Answer:
L=13.715
Step-by-step explanation:
Given that
x=t + cos t
y= t - sin t
0 ≤ t ≤ 3π
[tex]\dfrac{dx}{dt}=1-sin\ t[/tex]
[tex]\dfrac{dy}{dt}=1-cos\ t[/tex]
We know that length of parametric curve given as
[tex]L=\int_{a}^{b}\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2}dt[/tex]
[tex]\left(\dfrac{dx}{dt}\right)^2=1+sin^2 t-2t\ sint[/tex]
[tex]\left(\dfrac{dy}{dt}\right)^2=1+cos^2 t-2t\ cost[/tex]
Now by putting the values
[tex]L=\int_{0}^{3\pi}\sqrt{3-2sin\ t-2cos\ t}\ dt[/tex]
Now by using calculator
L=13.715
To find the curve length for ( x = t + cos t ) and ( y = t - sin t ) over [tex]\( 0 \le t \le 3\pi \):[/tex]
1. Calculate derivatives:
[tex]\[ \frac{dx}{dt} = 1 - \sin t, \quad \frac{dy}{dt} = 1 - \cos t \][/tex]
2. Set up integral:
[tex]\[ L = \int_0^{3\pi} \sqrt{(1 - \sin t)^2 + (1 - \cos t)^2} \, dt \][/tex]
3. Simplify integrand:
[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]
4. Calculate numerically:
[tex]\[ L \approx 21.2694 \][/tex]
The curve length is approximately ( 21.2694 ).
To find the length of the curve given by the parametric equations ( x = t + cos t ) and ( y = t - sin t ) for[tex]\( 0 \le t \le 3\pi \)[/tex] , we use the formula for the arc length of a curve defined by parametric equations:
[tex]\[ L = \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt \][/tex]
1. **Find the derivatives of ( x ) and ( y ) with respect to ( t ):**
For [tex]\( x = t + \cos t \):[/tex]
[tex]\[ \frac{dx}{dt} = 1 - \sin t \][/tex]
For[tex]\( y = t - \sin t \):[/tex]
[tex]\[ \frac{dy}{dt} = 1 - \cos t \][/tex]
2. **Set up the integral for the arc length:**
[tex]\[ L = \int_0^{3\pi} \sqrt{\left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2} \, dt \][/tex]
3. **Simplify the integrand:**
[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 \][/tex]
Expand both terms:
[tex]\[ \left(1 - \sin t\right)^2 = 1 - 2\sin t + \sin^2 t \][/tex]
[tex]\[ \left(1 - \cos t\right)^2 = 1 - 2\cos t + \cos^2 t \][/tex]
Add the expressions together:
[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 = (1 - 2\sin t + \sin^2 t) + (1 - 2\cos t + \cos^2 t) \][/tex]
[tex]\[ = 1 - 2\sin t + \sin^2 t + 1 - 2\cos t + \cos^2 t \][/tex]
[tex]\[ = 2 - 2\sin t - 2\cos t + \sin^2 t + \cos^2 t \][/tex]
Recall that[tex]\( \sin^2 t + \cos^2 t = 1 \):[/tex]
[tex]\[ = 2 - 2\sin t - 2\cos t + 1 \][/tex]
[tex]\[ = 3 - 2(\sin t + \cos t) \][/tex]
So the integrand becomes:
[tex]\[ \sqrt{3 - 2(\sin t + \cos t)} \][/tex]
4. **Set up the integral for the arc length:**
[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]
5. **Calculate the integral:**
This integral is complex and generally requires numerical methods or a calculator to evaluate.
Using a calculator:
[tex]\[ L \approx \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \approx 21.2694 \][/tex]
Thus, the length of the curve, correct to four decimal places, is approximately ( 21.2694 ).
Sydney Blackwell manages an office building with leases of $60,000 per year. Her management agreement is for 7 years, with fees as follows: 7% the first year; 5% the second and third years; and 3 % the remaining years. What will be Sydney's total management fee?
Answer:
total management fee is $16200
Step-by-step explanation:
given data
leases = $60000 per year
time = 7 year
fees 1st year = 7%
fees 2nd and 3rd year = 5%
fees remaining year = 3%
to find out
total management fee
solution
we find here commission for each here
for 1st year = 7% of $60000 = $4200 ............1
for 2nd and 3rd year = 5% of $60000 = $3000 ............2
for remaining year = 3% of $60000 = $1800 ................3
and that is 4 year so fees = 1800 × 4 = $7200 ................4
now add all these to get total
total fees = 4200 + 3000 + 1800 + 7200
total fees = 16200
so total management fee is $16200
Sydney Blackwell's total management fee for a 7-year period, with varying annual rates applied to a $60,000 lease, amounts to $17,400.
Explanation:Calculating Sydney's Total Management Fee
To calculate Sydney Blackwell's total management fee for managing an office building, we need to apply the corresponding percentage rates to the annual lease amount over the span of the management agreement. The lease amount is $60,000 per year, and the management agreement spans 7 years with varying fees each year.
Here's the breakdown of fees per year and total fee calculation:
First year: 7% of $60,000 = $4,200Second and third years: 5% of $60,000 = $3,000 per year, for a total of $6,000 over two yearsRemaining four years: 3% of $60,000 = $1,800 per year, for a total of $7,200 over four yearsAdding up the fees from all years:
$4,200 + $6,000 + $7,200 = $17,400
Therefore, the total management fee Sydney will receive over the 7-year period is $17,400.
Zoey is reading a 100-page novel. If she averages reading 1 page in 1 minute, which is a reasonable estimate of the amount of time it will take her to read the novel? A) between 1 1/2 and 2 hours B) between 1 and 1/2 hours Eliminate C) between 2 and 3 hours D) between 0 and 1 hour
Answer:
The answer to your question is: letter A
Step-by-step explanation:
data
Book = 100 pages
Zoey reads 1 page per minute
Now we solve it using rule of three
1 page ------------------ 1 min
100 pages ---------------- x
x = 100x1/1 = 100 min will take Zoey to read the book
60 min ------------------ 1 hour
100 min --------------------- x
x = 100/60 = 10/6
and convert it to a mix fraction = 1 2/3 = 1 hour 40 minutes
Then, the answer is letter A
Answer:
A
Step-by-step explanation:
well since she reads 1 page per minute and there are 100 pages then that means it takes 100 minutes.
100 minutes= 1 2/3 hours which is in between 1 1/2 and 2 so the answer would be A
Alice and Bob play the following game: they start with an empty 2008x2008 matrix (p.s. take a wild guess which year this was) and take turns writing numbers in each of the 20082 positions. Once the matrix is filled, Alice wins if the determinant is nonzero and Bob wins if the determinant is zero. If Alice goes first, does either player have a winning strategy?
Answer:
Bob wins
Step-by-step explanation:
Think first in a simpler case. In a 2x2 matrix the determinant is zero if two columns or rows are proportional. So Alice writes the first number, then Bob write the same number in the same column but in the other row. Bob repeat the procedure after Alice's second number, and win.
If the matrix is nxn where n is even (like 2008) Bob will win following the previous procedure. Alice writes a number anywhere, Bob writes the same number in the same column in the above (or below) row. Every time Alice write a number in the same row as her first one, Bob copy that number in the above (or below) row. Any other rows are not important, i.e, the determinant will be zero with any values in them.
Simplify (-2)(-3)^2 -2(2 - 5)
To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.
Explanation:To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:
First, we calculate (-3)^2, which is equal to 9.Next, we substitute the values in the expression: (-2)(9) - 2(2 - 5).Then, we simplify the expression inside the parentheses: (-2)(9) - 2(-3).Multiplying -2 by 9 gives us -18, and multiplying 2 by -3 gives us -6.Finally, we subtract -6 from -18 to get the final result, which is -12.Therefore, the simplified expression is -12.
Learn more about Simplifying expressions here:https://brainly.com/question/29003427
#SPJ2
solve each
14 is 38% of what?
92% of what is 110
please explain how to do i wanna understand
Answer:
36.84119.57Step-by-step explanation:
"Of" means "times"; "is" means "=". Write the English expression as a math expression and solve for "what".
14 = 38% × what
14/0.38 = what ≈ 36.84 . . . . . . divide by the coefficient of "what"
14 is 38% of 36.84
__
92% × what = 110
what = 110/0.92 ≈ 119.57 . . . . . divide by the coefficient of "what"
92% of 119.57 is 110.
Sherita's club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more
boxes must they sell to raise $270?
A. 135 boxes
116 boxes
B.
c.
157 boxes
OD. 114 boxes
Answer: 156.7
Step-by-step explanation:
1.35x84= 113.4
270-113.4=156.60
Answer:
B
Step-by-step explanation:
1.35 x 84 = $113.40
270 - 113.40 = $156. 60
156.60 / 1.35 = 116 boxes
Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form.
2x + y − 3z= −20
x + 2y + z= −3
x − y + 5z= 19
What is the solution to the system of equations?
Take the augmented matrix,
[tex]\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right][/tex]
Swap the row 1 and row 2:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right][/tex]
Add -2(row 1) to row 2, and -1(row 1) to row 3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right][/tex]
Add -1(row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right][/tex]
Multiply through row 3 by 1/9:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right][/tex]
Add 5(row 3) to row 2:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right][/tex]
Multiply through row 2 by -1/3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]
Add -2(row 2) and -1(row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]
So we have [tex]\boxed{x=-3,y=-2,z=4}[/tex].
Answer:
1 0 0 -3
0 1 0 -2
0 0 1 4
AND
(-3, -2, 4)
Step-by-step explanation:
I don't have a step-by-step explanation because I still don't understand this sh*t myself. The reason I know it's the right answer is because I just got a 30% on my quiz and it shows you the right answers after. Good luck in this class! You're gonna need it.
You are considering two securities. Security A has a historical average annual return of 7% and a standard deviation of 3%. Security B has a historical average annual return of 7% and a standard deviation of 9%. From this information you can conclude that:
Answer:
Security B is riskier than Security A.
Step-by-step explanation:
Security A and B have the same historical average annual return which is 7%, meaning that both of them have had the same results over the years.
However, the standard deviation of A is 3% and the standard deviation of B is 9%, therefore we can conclude that Security A is safer than Security B because a low standard deviation indicates that the annual returns tend to be close to the average (mean), while a high standard deviation indicates that the annual returns are spread out over a wider range of values.
For example:
Security A has this values over the years:
6, 7, 8, 7 where mean is 7.
Security B has this values over the years:
1, 13, 4, 12 where the mean is also 7.
But, A has a lower standard deviation and B a higher one, therefore, Security B is riskier.
Midpoint of ST is (5,-8). T is (4.5,-2.5) Find S.
Answer:
(5.5, -13.5)
Step-by-step explanation:
Midpoint M satisfies ...
M = (S +T)/2
So ...
2M = S + T
2M -T = S
2(5, -8) -(4.5, -2.5) = S = (10 -4.5, -16 +2.5)
S = (5.5, -13.5)
Brian is a salesman at a furniture store. He is paid a weekly salary of $300 plus a 10% commission on any sale he closes. Last week, Brian was paid $900. How much merchandise did Brian sell last week?
A.) $6000
B.) $4500
C.) $2000
D.) $5000
E.) $2500.
Answer:
here merchandise sell is $6000
correct option is A
Step-by-step explanation:
given data
salary = $300 + 10 % commission
paid = $900
to find out
merchandise sell
solution
we consider here sell is x
so paid will be
paid = salary + 10% of x
so here put value
900 = 300 + 10% × x
900 - 300 = 10% × x
x = 600 / 10%
x = 6000
so here merchandise sell is $6000
correct option is A
Write this expression in standard form by collecting like terms:
9 (a - b) + 5 (2a - 2b)
A. 14a - 14b
B. 8a - 7b
C. 19a - 19b
D. -19a + 14b
please help asap, thank you!
9 (a - b) + 5 (2a - 2b)
mutiply the first bracket by 9
(9)(a)= 9a
(9)(-b)= -9b
mutiply the second bracket by 5
(5)(2a)=10a
(5)(-2b)= -10b
9a-9b+10a-10b
9a+10a-9b-10b ( combine like terms)
Answer : C. 19a - 19b
To simplify the expression 9(a - b) + 5(2a - 2b), we first distribute each term in the parentheses by the factor outside the parentheses and then gather like terms, getting 19a - 19b.
Explanation:To solve this problem, we need to distribute each term in the parentheses by their respective factor outside the parentheses and then collect like terms.
Step 1: Distribute the terms
9(a - b) becomes 9a - 9b
5(2a - 2b) becomes 10a - 10b
Step 2: Collect like terms
9a + 10a = 19a
-9b - 10b = -19b
So, the expression 9(a - b) + 5(2a - 2b) simplifies to 19a - 19b, which is answer choice C.
Learn more about Simplifying Algebraic Expressions here:https://brainly.com/question/36963724
#SPJ3
PLEASE!!! HELP NEEDED!!!
Given the following equation, x^4 - x^3 - 3x - 2. Use synthetic division to test the following 3 points and show which one is a root. Must show synthetic division for all 3 of the following test points. Test these 3 possible root points also called possible zeros using synthetic division: (x,y) = (-1, 0) (-3, 0) (2, 0).
PLEASE SHOW YOUR WORK!!!
Answer:
(x, y) = (-1, 3), (-3, 115), (2, 0)
Step-by-step explanation:
The first two test points are not roots. The last one is a root.
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
A. $0.60B. $0.70C. $0.80D. $0.90E. $1.00
Answer:
Option B. $0.70
Step-by-step explanation:
First day fine = $0.10
Second day fine (doubled or $0.30 which is lesser)
= $0.10 + $0.10 [$0.10 is lesser than $0.30]
= $0.20
Third day fine = $0.20 + $0.20 [ $0.20 is lesser than $0.30]
= $0.40
Fourth day fine = $0.40 + $0.30 = $0.70
[$0.30 is cheaper than doubling the amount $0.40 + $0.40]
Therefore, the total fine for a book on the fourth day is $0.70
If a company charges x dollars per item, it finds that it can sell 1500 - 3x of them. Each item costs $8 to produce.
(a) Express the revenue, R(x), as the function of price.
(b) Express the cost, C(x), as a function of price.
(c) Express the profit, P(x), which is revenue minus cost, as a function of price.
The profit is $496.30
a. The revenue function will be calculated thus:
R(x) = (1500 - 3x) × x
R(x) = 1500x - 3x²
b. The cost function will be:
C(x) = 8 × x = 8x
c. The profit function will be:
P(x) = Revenue - Cost
= 1500x - 3x² - (8x)
= 1500x - 3x² - 8x
Divide through by x
= (1500x - 3x² - 8x) / x
= 1500 - 3x - 8
1500 - 3x - 8 = 0
Collect like terms
3x = 1500 - 8.
3x = 1492
x = 1492/3
x = 496.3
The profit is $496.30
Read related link on:
https://brainly.com/question/10921760
The area of the southern ocean is about 7.85 x 10^6 square miles. The difference between the areas of the indian ocean and the southern ocean is about 1.865 x 10^7 square miles. Explain how to find the area of the indian ocean. Then find the area.
Answer:
The answer to your question is: 2.65 x 10⁷ square miles
Step-by-step explanation:
Data
Southern ocean area = 7.85 x 10⁶ square miles
Difference between areas Indian ocean = 1.865 x 10⁷ square miles
and the southern ocean
Process
a) To find the area of the Indian ocean we need to sum of the values of the area of the Southern ocean and the area of the difference between the Indian ocean and the southern ocean.
b)
Area of the Indian Ocean = 1.865 x 10⁷ + 7.85 x 10⁶
= 2.65 x 10⁷ square miles
Answer:
The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Step-by-step explanation:
Given : The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles. The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
To find : Explain how to find the area of the Indian ocean. Then find the area.
Solution :
The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles.
i.e. [tex]A_s=7.85\times 10^6[/tex]
The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
i.e. [tex]A_i-A_s=1.865\times 10^7[/tex]
Substitute the value of [tex]A_s[/tex]
[tex]A_i-7.85\times 10^6=1.865\times 10^7[/tex]
[tex]A_i=1.865\times 10^7+7.85\times 10^6[/tex]
[tex]A_i=1.865\times 10^7+0.785\times 10^7[/tex]
[tex]A_i=(1.865+0.785)\times 10^7[/tex]
[tex]A_i=2.65\times 10^7[/tex]
Therefore, The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Solve the inequality.
[tex]12( \frac{1}{2} \times - \frac{1}{3} ) > 8 - 2 \times [/tex]
A.
[tex] \times > - \frac{1}{2} [/tex]
B.
[tex] \times > \frac{3}{2} [/tex]
C.
[tex] \times > \frac{1}{2} [/tex]
D.
[tex] \times > 3[/tex]
A package of 4 mechanical pencils comes with 2 free erasers. If you get a total of 12 free erasers, how many packages of pencils did you buy? If you get 18 free erasers,how many packages of pencils did you buy?
Answer:
6 packs, 9 packs
Step-by-step explanation:
The ratio of mechanical pencil to free eraser is 2:4, or 1:2.
So that means, for every free eraser you get, you bought the double amount of pencils.
12 free erasers x 2 = 24 pencils
18 free erasers x 2 = 36 pencils
And a pack of pencils contains 4.
24/4 = 6 packs
36/4 = 9 packs
Answer:
6 packs and 9 packs
Step-by-step explanation:
NEED A QUICK ANSWER.
solve for x.
Enter your answer in the box.
x =
°
brainliest will be given to whoever answers correctly.
90 + x + 107 + 144 + 138 = 540
479 + x = 540
x = 540 - 479
x = 61
Answer:
x=61°
Step-by-step explanation:
There are 5 sides in a polygon.
Sum of interior angles = (n-2) times 180
[tex](5-2) \cdot 180=540[/tex]
The sum of interior angles in a polygon is 540 degree
Now add all the interior angles and set it to 540
Right angle is 90 degree
[tex]90+x+138+144+107= 540[/tex]
[tex]479+x= 540[/tex]
Subtract 479 from both sides
[tex]x=61[/tex]
Let M ∈ N >1 . Let M be a non-perfect square. Or in other words M /∈ {4, 9, 16, · · · } (a) Prove that there exists a prime p, whose exponent in the prime factorization of M is odd. [Hint: Prove by a method of contradiction]
Answer:
Step-by-step explanation:
By the fundamental theorem of arithmetic given [tex]n\in \mathbb{N}_{\ge2}[/tex] there exists primes [tex]p_{i}[/tex] and integers [tex]\alpha_i[/tex] such that [tex]n[/tex] can be written as [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}[/tex], now suppose that [tex]n[/tex] is a non-perfect square, we are going to prove that there exists [tex]\alpha_i[/tex] such that is odd. By contradiction, suppose that [tex]\alpha_i[/tex] is even for all [tex]i[/tex], then writing [tex]\alpha_i=2\beta_i[/tex] for all [tex]i[/tex], we can write [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}= p_1^{2\beta_1}p_2^{2\beta_2}p_3^{2\beta_3}\cdots p_t^{2\beta_t}=(p_1^{\beta_1}p_2^{\beta_2}p_3^{\beta_3}\cdots p_t^{\beta_t})^2[/tex], thus we conclude that [tex]n[/tex] is perfect square, a contradiction, and then we conclude that there exists [tex]\alpha_i[/tex] such that is odd.
What is the solution to this system of equations?
4x−3y=26
3x+2y=11
5,2
8,2
-2,5
5,-2
Answer:
(x, y) = (5, -2)
Step-by-step explanation:
A graphing calculator provides a quick and easy way to find the solution.
_____
There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:
The intercepts of the first equation are ...
x-intercept = 26/4 = 6 1/2y-intercept = -26/3 = -8 2/3So the graph of it will form a triangle with the axes in the 4th quadrant.
The intercepts of the second equation are ...
x-intercept = 11/3 = 3 2/3y-intercept = 11/2 = 5 1/2So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.
The only 4th-quadrant answer choice is (5, -2).
Which of the following is a factor of 5x3 − 135?
135
x + 3
x2 + 3x + 9
x - 5
Answer:
The answer to your question is:
Step-by-step explanation: The third one is a factor
Factor
5x³ − 135
Find the prime factors of 135
135 3
45 3
15 3 Then 135 = 3³ x 5
5 5
1
5x³ - 5(3)³
Factor 5
5[ x³ - (3)³]
5 [ (x - 3)(x² + 3x + 9)]
Answer:
5 [ (x - 3)(x² + 3x + 9)]
Step-by-step explanation:
IF the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.
a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?
Answer:
a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel
b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel
c. The wheel was moving at 0.70 [tex]\frac{rad}{min}[/tex]
Step-by-step explanation:
Navy pier wheel circumference = Cn
First ferris wheel circumference = Cf
Cn = 0.56*Cf
a.
Circumference Perimeter = 2*π*Radius
Navy pier wheel radius = Rn
First ferris wheel radius = Rf
Cn = 0.56*Cf
2*π*Rn = 0,56*2*π*Rf (equation 1)
dividing both sides by 2π
Rn = 0,56*Rf
b.
From equation 1
2*π*Rn = 0,56*2*π*Rf
dividing both sides by 2π
Rn = 0.56*Rf
dividing both sides by 0.56
Rf = [tex]\frac{1}{0.56}[/tex]*Rn
Rf = 1.79*Rn
c.
9 minutes / revolution
1 revolution = 2π radians
The wheel makes 2π radians in 9 minutes
Wheel velocity = [tex]\frac{2\pi }{9} \frac{rad}{min}[/tex]
Wheel velocity = 0.70 [tex]\frac{rad}{min}[/tex]
For FHG find the measure of the smallest angle
Answer:
m∠HFG=16°
Step-by-step explanation:
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
In this problem
m∠HFG+m∠GHF+m∠HGF=180°
we have
m∠GHF=92°
m∠HGF=72°
substitute the given values and solve for m∠HFG
m∠HFG+92°+72°=180°
m∠HFG+164°=180°
m∠HFG=180°-164°
m∠HFG=16°
For the lines defined by the following equations indicate with a "V" if they are vertical, an "H" if they are horizontal, and an "S" (for slanted) if they are neither vertical nor horizontal. S 3x+4y+5=0
Answer:
The answer is the function 3x+4y+5=0 is Slanted
Step-by-step explanation:
To be able to to know if this function is horizontal, vertical or slanted we should look at the gradient.
If the gradient is zero, then the line is horizontal.
If the gradient is infinite, then the line is vertical.
if not, then the line is slanted
We can look the gradient by the general form equation of a line:
y = mx + c
where y = dependent variable, x = independent variable, m = gradient, c = intercept.
With our equation, we can change things around to get the general form equation:
3x + 4y + 5 = 0
4y = 3x - 5
[tex]y = \frac{3}{4}x - \frac{5}{4}[/tex]
Where the gradient is 3/4
Therefore, as the gradient is a number other than zero or infinite, we know that this function is slanted.
3. The population of Columbus, Ohio, in 2014 was about 823,000. The population of the United States was about 319 million in 2014. (a) Write each population in scientific notation. (b) About how many times larger was the population of the United States than the population of Columbus, Ohio? Show your work. Answer:
Answer:
The answer to your question is:
a)
8.23 x 10 ⁵
3.19 x 10⁸
b)
387.6 ≈ 388 times
Step-by-step explanation:
Columbus, Ohio population = 823, 000
United states population = 319 million
a)
823 000 = 8.23 x 10 ⁵ move the decimal point 5 places to the left
319 000 000 = 3.19 x 10⁸ move the decimal point 8 places to the left
b)
To find the answer, just divide the USA population by the Columbus, Ohio population
3.19 x 10⁸ / 8.23 x 10 ⁵ = 387.6 ≈ 388 times
Final answer:
a) The population of Columbus, Ohio in scientific notation is 8.23 × 10⁵ and that of the United States is 3.19 × 10⁸. and b) the US population is 388 times larger as compared to Columbus.
Explanation:
a)The population of Columbus, Ohio, in 2014 was about 823,000. This can be written in scientific notation as 8.23 × 10⁵.
The population of the United States in 2014 was about 319 million. In scientific notation, this is 3.19 × 10⁸.
b) To determine how many times larger the population of the United States was than the population of Columbus, Ohio, we divide the population of the United States by that of Columbus:
3.19 × 10⁸ / 8.23 × 10⁵ = 387.605 approx 388 times larger
Therefore, the population of the United States was about 388 times larger than the population of Columbus, Ohio in 2014.
Take as input two opposite corners of a rectangle: (x1,y1) and (x2,y2). Finally, the user is prompted for the coordinates of a third point (x,y). Find whether the point (x,y) lies inside the rectangle.
Answer:
The answer is a point [tex](x,y) / x1\leq x\leq x2 , y1\leq y\leq y2[/tex]
Step-by-step explanation:
That happens because the points you have are in opposite corners, which means that they are the limits of the rectangle. so any point inside the rectangle is between that segment
Could someone just show me how to solve this? I don't want an answer, I would like to solve it on my own, I just don't know how to write an equation for this. Please help!
You would set up a ratio for the two known sides to equal the known side and x:
8/2 = 18/x
Cross multiply:
(2 * 18) = (8 * x)
Simplify:
36 = 8x
Solve for x by dividing both sides by 8:
x = 36/8
x = 4.5
Point \blue{A}Astart color blue, A, end color blue is at \blue{(-4, 8)}(−4,8)start color blue, left parenthesis, minus, 4, comma, 8, right parenthesis, end color blue and point \purple{M}Mstart color purple, M, end color purple is at \purple{(1, 7.5)}(1,7.5)start color purple, left parenthesis, 1, comma, 7, point, 5, right parenthesis, end color purple. Point \purple{M}Mstart color purple, M, end color purple is the midpoint of point \blue{A}Astart color blue, A, end color blue and point \green{B}Bstart color green, B, end color green. What are the coordinates of point \green{B}Bstart color green, B, end color green?
Answer:
The coordinates of point B are (6,7).
Step-by-step explanation:
Given points are
Blue = A(-4,8)
Purple = M(1,7.5)
Green = B
It is given that point M is the midpoint of point A and B.
Let coordinates of points are (a,b).
Midpoint of two points is
[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]M=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]
Coordinates of midpoint are (1,7.5).
[tex](1,7.5)=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]
On comparing both sides we get
[tex]1=\dfrac{-4+a}{2}\Rightarrow 2=-4+a\Rightarrow a=6[/tex]
[tex]7.5=\dfrac{8+b}{2}\Rightarrow 15=8+b\Rightarrow b=7[/tex]
Therefore, the coordinates of point B are (6,7).
what is the probability of drawing a black card or a card with a letter?
Standard deck of 52
A:
4/12
1/2
21/26
17/26
Answer:
17/26.
Step-by-step explanation:
Prob(Drawing a black card) = 26/52 = 1/2.
Prob(Drawing a card with a letter)
= Prob( Ace, King, Queen or Jack of either Hearts or Diamonds)
= 8/52.
So the required probability = 26/52 + 8/52
= 34/52
= 17/26.
and a list of numbers the pattern increases by 0.001 as you move to the right if the third number list is 0.0 64 what is the first number in the list answer
Answer:
0.062
Step-by-step explanation:
The numbers will decrease by 0.001 as you move the the left, so the list of numbers can be found as ...
3rd number: 0.064
2nd number: 0.064 -0.001 = 0.063
1st number: 0.063 -0.001 = 0.062