Answers
Step-by-step explanation:
x² + (y − 1)² = 9
This is a circle with center (0, 1) and radius 3. We can parameterize it using sine and cosine.
Use the starting point to determine which should be sine and which should be cosine.
Use the direction to determine the signs.
Use the number of revolutions and the interval to determine coefficient of t.
(A) Once around clockwise, starting at (3, 1). 0 ≤ t ≤ 2π.
The particle starts at (3, 1), which is 0 radians on a unit circle. It makes 1 revolution (2π radians). Therefore:
x = 3 cos t
y = 1 − 3 sin t
(B) Two times around counterclockwise, starting at (3, 1). 0 ≤ t ≤ 4π.
The particle starts at (3, 1), which is 0 radians on a unit circle. It makes 2 revolutions (4π radians). Therefore:
x = 3 cos t
y = 1 + 3 sin t
(C) Halfway around counterclockwise, starting at (0, 4). 0 ≤ t ≤ π.
The particle starts at (0, 4), which is π/2 radians on a unit circle. It makes 1/2 revolution (π radians). Therefore:
x = -3 sin t
y = 1 + 3 cos t
Related Questions
how many even integer numbers are between 12/5 and 56/5
Answers
Answer:
4
Step-by-step explanation:
12/5=2.4
56/5=11.2
so the even integers between them are
4,6,8, and 10
4 inegers
There are four even integers number that lies between 12/5 and 56/5. Then the numbers are 4, 6, 8, and 10.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.
If the integer number is divisible by 2, then the number will be known as even number.
The two integers are 12/5 and 56/5.
Convert the numbers into decimal form.
2.4 and 11.2
There are 4 even integers that are 4, 6, 8, and 10.
There are four even integers number that lies between 12/5 and 56/5. Then the numbers are 4, 6, 8, and 10.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos or videos online that they have taken themselves. Let A be the event an Internet user posts photos that they have taken themselves, and B be the event an Internet user posts videos that they have taken themselves. A research center finds that P(A) = 0.47, P(B) = 0.28,and P(A or B) = 0.52.
Required:
What is the conditional probability that an Internet user posts photos that they have taken themselves, given that they post videos that they have taken themselves?
Answers
Answer:
0.82
Step-by-step explanation:
Given:
A be the event that an Internet user posts photos taken by themselves.
B be the event that an Internet user posts photos taken by themselves.
P(A) = 0.47
P(A) = 0.28
P(A or B) = [tex]P(A\cup B)[/tex] = 0.52
To find:
Conditional probability that an Internet user posts photos given that they post videos.
OR
P(A/B) = ?
Solution:
Formula to be used to find the required conditional probability:
[tex]P(A/B) = \dfrac{P(A \cap B)}{P(B)}[/tex]
For this, [tex]P(A \cap B)[/tex] is required.
Formula
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.52=0.47+0.28-P(A\cap B)\\\Rightarrow P(A\cap B)=0.23[/tex]
Now, the required conditional probability is:
[tex]P(A/B) = \dfrac{P(A \cap B)}{P(B)}\\\Rightarrow P(A/B) = \dfrac{0.23}{0.28}\\\Rightarrow \bold{P(A/B)} = 0.82}[/tex]
So, the answer is 0.82.
What is the meaning of the expression (94+33)-3
Answers
124
i added 94+33 then substracted 3 hope it helps you
I need help fast! This is polynomials help
Answers
Answer:
incorrectcorrectincorrectStep-by-step explanation:
A + B = (-4x^2 +2x -5) +(3x^2 +6) = x^2(-4+3) +x(2) +(-5+6) = -x^2 +2x +1
The given sum is Incorrect.
__
A - C = (-4x^2 +2x -5) -(-5x -4) = -4x^2 +x(2+5) +(-5+4) = -4x^2 +7x -1
The given difference is Correct.
__
B + C = (3x^2 +6) +(-5x -4) = 3x^2 -6x +2
The given sum is Incorrect.
Which of the following represents the shaded area as a fraction, a decimal, and a percent of the whole?
Answers
Answer:
3
Step-by-step explanation:
What is the value of y?
Answers
-6 -6
46/14=14x/14
3.28
So- all the sides of the triangle is 180 degrees, right? And you are trying to find y.
I think the first equation would be y+(x+6)+52=180
Let’s solve that.
It would be y+(x+6)= 128 is y+x=122
Then y=122-x, if you move x over to the right.
Note: If there are two variables, then there should be 2 equations to solve this questions. The first equation was the equation we just went over with, and we found what y was.
Now that we found what y was, let’s move it to our regular equation: y+(x+6)+52=180
It would become 122-x+(x+6)=180!
Let’s solve that.
122-x+x+6=180
—> 122-x+x=174
—>-x+x=52
—>0=52
Therefore, I think it is impossible to find x...in my opinion.
Even though finding x is impossible, y would be 52, because angle 52 and angle y are the same.
M/n: I never tried college math before, so you can just mentally slap me if this is wrong.
Answer: Y=52degrees
4/7 x 9/20 will give brainliest
Answers
Answer:
9/35 or 0.2571428
Answer:
9/35 (Already Simplified)
Step-by-step explanation:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
4×97×20=36140
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 36 and 140 using
GCF(36,140) = 4
36÷4140÷4=935
Therefore:
47×920=935
Solution by Formulas
Apply the fractions formula for multiplication, to
47×920
and solve
4×97×20
=36140
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(36,140) = 4
36÷4140÷4=935
Therefore:
4/7×9/20=9/35
In George's school, 0.386 of the students participated in an event. If there are one thousand students in George's school, how many participated in the event?
Answers
Plz help!!
Point H is the circumcenter of triangle DEF.
Which must be true? Select two options.
Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
Line segment H E is-congruent-to line segment H D
Line segment L H is-congruent-to line segment N H
Line segment F L is-congruent-to line segment F N
Answers
Answer:
a & c
Step-by-step explanation:
edge
Answer:
A. Point H is the center of the circle that passes through points D, E, and F
C. HC≈HD
Maria and John decide to shop for furnishings for the new house. They choose items that amount to $5600.00. The store has 2 fixed installment simple interest loan options for purchasing:
Option 1: 20% down payment and financing at 5% simple interest per year for 3 years.
Option 2: no down payment and financing at 5.25% simple interest for 4 years.
Answer each of the following questions separately, showing all your work to reach each answer.
A. Which option will result in smaller finance charge (interest)? What will that finance charge/interest be?
B. Which option will result in the smaller monthly payment on this fixed installment loan? What will that monthly payment be?
C. They decide to defer any purchases and invest a $5600 bonus that Maria will be getting from work in a savings account. The APR is 21.6% compounded monthly. How much interest will they earn in 4 years?
D. They decide to defer any purchases and loan the $5600 bonus to a needy relative at 1.5% simple interest per year. How long will the term of the loan need to be if they want to earn $500 in interest (assuming the loan is not paid off early).
Answers
Answer:
A. The option that results in the smaller finance charge/interest is option 1
B. The option that will result in the smaller monthly payment is option 1
C. The interest they will earn in 4 years, I = $6,643.972
D. The time it will take for them to earn an interest of $500 by loaning $5,600 at 1.5% is approximately 5.95 years
Step-by-step explanation:
A. The simple interest, I, formula is given as follows;
[tex]I = \dfrac{P \times R \times T }{100}[/tex]
Where;
P = The principal
R = The rate
T =The time given for the loan
For Option 1 the first option, we have;
Down payment = 0.2 × $5600.00 = $1,120.00
Principal = $5600.00 - $1,120.00 = $4,480.00
[tex]\therefore I = \dfrac{\$ 4480\times 5 \times 3 }{100} = \$672[/tex]
For Option 2. the second option, we have;
P = $5600.00
[tex]\therefore I = \dfrac{\$ 5600 \times 5.25 \times 3 }{100} = \$1176[/tex]
The option that results in the smaller finance charge is option 1
B. For option 1, the total amount = Principal + Interest
∴ The total amount remaining = $4480 + $672 = $5,152
The monthly payment = A/N
Where;
A = The total amount yet to be paid out of the loan = $5,152
N = The number of time periods = 3 × 12 = 36 months
The monthly payment = $5,152/36 = [tex]\$ 143.\overline{111}[/tex]
For option 2, the total amount = Principal + Interest
∴ The total amount remaining = $5,600 + $1176 = $6776
The monthly payment = A/N
Where;
A = The total amount yet to be paid out of the loan = $6,776
N = The number of time periods = 3 × 12 = 36 months
The monthly payment = $6,776/36 = [tex]\$ 188.\overline{222}[/tex]
Therefore, the option that will result in the smaller monthly payment is option 1
C. For a compound interest on a principal of $5,600 invested for 4 years in a savings account that gives an interest rate 21.6% per annum, we have;
[tex]A = P \times \left(1 + \dfrac{r}{n} \right)^{(n\times t)}[/tex]
We have, using the annual rate, rather than calculating for the monthly rate;
[tex]A = 5600 \times \left(1 + 0.216 \right)^{4} \approx 12243.972[/tex]
Therefore, the amount they will have in 4 years ≈ $ 12,243.972
The interest they will earn in 4 years, I = A - P ≈ $ 12,243.972 - $5,600 = $6,643.972
The interest they will earn in 4 years, I = $6,643.972
D. To earn an interest of $500 at an interest rate of 1.5%, we have;
[tex]500 = \dfrac{5600 \times 1.5 \times T}{100} = 84 \times T[/tex]
From which we have;
[tex]T = \dfrac{500}{84} = \dfrac{125}{21} = 5\frac{20}{21} \approx 5.95[/tex]
Therefore, the time it will take for them to earn an interest of $500 by loaning $5,600 at 1.5% is approximately 5.95 years.
Marlene decided to buy 2 bags of apples weighting 3 1/4 pounds each, instead of buying 3 bags weighting 2 2/5 pounds each. Did she end up with more apples or fewer apples but buying bigger bags
Answers
Answer:
c onedge
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
QUADRATIC FORMULA
X = ?
Answers
Answer:
quad form is (plus or minus)
Step-by-step explanation:
[tex]-b +-\sqrt{b^2-4ac}/2a[/tex]
Answer:
x=5
Step-by-step explanation:
well first 2(2x-5) turns to 4x-10 because of distributive prperty
then simplify the other side 3x+x-2x to 4x-2x to 2x
then subtract 4x from both sides and you get -10= -2x
after divied -2x/-2 and -10/-5
and get x=5
then plug in 5 into x to make sure both sides are equal
and they equal 10=10
Which equation can be used to graph the line that passes through (6,15) and is perpendicular to the graph y-7= 1/2 (x+2)
Answers
Answer:
Option A. y = –2x + 27
Step-by-step explanation:
y – 7 = ½(x + 2)
We'll begin by calculating the slope of the equation above. This can be obtained as follow:
y – 7 = ½(x + 2)
Clear bracket
y – 7 = ½x + 1
Rearrange
y = ½x + 1 + 7
y = ½x + 8
Comparing
y = ½x + 8
with
y = mx + c
The slope (m) = ½
Next, we shall determine the slope (m2) of the equation perpendicular to the line. This can be obtained as follow:
For perpendicularity,
m1 × m2 = –1
m1 = ½
½ × m2 = –1
m2 /2 = –1
Cross multiply
m2 = 2 × –1
m2 = –2
Therefore, the slope of the equation perpendicular to the line is –2
Finally, we obtained the equation of the line as follow:
Coordinate = (6, 15)
x1 coordinate = 6
y1 coordinate = 15
Slope (m) = –2
y – y1 = m(x – x1)
y – 15 = –2(x – 6)
Clear bracket
y – 15 = –2x + 12
Rearrange
y = –2x + 12 + 15
y = –2x + 27
Therefore, the equation is y = –2x + 27
I will give you brainliest if you answer this
The predicted high temperature for yesterday was 55 ℉. The actual high temperature was 47 ℉. Calculate the percent error.
Answers
Task #4: Waiting in Line You’re attending a concert with five friends but each of you arrived at the venue at different times. The fractions below tell how much of the distance they have already moved since they got in line. (Think about fractions as area models if you need some help!) You 3 / 4 Andrea 1/ 2 Bart 4 /5 Camden 7 /8 Drake 3/ 7 Ethan 2 /3 1. Who do you know is not going to get in the gate first? 2. How do you know? 3. Who is getting in the gate first? Who is getting in the gate last?
Answers
Step-by-step explanation:
Given data:
You = 3/4
Andrea = 1/2
Bart = 4/5
Camden = 7/8
Drake = 3/7
Ethan = 2/3
1. Drake would not be getting into the gate first because he is far behind at 3/7.
2. each fraction represents how far each have travelled Or moved on the line. Just like how you have move 3/4 on the line which represents three quarter of the line, and Andrea has moved half way through the line at 1/2.
3. Camden 7/8 would get to the get first and Drake 3/7 would get in last.
-6 - (-8) + 6 =
What is the value?
Answers
Answer:
The answer is 8
Step-by-step explanation:
use order of operations.
*remember that there is an understood -1 in -(-8). this can also be written as -1(-8)*
[tex]-6-(-8)+6\\-6+8+6\\2+6\\8[/tex]
hope this helps!
If f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to (f circle g) (10)?
Answers
Answer:
37
Step-by-step explanation:
Answer:
it's A
Step-by-step explanation:
on edg
Which relation is a function? It would be epic if you answer today lol
Answers
Answer:
Step-by-step explanation:
Pretty sure it's the third picture where it makes a U shape, since it passes the vertical line test.
Determine the degree of the polynomial -57
Answers
Answer:
linear polynomial
Step-by-step explanation:
as no degree is given
Name the remainder for the quotient and describe or show how you found the remainder.
(x^3 - x^2 - 17x -15) ÷ (x-5)
Answers
Answer:
Step-by-step explanation:
The expression x^3 - x^2 - 17x -15) ÷ (x-5) shows that x+5 is one of the factor if the polynomial function. According to factor theorem, we will equate the factor to zero and find x;
x+5 = 0
x = -5
Next is to generate the remainder.
Substitute x = -5 into the polynomial function
P(x) = x^3 - x^2 - 17x -15
P(-5) = (-5)^3 - (-5)^2 - 17(-5) -15
P(-5) = -125-25+85-15
P(-5) = -150+70
P(-5) = -80
Hence the remainder is -80
Answer:
Qoutient=x^2+4x+3
Remainder=0
-3/5 divided by - 3/4 PLEASE HURRY make it in simplest form please
Answers
Answer: Exact Form: 4 /5
Decimal Form: 0.8
Step-by-step explanation:
Answer:
Step-by-step explanation:
Cancel -3
[tex]\frac{1}{5x4}[/tex]
Simplify 5 x 4 to 20.
[tex]\frac{1}{20}[/tex]
Decimal Form: 0.05
what is set builder notation of[1, 3,5,39]
Answers
Answer:
{ x : x = odd natural numbers < 41 }
Step-by-step explanation: Hope this helps!
Find area of triangle. Picture included.
Answers
Answer:
5040
your welcome
Answer:
A=35
hope this helps
can you also please mark me as brainliest?
Desperate need for help!
Maths!
Will award brainliest!
Answers
Step-by-step explanation:
fg(x) =
[tex] {(x - 4)}^{2} + 3(x - 4)[/tex]
=
[tex] {x}^{2} + 16 - 8x + 3x - 12[/tex]
=
[tex] {x}^{2} - 5x + 4[/tex]
What is the slope between the two points (9,7) and
(5,5)
Answers
Answer:
The answer is
[tex] \huge \boxed{ \frac{1}{2} }[/tex]
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(9,7) and (5,5)
The slope is
[tex]m = \frac{5 - 7}{5 - 9} = \frac{ - 2}{ - 4} = \frac{2}{4} = \frac{1}{2} \\ [/tex]
We have the final answer as
[tex] \frac{1}{2} \\ [/tex]
Hope this helps you
what is (3 x 10) + (4 x 1) + (5 x 1/10) + (5 x 1/100) + (6 x 1/1000)
Answers
Answer:
34.556
Step-by-step explanation:
Hope this helps!
Determine the slope of line (AB) and the slope of line (CD). Determine whether line (AB) and line (CD) are parallel, perpendicular, or just intersecting (neither). Points A and B line on the line y = 2/3x + 4. Points C and D line on the line 6x + 4y = 16.
Answers
Answer:
The slopes are perpendicular
Step-by-step explanation:
Points A and B line on the line y = 2/3x + 4.
This line is in the form
y = mx+b where m is the slope
The slope is 2/3
Points C and D line on the line 6x + 4y = 16.
Solve for y
6x+4y = 16
4y = -6x +16
Divide by 4
4y/4 = -6/4x + 16/4
y = -3/2 x +4
The slope is -3/2
The slopes multiply to -1
2/3 * -3/2 = -1
so they are perpendicular
kest kuy is offering a sale on its laptop computers with a 20 percent discount off its original price. there is 8% sales tax added to the discounted price to get the final price of the computer. if x is the original price and y is the final price, write an equation to determine the final price based upon the original price.
Answers
Answer:
[tex]y = 0.88x[/tex]
Step-by-step explanation:
Given
[tex]Discount = 20\%[/tex]
[tex]Sales\ Tax = 8\%[/tex]
Required
Determine the final price
First, we need to determine the sales price after the discount.
[tex]Discount = 20\% * x[/tex]
[tex]Discount = 0.20 * x[/tex]
[tex]Discount = 0.20x[/tex]
[tex]Sales\ Price = x - Discount[/tex]
[tex]Sales\ Price = x - 0.20x[/tex]
[tex]Sales\ Price = 0.80x[/tex]
Next, is to determine the sales tax.
[tex]Sales\ Tax = 8\% * x[/tex]
[tex]Sales\ Tax = 0.08 * x[/tex]
[tex]Sales\ Tax = 0.08x[/tex]
Final Price, y is then calculated as thus:
[tex]y = Sales\ Price + Sales\ Tax[/tex]
[tex]y = 0.80x + 0.08x[/tex]
[tex]y = 0.88x[/tex]
Find the distence between each pair points (-4,-1) (-3,3)
Answers
Answer:
4.1231 or 4
Step-by-step explanation:
Two random variables x and y are independent if the value of x does not affect the value of y. If the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random variables. If a random variable x has mean μx and a random variable y has mean μy then the means of the sum and difference of the variables are given by the following equations. μx+y=μx+μy μx−y=μx−μy The distribution of a test's scores for college-bound male seniors has a mean of 1528 and a standard deviation of 319. The distribution of a test's scores for college-bound female seniors has a mean of 1498 and a standard deviation of 304. One male and one female are randomly selected. Assume their scores are independent.What is the average sum of their scores? What is the average difference of their scores?
Answers
Answer: [tex]\mu_{x+y} =[/tex] 3026
[tex]\mu_{x-y}=[/tex] 30
Step-by-step explanation: Average sum of the female and male's test score is the sum of expected value of each gender:
[tex]\mu_{x+y}=\mu_{x}+\mu_{y}[/tex]
Assuming x represents the random male selected and y represents the random female selected:
[tex]\mu_{x+y}=1528+1498[/tex]
[tex]\mu_{x+y}=[/tex] 3026
The average sum of their scores is 3026.
Average difference is the difference between the expected value (mean) of each gender:
[tex]\mu_{x-y}=\mu_{x}-\mu_{y}[/tex]
[tex]\mu_{x-y}=[/tex] 1528 - 1498
[tex]\mu_{x-y}=[/tex] 30
The average difference of their scores is 30.