Answers
Answer:
Step-by-step explanation:
Hello,
We can write three equations thanks to Pythagoras
[tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]
So it comes
[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]
Hope this helps
Answer:
x = [tex]\sqrt{21}[/tex]
Step-by-step explanation:
Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values
[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
x² = 21 ( take the square root of both sides )
x = [tex]\sqrt{21}[/tex]
Related Questions
Copy the problem, mark the givens in the diagram. Given: CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC, Prove: CR ≅ HS
Help urgently needed
Answers
Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
need help thanksssssssss
Answers
Answer:
Volume: 112 m³.
Surface area: 172 m².
Step-by-step explanation:
The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.
The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.
2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².
Hope this helps!
How to calculate a circumference of a circle?
Answers
Answer: Pi multiplied by the diameter of the circle
Step-by-step explanation:
Answer:
The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answers
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
Find the largest integer which belongs to the following interval: [−∞, 31]
Answers
Answer:
Largest integer in the interval [−∞, 31] is 31.
Step-by-step explanation:
Given the interval: [−∞, 31]
To find: The largest integer in this interval.
Solution:
First of all, let us learn about the representation of intervals.
Two kind of brackets can be used to represent the intervals. i.e. () and [].
Round bracket means not included in the interval and square bracket means included in the interval.
Also, any combination can also be used.
Let us discuss one by one.
1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.
Smallest p
Largest q
2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.
Smallest value just greater than p.
Largest value just smaller than q.
3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.
Smallest value p.
Largest value just smaller than q.
4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.
Smallest value just greater than p.
Largest value q.
As per above explanation, we can clearly observe that:
The largest integer which belongs to the following interval: [−∞, 31] is 31.
Hypothesis Testing
Problem 1. Adults saving for retirement
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does
the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?
Problem 2: Google Stock
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has
decreased substantially. In 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo!Enance. A random sample of 35 trading days in 2014 resulted in a
sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of
significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why
8. What do you conclude?
Answers
Answer:
Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2: We conclude that the volume of Google stock has changed.
Step-by-step explanation:
Problem 1:
We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.
Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50% {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}
Alternate Hypothesis, [tex]H_A[/tex] : p > 50% {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}
This is a right-tailed test.
The test statistics that would be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53
n = sample of adult Americans = 295
So, the test statistics = [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]
= 1.03
The value of z-test statistics is 1.03.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)
= 1 - 0.8485 = 0.1515
Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2:
We are given that a random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.
Let [tex]\mu[/tex] = mean daily volume in Google stock
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares {means that the volume of Google stock has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares {means that the volume of Google stock has changed}
This is a two-tailed test.
The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares
s = sample standard deviation = 1.68 million shares
n = sample of trading days = 35
So, the test statistics = [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= -7.606
The value of t-test statistics is -7.606.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%
Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the volume of Google stock has changed.
2.CommerceThe weight distribution of parcels sent in a certain manner is normal with meanvalue 12 pounds and standard deviation 3.5 pounds. The parcel service wishes to establish aweight valuecbeyond which there will be a surcharge. What value ofcis such that 99% ofall parcels are under the surcharge weight
Answers
Answer:
the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Step-by-step explanation:
Given that :
The mean value [tex]\mu[/tex] = 12
The standard deviation [tex]\sigma[/tex] = 3.5
Let Consider Q to be the weight of the parcel that is normally distributed .
Then;
Q [tex]\sim[/tex] Norm(12,3.5)
The objective is to determine thewight value of c under which there is a surcharge
Also, let's not that 99% of all the parcels are below the surcharge
However ;
From the Percentiles table of Standard Normal Distribution;
At 99th percentile; the value for Z = 2.33
The formula for the Z-score is:
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]
2.33 × 3.5 = X - 12
8.155 = X - 12
- X = - 12 - 8.155
- X = -20.155
X = 20.155
the weight value of c under which there is a surcharge = X + 1 (0) since all the pounds are below the surcharge
c = 20.155 + 1(0)
c = 20.155
Thus ; the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answers
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?
Answers
Answer:
3.54%
Step-by-step explanation:
This question represents a binomial distribution. A binomial distribution is given by:
[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]
Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.
Given that:
A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.
The total number of trials (n) = 20 shots
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)
P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]
P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]
P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%
The cost of plastering the 4 walls of a room which is 4m high and breadth one third of its length is Rs. 640 at the rate of Rs. 5/m². What will be the cost of carpeting its floor at the rate of Rs. 250/m².
Answers
Answer:
Rs. 32,000
Step-by-step explanation:
height = 4m
let length = x m
breadth = x/3 m
Area of the 4 walls = 2(length × height) + 2(breadth × height)
Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3
Area = (32x)/3 m²
1 m² = Rs. 5
The cost for an area that is (32x)/3 m²= (32x)/3 × 5 Rs.
The cost of plastering 4 walls at Rs.5 per m² = 640
(32x)/3 × 5 = 640
(160x)/3 = 640
x = length = 12
Area = (32x)/3 m² = (32×12)/3 = 128m²
The cost of carpeting its floor at the rate of Rs. 250/m²:
= 128m² × Rs. 250/m² = 32,000
The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000
A rectangle's length and width are in a ratio of 10:1. The perimeter is 66 feet. What are the length and width?
Answers
hii
Step-by-step explanation:
length-10x
width-x
perimeter-2(l+b)
66=2(10x+x)
66-2=10x+x
64=11x
x=11/64
lenght-11
width-64
Width-64
Hope it helps
A sector with a central angle measure of 200 degrees has a radius of 9 cm. What is the area of the sector?
Answers
Answer:
[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]
Step-by-step explanation:
Radius = r = 9 cm
Angle = θ = 200° = 3.5 radians
Now,
[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]
Area = 1/2 (9)²(3.5)
Area = 1/2 (81)(3.5)
Area = 282.7 / 2
Area of sector = 141.4 cm²
Answer:
45 pi cm^2 or 141.3 cm^2
Step-by-step explanation:
First find the area of the circle
A = pi r^2
A = pi (9)^2
A = 81 pi
A circle has 360 degrees
The shaded part has 200
The fraction that is shaded is
200/360 =5/9
Multiply by the total area
5/9 * 81 pi
45 pi
Using 3.14 for pi
141.3
45 pi cm^2 or 141.3 cm^2
What is the measure of x?
Answers
Answer:
9 in.
Step-by-step explanation:
Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9
Is 3 a solution to the equation 6x – 7 = 12?
Answers
Answer:
3 is not a solution
Step-by-step explanation:
6x – 7 = 12?
Substitute 3 in for x and see if the equation is true
6*3 - 7 = 12
18-7 = 12
11 =12
This is false so 3 is not a solution
6x = 12 +7
6x = 19
x = 19 / 6
x = 3.2 (1 dp)
I HOPE THIS HELPS:)
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answers
Answer:
Perimeter= 40 units
Step-by-step explanation:
Ok
We are asked to look for the perimeter.
We have some clue given.
All at right angle and some sides are given it's full length.
We have the bae to be 11 unit
The height to be 7 unit.
What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.
Let's go for the other side of the height.
Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.
So we have 7+7+11
But it's not complete yet.
We are given a dimension 2.
And the 2 is in two places so it's total 2*2= 4
The two is for a small base .
The base is actually an extra to the 11 of the other base.
So summing up
We have 2*11 + 2*7 + 2*2
Perimeter= 22+14+4
Perimeter= 40 units
Please help
ASAP
ANSWERS
A-48.21
B-66.35
C-53.68
D-28.34
Answers
Answer:
B
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )
AB × cos54° = 39 ( divide both sides by cos54° )
AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B
A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nearest thousandth
Answers
Answer: 0.476
Step-by-step explanation:
Let A = Event of choosing an even number ball.
B = Event of choosing an 8 .
Given, A lottery game has balls numbered 1 through 21.
Sample space: S= {1,2,3,4,5,6,7,8,...., 21}
n(S) = 21
Then, A= {2,4,6,8, 10,...(20)}
i.e. n(A)= 10
B= {8}
n(B) = 1
A∪B = {2,4,6,8, 10,...(20)} = A
n(A∪B)=10
Now, the probability of selecting an even numbered ball or an 8 is
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]=\dfrac{10}{21}\approx0.476[/tex]
Hence, the required probability =0.476
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answers
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
25 points will mark brainlest as part of the save nature campaign the city Forest department has decided to grow more trees to kick off the campaign they start by planting 2 pine trees it has been decided that every year they will increase the amount of trees but 1 tree less than the square of the previous year's count which of the following recursives formulas can be used to determine the total number of tree planted in the future assume there is in limited space for trees and n is the number of years of the program's operation
Answers
Answer:
N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2
or equivalently
N(n) = N(n-1)^2 - 1, n>0, N(0) = 2
Step-by-step explanation:
Year 0 = 2 trees
year 1 = 2^2-1 = 3
year 2 = 3^2-1 =8
year 2 = 8^2-1 =63
...
Recursive formula
Let
n = integer year number
N(n) = number of trees to plant in year n
N(n+1) = N(n)^2-1, n>=0, N(0) = 2
or equivalently
N(n) = N(n-1)^2, n>0, N(0) = 2
Whats the options???
The solutions to the inequality ys-x+1 are shaded on
the graph. Which point is a solution?
(2, 3)
(3,-2)
(2.1)
(-1,3)
Answers
Answer:
the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)
Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answers
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
I need help with this !!
Answers
Answer:
A
Step-by-step explanation:
When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.
Step 2 should be:
⅓X +7 -7= 15 -7
What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.
⅓X= 8
X= 8 ×3
X= 24
The graph of a linear equation g(x)=-1/3x +2 can be obtained from the graph f(x)=1/3x by using infinite sets of elementary translation (i.e reflection and shifting). List out five of those sets
Answers
Answer:
{Rx, T(-6, 4)}{Rx, T(-3, 3)}{Rx, T(0, 2)}{Rx, T(3, 1)}{Rx, T(9, -1)}Step-by-step explanation:
We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.
The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).
The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}
Along the same lines, other possibilities are ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}
g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}
g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}
g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}
___
Additional comment
All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.
Which sequence of transformations on preimage Triangle ABC will NOT produce the image A’B’C’
Answers
Answer:
b
Step-by-step explanation:
Find the difference of functions at x= - 3, (g - f)(-3), given f(x) and g(x): g(x) = x^2−15, and f(x) =2x
Answers
Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
[tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
[tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]
Now evaluate the above determined function at x = -3 as follows:
[tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 16, y ≥ 0, oriented in the direction of the positive y-axis.
Answers
Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
Parameterize this circle by
[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]
with [tex]0\le t\le2\pi[/tex].
The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.
Now compute the line integral of F along C :
[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]
[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]
Step-by-step explanation:
Given :
Hemisphere - [tex]x^2 +y^2+z^2=16[/tex]
Calculation :
Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
then parameterize the circle,
[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]
with , [tex]0\leq t\leq 2\pi[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]
[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]
[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]
[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]
[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]
[tex]= -16\pi[/tex]
For more information, refer the link given below
https://brainly.com/question/8130922?referrer=searchResults
Need Answers ASAP!!!!
Answers
Answer:
15.9degrees
Step-by-step explanation:
in photo above
Answer:
[tex]\boxed{15.95\°}[/tex]
Step-by-step explanation:
The angle can be found by using trigonometric functions.
tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]
tan (θ) = [tex]\frac{4}{14}[/tex]
θ = [tex]tan^{-1} \frac{4}{14}[/tex]
θ = 15.9453959
θ ≈ 15.95
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answers
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
WILL MARK AS BRAINLIEST 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: 52C3=52!/49!3! 52C3=22100 Calculate the probability of getting a hand that has exactly two aces in it (A A X). Do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points)
Answers
Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder? 17.1π mm2 33.6π mm2 60π mm2 84π mm2
Answers
Answer:
84π mm^2
Step-by-step explanation:
formula for circumference is 2πr where r is the radius of circle
Given,The circumference of the base of a cylinder is 24π mm
Thus,
2πr= 24π mm
=> r = 24π mm/2π = 12 mm
________________________________________
A similar cylinder has a base with circumference of 60π mm.
radius for this cylinder will be
2πr= 60π mm
r = 60π mm/2π = 30mm
______________________________________________
Given
The lateral area of the larger cylinder is 210π mm2
lateral area of cylinder is given by 2πrl
where l is the length of cylinder
thus,
r for larger cylinder = 30mm
2π*30*l = 210π mm^2
=> l = 210π mm^2/2π*30 = 3.5 mm
___________________________________________
the lateral area of the smaller cylinder
r = 12 mm
l = 3.5 mm as both larger and smaller cylinder are same
2πrl = 2π*12*3.5 mm^2 = 84π mm^2 answer
Answer:
33.6pi mm2 is the correct answer
edge 2021
Step-by-step explanation:
The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.
What is the lateral area of the smaller cylinder?
17.1π mm2
33.6π mm2
60π mm2
84π mm2