∑
j=0
3
i
2
j
3The formula is given below for the above expression= ∑
i=0
m
∑
j=0
n
(a i.b j)= [a 0+ a 1+ … + a m b 0+ b 1+ … + b n ]a)∑
i=0
2
∑
j=0
3
i
2
j
3 is the sum of i2j3 where i runs from 0 to 2 and j runs from 0 to 3. Using the formula, we have the following result∑
i=0
2
∑
j=0
3
i
2
j
3= 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 + 162 + 1944 = 2214
Therefore, the required double sums are as follows:a) 3b) 18c) 9d) 2214.
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Four more than three times a number is 16
Find the number
Answer:
n = 4
Step-by-step explanation:
We can find the number, n, using the equation:
3n + 4 = 16
3n = 12
n = 4
Factorize mn-nq+mo-oq
mn-nq+mo-oq
n(m-q) + o(m-q)
final ans:(n+o) (m-q)
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²
3x-5
2x+6 x+3
OA.
OB.
O C.
O D.
O E.
21x³-35x2
2x² +12x+18
7x²
6x-10
7x³ +21x²
6x² +8x-30
6x-10
7x²
6x² +8x-30
7x³+21x²
The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10
To simplify the expression 7x² / 3x-5 / 2x+6 / x+3
We need to perform the following steps:
Invert the divisor.
Change the division to multiplication.
Factor the numerator and denominator.
First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.
Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.
2x + 6 | 7\(x^2\) + 3x - 5
- (6x + 18)
_______
-3x - 23
Then subtract the following term from the numerator: -3x.
Dividing -3x by 2x gives -3/2.
Multiply (2x + 6) by -3/2. The result is -3x - 9.
Subtract this from the previous result.
3 - (3/2)x
_________
2x + 6 | - 14
The result of polynomial long division is -14.
Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.
So the correct answer is option D: -14.
Cancel out any common factors.
Multiply the remaining terms to get the answer.
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Which of the following options best explains the following statement? Populations of a bird have different average bill sizes in different seasons.
a.disruptive selection
b.sexual selection
c.directional selection
d.Frequency dependent selection
The best option to explain the statement "Populations of a bird have different average bill sizes in different seasons" is c. directional selection.
Directional selection occurs when a particular trait in a population becomes more or less common over time due to selective pressures favoring individuals with extreme values of that trait. In this case, the bird population's average bill size changes in different seasons, indicating that there is a consistent trend or direction in the selection of bill sizes.
For example, let's say the bird population primarily feeds on a specific type of food during one season. If the size of the bills affects the bird's ability to efficiently gather that food, then birds with larger bills may be better adapted and have a higher survival rate during that season. As a result, the average bill size of the population may increase. In the next season, if the food source changes and favors birds with smaller bills, the average bill size may decrease.
Directional selection is characterized by a shift in the average value of a trait in a population over time. It does not necessarily result in extreme values of the trait, like in disruptive selection, or selection based on traits that increase the chance of mating, like in sexual selection. It is also different from frequency-dependent selection, where the fitness of a trait depends on its frequency relative to other traits in the population.
Therefore, c. directional selection best explains the variation in average bill sizes observed in different seasons in the bird populations.
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Make x the subject
gk=(x+a)^2/10
The answer of the question based on the equation is x = √(10gk) - a or x = -√(10gk) - a .
What is Formula?A formula is a mathematical expression or equation that describes a relationship between variables or quantities. Formulas can be used to calculate values based on known inputs, or to derive relationships between different variables.
Formulas can take many different forms, depending on the problem or situation being analyzed. Formulas are used extensively in mathematics, science, engineering, and many other fields to solve problems and make predictions.
To make x subject of formula:
gk = (x + a)²/10
We can start by multiplying both sides by 10 to eliminate the denominator:
10gk = (x + a)²
Next, we will take square root on both the sides:
±√(10gk) = x + a
To isolate x, we can subtract a from both sides:
x = ±√(10gk) - a
So the final answer is:
x = √(10gk) - a or x = -√(10gk) - a
Note that there are two possible solutions, because the square root can be positive or negative.
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