(a) You can parameterize C by the vector function
r(t) = (x(t), y(t) ) = P (1 - t ) + Q t = (2 - 2t, 7t )
where 0 ≤ t ≤ 1.
(b) From the above parameterization, we have
r'(t) = (-2, 7) ==> ||r'(t)|| = √((-2)² + 7²) = √53
Then
ds = √53 dt
and the line integral is
[tex]\displaystyle\int_C(9x(t)+5y(t))\,\mathrm ds = \boxed{\sqrt{53}\int_0^1(17t+18)\,\mathrm dt}[/tex]
(c) The remaining integral is pretty simple,
[tex]\displaystyle\sqrt{53}\int_0^1(17t+18)\,\mathrm dt = \sqrt{53}\left(\frac{17}2t^2+18t\right)\bigg|_{t=0}^{t=1} = \boxed{\frac{53^{3/2}}2}[/tex]
Tyra has recently inherited $5400, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds semi-
annually at an annual rate of 3.1 % (Account 1) and an account that compounds continuously at an annual rate of 4 % (Account 2).
Step 2 of 2: How much would Tyra's balance be from Account 2 over 3.7 years? Round to two decimal places.
The focus here is the use of "Compounding interest rate" and these entails addition of interest to the principal sum of the deposit.
Tyra will definitely prefer the Account 2 over the Account 1 Tyra balance from account 2 over 3.7 years is $6,261.37
The below calculation is to derive maturity value when annual rate of 3.1% is applied.
Principal = $5,400
Annual rate = 3.1% semi-annually for 1 years
A = P(1+r/m)^n*t where n=1, t=2
A = 5,400*(1 + 0.031/2)^1*2
A = 5,400*(1.0155)^2
A = 5,400*1.03124025
A = 5568.69735
A = $5,568.70.
In conclusion, the accrued value she will get after one years for this account is $5,568.70,
- The below calculation is to derive maturity value when the amount compounds continuously at an annual rate of 4%
Principal = $5,400
Annual rate = 4% continuously
A = P.e^rt where n=1
A = 5,400 * e^(0.04*1)
A = 5,400 * 1.04081077419
A = 5620.378180626
A = 5620.378180626
A = $5,620.39.
In conclusion, the accrued value she will get after one years for this account is $5,620.39.
Referring to how much would Tyra's balance be from Account 2 over 3.7 years. It is calculated as follows:
Annual rate = 4% continuously
A = P.e^rt where n=3.7
A = 5,400 * e^(0.04*3.7)
A = 5,400 * e^0.148
A = 5,400 * 1.15951289636
A = 6261.369640344
A = $6,261.37
Therefore, the accrued value she will get after 3.7 years for this account is $6,261.37
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f(x) = 1 + 9. Find f '(x) and its domain.
A. f-1 (z) = (x – 9)?: x2 9
B. f-1(x) = (x – 9)?; x20
c. f-1 (2) = x2 – 9;x2 9
D. f-1 (x) = x2 – 9; x2 0
Answer:
B
Step-by-step explanation:
f(x) = sqrt(x) + 9
f(x) - 9=sqrt(x)
f^(-1)(x)=(x-9)^2 and it's domain is greater than 0
A local grocery store receives strawberries from suppliers in Florida and California. Currently there are 18 strawberry containers on the shelf and 11 of them are from Florida. A shopper selects three containers to purchase. What is the probability that exactly one of the containers is from the Florida supplier
Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 18 containers, hence [tex]N = 18[/tex]11 of those are in Florida, hence [tex]k = 11[/tex].A sample of 3 containers is taken, hence [tex]n = 3[/tex]The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831[/tex]
0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
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By how many minutes is 2¾h longer than 1h 55min?
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
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Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
What dimensions would you need to calculate the volume of a basketball?
radius and height
length, width and slant height
radius
length, width, and height
Answer:
Radius on it's own is enough
Step-by-step explanation:
you could get the radius from the other informations, but after all you will calculate the volume with it and not the otheds, so just take radius. a sphere is, in terms of information, the simplest 3D-body to describe, like with a circle in 2D
The dimensions would you need to calculate the volume of a basketball is Radius on its own is enough
We have given that,
radius and height
length, width, and slant height
radius
length, width, and height
We have to determine the dimensions would you need to calculate the volume of a basketball.
What is the dimension?
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.
you could get the radius from the other information, but after all, you will calculate the volume with it and not the others, so just take the radius.
A sphere is, in terms of information, the simplest 3D body to describe, like a circle in 2D.
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Find the missing side lengths leave your answer as a racials simplest form
Answer:
y=3 and x=3*sqrt(3)
Step-by-step explanation:
sin(30)=y/6
1/2=y/6, y=3. As it's a right angled triangle, 6^2-3^2=x^2, x=3*sqrt(3)
Answer:
x = 3 sqrt(3)
y = 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 30 = y /6
6 sin 30 = y
6 (1/2) = y
3 = y
cos theta = adj / hyp
cos 30 = x /6
6 cos 30 =x
6 ( sqrt(3)/2) =x
3 sqrt(3) = x
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. SAS Postulate
Answer:
HJ = FG
Step-by-step explanation:
SAS means side - (included) angle - side.
we have one angle confirmed (at H and at G).
we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.
so, we need the confirmation of the second side enclosing the confirmed angle.
Which of the following words is generally used to describe what managers do as opposed to what leaders do b) Organize c) Inspire O d) Innovate
Answer:
Innovate
Step-by-step explanation:
Straight forward
Write an equivalent fraction for each 1/4 = /10
Answer:
[tex]x = \frac{5}{2}[/tex]
Step-by-step explanation:
Step 1: Find an equivalent fraction
[tex]\frac{1}{4} = \frac{x}{10}[/tex]
[tex]4(x) = 1(10)[/tex]
[tex]4x = 10[/tex]
[tex]x = \frac{10}{4}[/tex]
[tex]x = \frac{5}{2}[/tex]
Answer: [tex]x = \frac{5}{2}[/tex]
Y=square root of x compare to y= - square root of x how they differ and why
Answer:
Simply because x=y2 doesn't imply that y=
√
x
.
what is the least common factor for 9 8 7
Answer:504
This is the answer
504
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
Find the probability that z lies between 0 and 1.56.
Answer:
P(0 < z < 1.56)=0.4406
Step-by-step explanation:
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
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Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
I need help ASAP thank you
Answer:D) Under-root 25.Under-root 3
Step-by-step explanation
Under-root 25 = 5
Answer:
Answer D and B.
Step-by-step explanation:
[tex]{ \bf{5 \sqrt{3} }} \\ = { \bf{ \sqrt{ {5}^{2} } \times \sqrt{3} }} \\ = { \bf{ \sqrt{25} . \sqrt{3} }}[/tex]
Complete the equation describing how X and Y are related X= -2, -1, 0, 1,2,3. Y= -8, -5,-2,1,4,7
Answer:
y = 3x - 2
Happy Studying
Mr. Rowley has 16 homework papers and 14 exit tickets to return. Ms. Rivera has 64 homework papers and 60 exit tickets to retum. For each teacher, write a ratio to represent the number of homework papers to number of exit tickets they have to return. Are the ratios equivalent? Explain.
Answer:
Mr. Rowley=16:14
=8:7
Ms.Rivera= 64:60
=16:15
HELP PLEASE HELP HELP
Answer:
The first one is the only one that makes sense.
Step-by-step explanation:
hope it helps!
Assuming that a person going to community college can't afford to go to a four-year college is an example of a) a generalization. b) discrimination. O c) a stereotype. O d) tolerance.
Answer:
a) generalization
Step-by-step explanation:
The statement is an example of a generalization. This is because the statement is assumming that all individuals who go to community college are poor. Therefore, this is why they cannot go to a four-year college, and instead go to a community college which is far cheaper. This assumption is being applied to all individuals who attend community college, without any further or more-specific information about each individual, therefore generalizing the entire situation.
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
Determine the sum of the measures of the exterior angles of a convex hexagon (6-sided polygon).
A. 540
B. 720
C. 1,080
D. 360
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Answer:
(d) 360°
Step-by-step explanation:
The sum of exterior angles of any convex polygon is 360°.
Một tàu biển trị giá 2.500.000 USD đang chở các lô hàng A, B,C có giá trị lần lượt là 100.000 USD; 300.000USD, 500.000USD và tiền cước chưa thu thuộc chủ tàu là 60.000 USD. Trong hành trình đi từ Indonesia về cảng Sài Gòn tàu bị mắc cạn, vỏ tàu bị thủng, nước tràn vào làm hư hỏng một số hàng hóa. Để cứu tàu và hàng, thuyền trưởng quyết định bịt lỗ thủng bằng các phương tiện trên tàu và vứt một số hàng để tàu nhẹ bớt, đồng thời thuyền trưởng cũng cho máy tàu làm việc vượt công suất nhằm giúp tàu thoát cạn. Sau sự việc, các tổn thất được xác định như sau:
- Vỏ tàu thủng dự kiến phải sửa chữa hết 100.000 USD
- Máy tàu hư do hoạt động quá công suất và dự kiến phải sửa hết 250.000 USD
- Lô hàng B bị nước tràn vào giảm giá trị thương mại 100%.
- Lô Hàng A bị vứt xuống biển toàn bộ.
- Thiệt hại để cứu tàu và chi phí cho thủy thủ trong việc cứu tàu là 10.000 USD.
a. Hãy xác định các tổn thất riêng của các bên
b. Hãy xác định tổng tổn thất chung của các bên
c. Hãy xác định giá trị chịu phân bổ tổn thất chung (giá trị đóng góp của từng chủ thể trên tàu)
d. Hãy xác định các khoản đóng góp vào tổn thất chung của các bên
Answer:
ask in English then I can help
Roulette is a casino game that involves spinning a ball on a wheel that is marked numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on a green space
Answer:
1/19
Step-by-step explanation:
There are a total of 36+2 = 38 spaces
2 are green
P(green) = green / total
= 2/38
=1/19
.052631579
The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
6. On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the midpoint of AB ?
A) 0
B) -2
C) -3
D) 4
9514 1404 393
Answer:
B) -2
Step-by-step explanation:
The midpoint is the average of the end points.
M = (A +B)/2
M = (-6 +2)/2 = -4/2 = -2
The coordinate of M is -2.
ABC are points; (2,3), (4,7), (7,3) respectively. Find the equation of the line through the point (3,-5) which is parallel to the line with the equation 3x+2y-5=0
Answer:
y = -3x/2 - 1/2
Step-by-step explanation:
slope m = -3/2
-5 = (-3/2)×3+b
or, b = -1/2
putting it into y = mx + b
y = -3x/2 - 1/2
Answered by GAUTHMATH
A jet flew 2660 miles in 4.75 hours. What is the rate of speed in miles per hour? (The proportion would be 2660 : 4.75 ::X:1 Set the proportion in fractional form and proceed to find x.)
Answer:
X = 560
Step-by-step explanation:
Speed = distance / time
Distance = 2660 miles
Time taken = 4.75 hours
Writing the equation in terms of proportion :
Rate or speed = Distance : time
Speed = 2660 : 4.75
Reducing to lowest term ;
Divide both sides by 4.75
Hence, we have ;
Speed = 2660/4.75 : 4.75/4.75
Speed = 560 : 1
Comparing with the proportion in the question, X = 560
