Answer:
2 is the coefficient
Step-by-step explanation:
2 is the coefficient bc a coefficient is the number next to a variable (such as x) and 2 is next to x and is the only one in the equation
Answer:
-2
Step-by-step explanation:
c) Consider the time 3:40pm where the initial side is the hour hand and terminal side is the
minute hand. Draw the angle between the two hands in standard position. State the angle in
positive degrees and then restate the angle as a negative angle. (2 pts.)
Answer:
210 degrees-150 degreesStep-by-step explanation:
When the time is 3:40pm
The Initial Side (hour hand) is at 3.Terminal Side (Minute hand) is at 8.(a)The angle between the two hands in standard position is drawn and attached below.
(b)Now, each hour = 30 degrees
Therefore, the angle between 3 and 8 in an anticlockwise movement
= 7 X 30 =210 degrees
Stating the angle as a negative angle, we have:
[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]
∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplementary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.
Option D is the correct answer.
Answer:
D. ∠B and ∠C are congruent.
Step-by-step explanation:
Since, ∠A and ∠B are supplementary.
Therefore,
∠A + ∠B = 180°.....(1)
Since, ∠A and ∠C are supplementary.
Therefore,
∠A + ∠C = 180°.....(2)
From equations (1) & (2)
∠A + ∠B = ∠A + ∠C
=> ∠B = ∠C
Hence, ∠B and ∠C are congruent.
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents
Estimate the area of the circle equal three decimal 14 round to the nearest hundredth if necessary9
Answer:
49π m² or 153.94 m²
Step-by-step explanation:
Area of a circle: A = πr²
We are given r as 7, so simply plug it in
A = π(7)^2
A = 49π m²
If the denominator of 5/9 is increased by a number and the numerator is doubled, the result is 1. Find the number.
◇Given :-
The denominator of a fraction is increased by a number and numerator will be doubled
To find
We have to find the required number or fraction
[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]
Now let us consided as the number be a
Then
[tex]\underline{\bigstar{\textit\ According\ to \ Question:-}}[/tex]The given fraction is 5/9
[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]
[tex]\underline{\therefore{\textit{\textbf { The \ required \ number \ is \ 1}}}}[/tex]Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Answer:
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Step-by-step explanation:
What is the area of the triangle below?
18
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
P(AB) can be read as "the probability that A occurs given that Bhas
occurred."
A. True
B. False
Answer:
False
Step-by-step explanation:
from *millermoldwarp*
"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."
hopes this helps
Answer:false
Step-by-step explanation:
What is the square root of 28
Answer:5. 291503
Step-by-step explanation:
√28
2√7
5. 291503
Which of the following statements are equivalent to the statement "Every integer has an additive inverse" NOTE: (The additive inverse of a number x is the number that, when added to x, yields zero. Example: the additive inverse of 5 is -5, since 5+-5 = 0) Integers are{ ... -3, -2,-1,0, 1, 2, 3, ...} All integers have additive inverses. A. There exists a number x such that x is the additive inverse of all integers.B. All integers have additive inverses.C. If x is an integer, then x has an additive inverse.D. Given an integer x, there exists a y such that y is the additive inverse of x.E. If x has an additive inverse, then x is an integer.
Answer:
B, C and D
Step-by-step explanation:
Given:
Statement: "Every integer has an additive inverse"
To find: statement that is equivalent to the given statement
Solution:
For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.
Here, 0 is the additive identity.
Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".
The Venn diagram below is used for showing odd numbers and prime numbers.
Place the numbers 1, 2, 3, 4 and 5 in the Venn diagram.
Answer:
See attached
Step-by-step explanation:
Given the numbers 1,2,3,4 and 5
Odd Numbers =1, 3 and 5Prime Numbers = 2, 3 and 5Let O be the event that the number is Odd
Let E be the event that the number is Prime
Then the intersection of Odd and Prime Numbers: [tex]O \cap P =\{3,5\}[/tex]
Since 4 is neither odd nor prime, we place it outside of the two circles.
See the attached diagram for the required Venn diagram.
write (n^3)^2 without exponets
Step-by-step explanation:
[tex]( {n}^{3} )^{2} = {n}^{6} = n \times n \times n \times n \times n \times n [/tex]
Answer:
n x n x n x n x n x n
Step-by-step explanation:
(n^3)^2 = n^6 = n x n x n x n x n x n
In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable.
Answer:
The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.
Step-by-step explanation:
The question is incomplete:
The probability distribution is:
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
4 0.04
The mean can be calculated as:
[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]
(pi is the probability of each class, Xi is the number of topping in each class)
The standard deviation is calculated as:
[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]
Answer:
mean: 1.14; standard deviation: 1.04
Step-by-step explanation:
Brian invests £8300 into his bank account. He receives 1.4% per year compound interest. How much will Brian have after 7 years? Give your answer to the nearest penny where appropriate.
Answer:
The nearest penny will be £9146.6
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)
A = 8300 [ 1 + {0.002}]^(49)
A= 8300 [ 1.002 ]^(49)
A = 8300 [ 1.102 ]
A = £9146.6
What is Compound Interest (CI) ?
Compound Interest is all about adding interest to principal amount of loan , deposit .
Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:
Answer:
N(L) = 20
The expected number of left handed people is 20.
Step-by-step explanation:
Given;
Percentage of left handed people P(L) = 10%
Total number of selected people N(T) = 200
The Expected number of left handed people N(L) is;
N(L) = Total number of selected people × Percentage of left handed people/100%
N(L) = N(T) × P(L)/100%
Substituting the given values;
N(L) = 200 × 10%/100%
N(L) = 200 × 0.1
N(L) = 20
The expected number of left handed people is 20.
How many different ways can the letters of "kissing" be arranged?
Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
Which leader was a member of the Kikuyu tribe?
A. Kwame Nkrumah
B. Marcus Garvey
C. Mohandas Gandhi
D. Jomo Kenyatta
Answer:
Jomo Kenyatta
Step-by-step explanation:
Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.
Answer:
Jomo Kenyatta
Step-by-step explanation:
took the test
What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
[tex]0.65a=a(1-\frac{b}{100})[/tex]
[tex]0.65=1-\frac{b}{100}[/tex]
[tex]\frac{b}{100}=1-0.65[/tex]
[tex]b=100(0.35)[/tex]
[tex]b=35[/tex]
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
Learn more about the Algebraic expressions for the statements here,
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What is the ratio 16 : 12 in its simplest form?
Answer:
4 : 3
Step-by-step explanation:
16 : 12 can be simplified by 4 to get 4 : 3
Answer:
[tex]4:3[/tex]
Step-by-step explanation:
[tex]16 : 12[/tex]
The common highest factor of the ratio is 4.
Simplify the ratio.
[tex]16 \div 4:12 \div 4[/tex]
[tex]4:3[/tex]
There are 11 students in our Science class left to give their presentations. Today we will have time for 6 presentations. How many different ways can the teacher choose the presenters?
Answer:
He has 2,772 ways
Step-by-step explanation:
Hello,
the teacher has to choose 6 students and there are 11 students in total.
When he chooses the first student he has 11 choices
if he has to choose 1 students he has 11 ways to do it
then for the second one he has 11-1=10 choices
if he has to choose 2 students he has (11*10)/2 ways to do it (we do not count the duplicate - for instance if he chooses Steve and then Nils or Nils and then Steve this is only one group (Steve, Nils) we do not care of the order)
Then for the third student he has 10-1=9 choices
if he has to choose 3 students he has (11*10*9)/(2*3) ways to do it (we do not take into account the order of ppl in the group)
and so on and so forth
...
if he has to choose 6 students he has (11*10*9*8*7*6)/(2*3*4*5)
so he has 2,772 ways
Answer:
C. 462 is correct. I did the test.
Step-by-step explanation:
AC =
Round your answer to the nearest hundredth.
A
5
35
B
C
Answer:
2.87 = AC
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 35 = AC /5
5 sin 35 = AC
2.867882182= AC
To the nearest hundredth
2.87 = AC
European car company advertises that their
car gers 9.4 Kilometers per liter of gasoline. Convert
this figure to miles per galllon
Answer:
22.11 miles per gallon
Step-by-step explanation:
1 km = 0.621371 miles
1 litre = 0. 264172 gallon
Given
Mileage of car = 9.4 Milometers per liter of gasoline
Mileage of car = 9.4 Km/ litres
now we will use 0.621371 miles for Km and 0. 264172 gallon for litres
Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon
Mileage of car = 9.4 * 2.3521 miles/ gallon
Mileage of car = 22.11 miles/ gallon
Thus, 9.4 Km/litres is same as 22.11 miles per gallon.
deandre saves rare coins. he starts his collection with 14 coins and plans to save 3 coins each month. write an equation to represent the number of coins saved, y, in terms of the number of months, x. if deandre saved for 30 months, how many coins will he have?
Answer:
equation: y = 3x + 14
number of coins after 30 months: 104 coins
Hope this helps :)
An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,
y = 14 + 3x
where y is the number of coins and x is the number of months.
After a period of x=30 months, the number of coins that will be with Deandre can be written as,
[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]
Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.
Learn more about Equation:
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⅝ of a school's population are girls. There are 129 boys. If each classroom can hold 25 students. How many classroom does the school have ?
Answer:
AT least 14 classrooms to hold the total number of students
Step-by-step explanation:
Since we don't know the numer of girls in the school, let's call it "x".
What we know is that the number of girls plus the number of boys gives the total number of students. This is:
x + 129 = Total number of students
Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:
"5/8 of the school's population are girls" as:
0.625 (x + 129) = x
then we solve for "x":
0.625 x + 0.625 * 129 = x
0.625 * 129 = x - 0.625 x
80.625 = x (1 - 0.625)
80.625 = 0.375 x
x = 80.625/0.375
x = 215
So now we know that the total number of students is: 215 + 129 = 344
and if each classroom can hold 25 students, the number of classroom needed for 344 students is:
344/25 = 13.76
so at least 14 classrooms to hold all those students
3. How many different arrangements can be made with the letters in the word
POWER?
O A 100
B 25
OC 20
OD 120
Answer:
D. 120
Step-by-step explanation:
Array formula: A (n, p) = n! / (n -p)!
At where:
n = Total number of elements in the set.
p = Quantity of elements per arrangement
A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!
By definition: 0! = 1
Then: 120/1 = 120
) Let an denote number of n-digit ternary sequences (sequences of 0,1 and 2) which have no consecutive 0’s in them. Find a recurrence relation for an. (Do not solve the recurrence. However, depending on the order of the recurrence, provide a sufficient number of initial conditions. )
Answer:
The recurrence relation for aₙ is aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8
Step-by-step explanation:
Solution
Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.
Ternary sequence is sequence with each of digits either 0, 1 or 2.
Now
Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.
Let us first find few initial values of aₙ
For n = 1
a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.
This 1-digit sequence can be either 0 or 1 or 2.
Thus,
a₁ = 3
For n =2
a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.
This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.
here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)
But one of these 9 sequence there are consecutive 0's .... (00)
So we eliminate this one sequence.
So, a₂ = 8
Now
let us find the recurrence relation
Fir n ≥ 3
aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.
For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2
Let assume the 1st digit of this n - digit ternary sequence is 1.
Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.
For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1
So,
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.
Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.
So
If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:
aₙ-1 + aₙ -1 = 2aₙ -1
For the second case: if 1st digit of this n - digit ternary sequence is 0
If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,
If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.
So there are 2 choices for 2nd digit.
After this there are more n-2 digits.
Then
For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them
For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.
Now,
The total number of sequence in this case is given as:
2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)
Hence
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3
Now,
The recurrence relation for aₙ is shown below:
aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3
With the initial conditions as a₁ =3; a₂ = 8
A group of campers is going to occupy 4 campsites at a campground. There are 14 campsites from which to choose. In how many ways can the campsites be chosen?
There are
possible ways to choose the campsites.
Check
Enter your answer in the answer box and then click Check Answer.
Clear All
All parts showing
Answer:
24024 are the total number of ways of choosing 4 campsites out of 14.
Step-by-step explanation:
We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.
It is a simple example of selection problem.
Number of ways to choose the first campsite = 14
Now, one campsite is chosen, 13 campsites are left.
Therefore,
Number of ways to choose the second campsite = 13
Now, one more campsite is chosen, 12 campsites are left.
Therefore,
Number of ways to choose the third campsite = 12
Now, one more campsite is chosen, 11 campsites are left.
Therefore,
Number of ways to choose the fourth campsite = 11
So, total number of ways for choosing 4 campsites out of 14:
14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024
Hence, answer is 24024.
For every 1% increase in
unemployment, there is a 2%
decrease in potential GDP. This
creates a GDP gap. What is the GDP
gap when there is 4.5%
unemployment?
Answer:
The GDP gap is 9 % when there is 4.5 % unemployment.
Step-by-step explanation:
The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:
[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]
The GDP gap at a given increase in unemployment can be estimated by the following expression:
[tex]\frac{g}{u} = r[/tex]
[tex]g = r\cdot u[/tex]
Where:
[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.
[tex]u[/tex] - Increase in unemployment rate, measured in percentage.
[tex]g[/tex] - GDP gap, measured in percentage.
If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:
[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]
[tex]g = 9\,\%\,GDP[/tex]
The GDP gap is 9 % when there is 4.5 % unemployment.
What type of error is present in the underlined
sentence?
Which is the best revision to fix the error?
Answer:
Type of error: Run-on(comma splice).
Best revision to fix it: Adding a semicolon after beginners .
Explanation:
A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.
In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:
'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'
Answer:
Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.
What type of error is present in the underlined sentence?
✔ run-on
Which is the best revision to fix the error?
✔ adding a semicolon after instrument
Step-by-step explanation:
Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]