The explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.
Given that x=2sin, y=2cos, and 0 are constants,
Simplify the parametric functions that are presented. Add their squares after taking them. The following trigonometric identity can be used:
sin2θ+cos2θ=1sin2θ+cos2θ=1
x=2sinθ,
y=2cosθ,0≤θ≤2πsinθ
=x2cosθ,
=y2x
Y=2sinθ,
y=2cosθ,0≤θ≤2πsinθ=x2cosθ=y2
Square them now and add them:
(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)
(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)
A parameter in a parametric equation can stand in for anything, including an angle. When a parameter is an angle—as opposed to a non-angle parameter—the plane curve can be graphed by choosing values for the angle and computing the x- and y-values.
Hence, the explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.
To learn more about parameter visit;
brainly.com/question/3302107
#SPJ1
The numbers of seats in the first 16 rows in a curved section of another arena form an arithmetic sequence. If there are 20 seats in Row 1-23 seats in Row 2, how many seats are in Row 16?
The total number of seats are there is row 16 is 65.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come along through a few specific terms in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as the values given in the question;
There are total 16 rows in the arena.
Thus, n = 16.
There are 20 seats present in row 1.
Consider the first term as 'a₁' = 20.
Similarly, there are 23 seats present at row 2.
Consider 'a₂' = 23 is the second term.
Now, calculate the common difference;
d = a₂ - a₁
Put the values in the 'd'.
d = 23 - 20 = 3.
Now, compute the total number of seats in 16th row bu nth formula.
n-th term: an = a + (n − 1) × d
a₁₆ = a₁ + (n - 1)d
a₁₆ = 20 + (16 - 1)3
a₁₆ = 20 + 45
a₁₆ = 65
Therefore, the total number of seats present in the 16th row is 65.
To know more about the arithmetic progression, here
brainly.com/question/24191546
#SPJ4
log_(2) (sqrt((2+14 )*(1+3))
The value of the expression is 3 using the concept of the logarithm.
A base must be raised to a certain exponent or power, or logarithm, to produce a specific number. If bˣ=n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.
Given the expression log₂√(2+14)(1+3)
Solving the square root we obtain,
[tex]log_{2} \sqrt{(16)(4)}\\[/tex]
Simplifying further we get,
[tex]=log_{2} (4)(2)[/tex]
[tex]=log_{2} (8)[/tex]
We know that the logarithm of 8 with base 2 is 3.
Hence, the given expression can be simplified as 3.
To know more about the concept of logarithms, visit:
https://brainly.in/question/1164782
#SPJ9
Solve 2y + xy = 6for y. Then find the value of y when x = -3
Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
How much water (as a fraction of a bottle) did Marianna put in her bottle at the water fountain?
Mari put 1/2 of a bottle of water at the water fountain .
Expression in maths is outlined because the assortment of numbers variables and functions by mistreatment signs like addition, subtraction, multiplication, and division.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping will all be pictured by mathematical symbols, which might even be accustomed indicate the logical syntax's order of operations and different options.Let the capacity of the bottle holding water be 100 .
It is given that Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
The amount of water is given by :
2/3 of 100 - 1/6 of 100 = 2/3 × 100 - 1/6 × 100
= 100( 2/3 - 1/6)
= 100(1/2)
= 50
Learn more about expression here :
brainly.com/question/20323470
#SPJ9
Here are the ingredients needed to make 8 pancakes.
250 ml milk
1 egg
140 g flour
5 g butter
Simon makes 4 pancakes.
Work out how much milk he needs.
Craig makes 12 pancakes.
Work out how much butter he needs.
Step-by-step explanation:
Simon only used 125ml milk
250÷2=125
Craig used 375ml milk
250x1.5=275
Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.
A
B
O
C
D
If mZAOB = (2x - 4) and mZBOD= (14x+12)°, what is the value of x?
Using supplementary angles, it is found that the value of x is of x = 10.75.
What are supplementary angles?Supplementary angles are angles whose measures add to 180º.
An entire pizza is 360º, hence half the pizza is 180º, meaning that angles AOB and BOD are supplementary.
Their measures are given as follows:
m<AOB = 2x - 4.m<BOD = 14x + 12.Since they are supplementary, they add to 180º and we can add their measures and solve for x as follows:
2x - 4 + 14x + 12 = 180
16x = 172
x = 172/16
x = 10.75.
More can be learned about supplementary angles at https://brainly.com/question/12919120
#SPJ1
What is 905.255 round to
Answer:
No decimal: 905
One decimal: 905.3
Write an explicit formula for each geometric sequence. Then find the first three terms.a₁ =3, r= 3/2
A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.
The general term for the geometric sequence is
an= a1 * r ^ (n-1)
where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.
where a₁ = 3 and r = 3/2
Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...
3rd value: 6.75.
More problems related to a similar concept are solved in the link below.
https://brainly.com/question/11266123?referrer=searchResults
#SPJ4
Evaluate the expression when a=7 and b=5 . 6a+b
Answer:
47
Step-by-step explanation:
6(7)+5=42+5=47
mark me brainliest if it helped
Find the geometric mean between pair of numbers.
14 and 21
To calculate the geometric mean, we take their product instead: 1 x 5 x 10 x 13 x 30 = 19,500 and then calculate the 5-th root of 19,500 = 7.21. This is equivalent to raising 19,500 to the 1/5-th power. Another way to calculate the geometric mean is with logarithms, as it is also the average of logarithmic values converted back to base 10.
A truck can be rented from Company A for $40 a day plus $0.7 per mile. Company B charges $20 a day plus $0.9 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
100 milesStep-by-step explanation:
Let the number of miles be x.
Company ATotal amount of rental is:
A = 40 + 0.7xCompany BTotal amount of rental is:
B = 20 + 0.9xSince A = B, substitute the values and solve the equation:
40 + 0.7x = 20 + 0.9x0.9x - 0.7x = 40 - 200.2x = 20x = 20/0.2x = 100what is 3 times 60? because i dont know
Answer: 180
Step-by-step explanation: 3 times 6 is 18 so just add a zero
Answer: 180
Step-by-step explanation:
3x60
60+60+60
Add or Subtract.
11/12 - 7/45
Solution=0.76
How to solve 11/12 - 7/45?
[tex]\frac{11}{12} -\frac{7}{45} \\=\frac{(11*45-7*12)}{540} \\=\frac{411}{540} \\=0.76[/tex]
What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size.Numerator and denominator are both natural numbers in positive common fractions. The denominator tells us how many of those equal parts there are in the numerator.The numerator tells us how many of those parts there are in the numerator. Zero pieces can never make up a whole, hence the denominator cannot be zero.Ex: 1/2 = 0.5
To learn more about fraction, refer:
https://brainly.com/question/1622425
#SPJ4
5. Points A, B, and C are collinear. AB = 5x, BC = 2x + 1, and AC = 50.
Solve for x
I would rly appreciate someones help need it by tonight
Answer:
x=7
Step-by-step explanation:
AB is 1 part of the line
BC is the other part of the line
the total length of the line is 50 units
when you add AB to BC you should get 50
5x+2x+1=50
7x+1=50
7x=49
x=7
Which equation demonstrates the distributive property? Responses
A.(3 + 8)5 = 5(3 + 8)
B.15 x 40 = 40 x 15
C.15 + 40 = 55
D.15 + 40 = 5(3 + 8)
The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.
What is the meant by the term distributive property?To "distribute" something means to divide it or give a fraction or portion of it.The distributive property corresponds to the distributive law of multiplication over basic arithmetic operations such as addition and subtraction.This property states that multiplying a sum of two or even more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.In other words, the distributive property requires an expression of the form: A (B + C) can be written as AB + BC.This property also applies to subtraction: A (B - C) can be written as AB - BC.This indicates that other two operands share operand A.From the given options;
Consider option D; 15 + 40 = 5(3 + 8).
It is the case of distributive addition.
where
5(3 + 8) = 5×3 + 5×8
5(3 + 8) = 15 + 40
Thus, the option D is the correct representation of the distributive law.
To know more about distributive property, here
https://brainly.com/question/2807928
#SPJ9
PLEASE HELP!! The area of a square is 16 square units. Since 4^2 = 16 and (-4)^2 = 16, both 4 and -4 are square roots for 16. Explain how "both square roots for 16, the area of the square, are the length of each side of the square" is incorrect.
I will mark brainliest!
we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
Why is the statement incorrect?So we have a square with an area of 16 square units, then the side length of that square will be given by:
S^2 = 16 square units
Now, there are two solutions for the above equation, these are:
S = 4 units
S = -4 units.
But being a solution of the equation does not mean that the solutions have sense in the context of the problem.
When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"
That does not make sense, remember that math is just a language, and it should be used to communicate things to others.
So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.
That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
If you want to learn more about square roots:
https://brainly.com/question/98314
#SPJ1
Which one of the following is not a power equation?
p= v2/r= vxi
p= v2xi p= i2xr
The equation that is not a power equation is p = v²×i
Power equationsFrom the question, we are to determine which of the given equations is not a power equation
Where the Voltage, V, and the Current, I, are given, the power, P is given by
P = IV
When the Voltage and the Resistance, R, are given
P = V²/R
When the Current and the Resistance are given,
P = I²R
∴ P = V²/R, P = IV, and P = I²R are power equations.
Hence, the equation that is not a power equation is p = v²×i
Learn more on Power here: https://brainly.com/question/9015563
#SPJ1
A bouncy ball is dropped such that the height of its first bounce is 6.5 feet and each successive bounce is 78% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answer:
Approximately [tex]0.7\; {\rm ft}[/tex].
Step-by-step explanation:
If the current bounce is of height [tex]h\; {\rm ft}[/tex], the next bounce would be of height [tex](78\%\, h)\; {\rm ft}[/tex], which is equal to [tex](0.78\, h)\; {\rm ft}[/tex].
It is given that the first bounce is of height [tex]6.5\; {\rm ft}[/tex]. Relative to this first bounce:
The [tex]n = 2[/tex] bounce is dampened [tex](2 - 1) = 1[/tex] time. The height of this bounce would be [tex]((0.78)\, 6.5)\; {\rm ft} = ((0.78)^{2 - 1} \, 6.5)\; {\rm ft}[/tex].The [tex]n = 3[/tex] bounce is dampened [tex](3 - 1) = 2[/tex] times. The height of this bounce would be [tex](0.78)\, ((0.78)\, 6.5)\; {\rm ft} = ((0.78)^{3 - 1} \, 6.5)\: {\rm ft}[/tex].In general, the [tex]n[/tex]th bounce would have been dampened [tex](n - 1)[/tex] times. The height of that bounce would be [tex]((0.78)^{n - 1}\, 6.5)\; {\rm ft}[/tex].
Thus, the [tex]10[/tex]th bounce would have been dampened [tex](10 - 1) = 9[/tex] times. The height of that bounce would be [tex]((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}[/tex] (rounded to the nearest tenth, one digit after the decimal point.)
Is 12/24 equivalent to 24/72?
Answer:
No
Step-by-step explanation:
12/24 = (1 * 12) / (2 * 12) = 1/2
24/72 = (1 * 24) / (3 * 24) = 1/3
1/2 ≠ 1/3
I need this answered please
The phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
What is the algebraic expression in the given phrase?Given the phrase in the question;
"54 less than twice Chrissy's age"
Let variable 'c' represent Chrissy's age
Translation
Chrissy's age ⇒ x
Twice Chrissy's age ⇒ 2 × x = 2x
54 less than ⇒ -54
Now combine terms
2x and - 54
2x - 54
Therefore, the phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
Learn more word problems here: brainly.com/question/2610134
#SPJ1
Each face of a cube is a square with a side length of 2 feet. What is the total area of all the faces of the cube?
The total area of all the faces of the cube is square feet
How to determine what is the total area of all the faces of the cube?The given parameter is
Side length, l = 2 feet
The total area of all the faces of the cube is calculated as
So, we have
Total area = 6 * Side length^2
This gives
So, we have
Total area = 6 * 2^2
Evaluate the exponent
So, we have
Total area = 6 * 4
Evaluate the product
So, we have
Total area = 24
Hence, the total area of all the faces of the cube is 24 square feet
Read more about area at
https://brainly.com/question/25292087
#SPJ1
Use the distance-rate-time formula (d = rt) to solve the following problem.
d = distance
r = rate of speed
t = time
A train carrying cattle left Miami and traveled toward New York. The train took 28 hours to arrive in
New York and traveled the distance of 1092 miles. Find the rate of speed of the cattle.
(a³b¹²c²) × (a³c²) × (b³c¹) ⁰ =
12.4
O A. a¹5¹24
○ в. a³b¹¹c³
8
O c. a³b¹²4
OD. a¹4b¹5c9
Answer:
Answer C is correct
Step-by-step explanation:
We know that,
[tex] \sf \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ \sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \: \: \: \: \: \: \: \: [/tex]
[tex]\sf (x) ^{0} = 1 \rightarrow \: Any \: number \: to \: the \: power \: 0 \: is \: 1[/tex]
Let us solve it now.
[tex] \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times ( {b}^{5} {c}^{4} )^{0} \\ \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{3} \times {a}^{5} \times {b}^{12} \times {c}^{2} \times {c}^{2} \times 1\\ \sf {a}^{3 + 5} \times {b}^{12} \times {c}^{2 + 2} \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} \times {b}^{12} \times {c}^{4} \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} {b}^{12} {c}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Find the coordinates of the midpoint of a segment with the given endpoints. A(0,0), C(3,-4)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(0, 0) and C(3, -4).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(0 + 3) / 2, (0 - 4) / 2]
(x, y) = (3/2, -4/2)
(x, y) = (1.5, -2)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
More about the mid-point of the line segment link is given below.
brainly.com/question/17188072
#SPJ4
SOMEONE PLEASE HELP :’( Solve the equation | 4x + 7| = 9. Graph
Answer:
-4
Step-by-step explanation:
Split the problem into two cases: one positive and one negative
|4x+7| =9
4x+7=9
(4x+7) =9
Subtract 7 from both sides
4x+7 - 7 = 9 - 7
Solution
x = 1/2
x = -4
16) Long John had 100 bags of silver. Each bag contained 9 3/4 lb. How much silver did he
have altogether?
Answer:
975 lbs.
Step-by-step explanation:
9 3/4 = 9.75
9.75 × 100 = 975
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-6,-4)
The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-6 - 0)^2 + (-4 - 0)^2
radius= √36 + 16
radius = √52
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √52
(x - 0)^2 + (y - 0)^2 = (√52)^2
x^2 + y^2 = 52
Learn more about equation of a circle here: https://brainly.com/question/14150470
#SPJ4
PLEASE HELP ME ASAP! Find the approximate side length of a square game board with an area of 205 in2
Answer:
Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,
Step-by-step explanation:
in chicago, the tenperature dropped from 21 degrees to -7 degreees over the course if 6 hours, identify the rational number that represents the average temperature change per hour
Answer:
4.6667
Step-by-step explanation:
For most people, the cost of a subscription to streaming music services is definitely a
discretionary expense. Marshal researched subscription costs and found the following monthly
rates for streaming services:
$10
$5 $10 $4 $12 $5
which is?
$6 $2.75 $3
a. What is the mean subscription fee?
303
of numbers
b. What is the median subscription fee?
c. What is the mode subscription fee?
d. If Marshal is looking to add another subscription how much would it have to be so the mean
$2.0.cdcas!
subscription is exactly $7 per month?
For the given subscriptions, we have that:
a) The mean is of $6.42.
b) The median is of $5.
c) The modes are of 5 and 10.
d) Marshall would have to add a subscription of $12.25.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For this problem, the observations are given as follows:
10, 5, 10, 4, 12, 5, 6, 2.75, 3.
Hence the mean is:
M = (10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3)/9 = $6.42.
With another observation, we want a mean of $7, hence:
(10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3 + x)/10 = 7
57.75 + x = 70
x = 12.25.
Hence, for item d:
Marshall would have to add a subscription of $12.25.
What is the median?The median of a data-set is the middle value, which is the value that 50% of the data-set is greater and 50% is lesser.
The ordered data-set in this problem is:
2.75, 3, 4, 5, 5, 6, 10, 10, 12.
The middle value is of 5, which is the median.
What is the mode of a distribution?The mode of a distribution is the observation that appears the most times in the distribution.
In this problem, those observations are 5 and 10, both of which appears twice, hence the distribution is bimodal.
More can be learned about the mean of a data-set at https://brainly.com/question/24628525
#SPJ1
