Answers
The polar equation of the curve with the given Cartesian equation is r = √7
How to convert polar equation to cartesian equationGiven the Cartesian equation: x² + y² = 7
The relationships between polar and cartesian equation :
x = r cosθ
y = r sinθ
Where r is the radius and θ is the angle
Put the values of x and y into the given cartesian equation:
(r cosθ)² + (r sinθ)² = 7
r²cos²θ + r²sin²θ = 7
r²(cos²θ + sin²θ) = 7
Since the trigonometric identity cos²θ + sin²θ = 1
r²(1) = 7
r² = 7
r = √7
Therefore, the polar equation for the represented curve is r = √7
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Related Questions
write an algebraic model for the statement then solve the model the sum of a number and -9 is -21
Answers
Answer:
[tex]x + ( - 9) = - 21[/tex]
[tex]x - 9 = - 21[/tex]
[tex]x = - 12[/tex]
What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
Answers
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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how do i expand -4(-x-8)
Answers
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
Use the quadratic formula to solve for X 5x^2 +2x=2
Answers
Given:
[tex]5x^2+2x=2[/tex]To solve for x using the quadratic formula, we simplify the given equation first:
[tex]\begin{gathered} 5x^2+2x=2 \\ 5x^2+2x-2=0 \end{gathered}[/tex]Next, we use the quadratic formula of the form ax^2+bx+c=0:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where:
a=5
b=2
c=-2
We plug in what we know:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2^{}-4(5)(-2)}}{2(5)} \\ \text{Simplify} \\ x_{1,2}=\frac{-2\pm\sqrt[]{44}}{10} \\ x_{1,2}=\frac{-2\pm2\sqrt[]{11}}{10} \end{gathered}[/tex]We separate the solutions:
[tex]x_1=\frac{-2+2\sqrt[]{11}}{10}=\frac{-1+\sqrt[]{11}}{5}=0.46[/tex][tex]x_2=\frac{-2-2\sqrt[]{11}}{10}=-\frac{1+\sqrt[]{11}}{5}=-0.86[/tex]Therefore,
[tex]x=0.46,-0.86[/tex]Equipment was purchased for $50,000. The equipment is expected to be used 15,000 hours over its useful life and has a residual value of $10,000. In the first two years of operation, the equipment was used for 2,700 hours and 3,300 hours, respectively. Using the activity-based method, what is the equipment’s accumulated depreciation at the end of the second year?
Answers
The equipment’s accumulated depreciation at the end of the second year is $16,000.
What is the accumulated depreciation?Depreciation is the process used in expensing the cost of an asset. The activity based method allocates the depreciation expense using the number of hours the asset was used. Accumulated depreciation is the sum of the depreciation over a period of time.
Depreciation expense using the activity based method = (cost of the asset - residual value) x (number of hours used in a year / total number of hours)
Depreciation expense in year 1 = ($50,000 - $10,000) x (2,700 / 15,000)
$40,000 x 0.18 = $7,200
Depreciation expense in year 2 = ($50,000 - $10,000) x (3,300 / 15,000)
$40,000 x 0.22 = $8,800
Accumulated depreciation = $8,800 + $7,200 = $16,000
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Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answers
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
I have no clue what I'm supposed to do I need helpFind the equation of line.
Answers
The general equation of line with slope m and point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line.
[tex]\begin{gathered} y-1=3(x+2) \\ y-1=3x+6 \\ y=3x+6+1 \\ =3x+7 \end{gathered}[/tex]So equation of line is y = 3x +7.
Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Answers
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.
Need help pleaseI was bad at math in school so lwant to learn
Answers
The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/tex]When 6 is subtracted from the 5 times of a number the sum becomes 9 find the number
Answers
Let that unknown number be x
⇒Mathematically this is written as
[tex]5(x)-6=9\\5x-6=9\\5x=9+6\\5x=15\\\frac{5x}{5} =\frac{15}{5} \\x=3[/tex]
This just means that the unknown number is 3
GOODLUCK!!
Answer:
nine plus six
= 15 ÷ five
answer Three
Reflect the following figure across the x-axis: S: (0, -3), T: (3, 1), U: (4, -3)
Answers
We are given the following coordinates.
[tex]\begin{gathered} S(0,-3) \\ T(3,1) \\ U(4,-3) \end{gathered}[/tex]We are asked to reflect them across the x-axis.
Recall that the rule for reflection across the x-axis is given by
[tex](x,y)\rightarrow(x,-y)[/tex]As you can see, the y-coordinate gets reversed.
Let us apply this rule on the given coordinates S, T, U
[tex]\begin{gathered} S(0,-3)\rightarrow U^{\prime}(0,3) \\ T(3,1)\rightarrow T^{\prime}(3,-1) \\ U(4,-3)\rightarrow U^{\prime}(4,3) \end{gathered}[/tex]Therefore, the above coordinates are reflected over the x-axis.
value of a machine10(thousands of dollars)01 2 3 4 5 6 7 8 9 10Age of Machine(years)Which equation best represents the relationship between x, the age of the machine in years, and y, thevalue of the machine in dollars over this 10-year period?F.y = -0.002x + 2,500G.y = -500x + 8,000H.y = 500x + 8,000J.y = 0.002x + 2,500
Answers
To find the right answer, first, we find the slope.
Let's use the slope formula, and the points (0,8) and (8,4).
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]m=\frac{4-8}{8-0}=\frac{-4}{8}=-\frac{1}{2}=-0.5[/tex]However, the Value is express in thousands of dollars, which means the slope is -500.
Observe that G is the only equation with the correct slope.
Therefore, G is the right answer.Determine which of the following are true statements. Check all that apply.
Answers
Substitute in each inequality the given corresponding solution (x,y) and prove if it makes a true math expression:
1.
[tex]\begin{gathered} -5x-9y\ge60 \\ (-3,-5) \\ \\ -5(-3)-9(-5)\ge60 \\ 15+45\ge60 \\ 60\ge60 \end{gathered}[/tex]As 60 is greater than or equal to 60, (-3,-5) is a solution for the inequality.2.
[tex]\begin{gathered} 4x-3y>1 \\ (5,7) \\ \\ 4(5)-3(7)>1 \\ 20-21>1 \\ -1>1 \end{gathered}[/tex]As -1 isn't greater than 1, (5,7) is not a solution for the inequality3.
[tex]\begin{gathered} -10x+8y<12 \\ (-9,-10) \\ \\ -10(-9)+8(-10)<12 \\ 90-80<12 \\ 10<12 \end{gathered}[/tex]As 10 is less than 12, (-9,-10) is a solution for the inequality.4.
[tex]\begin{gathered} 9x+7y\le98 \\ (9,3) \\ \\ 9(9)+7(3)\le98 \\ 81+21\le98 \\ 102\le98 \end{gathered}[/tex]As 102 is not less than or equal to 98, (9,3) is not a solution for the inequalityHallum hardware created flyers to advertise a carpet sale . A portion of the flyer is shown below. Based on the chart, which statement describes the relationship between area and the cost of carpet?
Answers
The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.
Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.
Ratio = cost / area
750 / 500 = 1.50
1500 / 1000 = 1.50
2,250 / 1500 = 1.50
3000 / 2000 = 1.50
Since the ratios are constant, the relationship is proportional.
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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.
Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
Answers
The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
Ashley watches a giant that has 16 equally spread seats. Identify w.
Answers
The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]2. (5 × 2 + 20/2) + (10 x 2/2 + 5) =
a. 35
b. 42
c. 103
Answers
Answer:
a.35
Step-by-step explanation:
10 + 20/2 equals 20
20/2+5 equals 15
20+15 equals 35
write the simplest polynomial equation with the given roots. -1, 2i please answer quickly
Answers
The polynomial equation with root of -1 and 2i is,
[tex]\begin{gathered} (x+1)(x+2i)(x-2i)=(x+1)(x^2-(2i)^2) \\ =(x+1)(x^2-4i^2) \\ =(x+1)(x^2+4) \\ =x^3+4x+x^2+4 \\ =x^3+x^2+4x+4 \end{gathered}[/tex]So simplest polynomial is,
[tex]x^3+x^2+4x+4[/tex]the difference of twice h and 5 is as much as the sum of h and 4
Answers
The value of h by solving the given relationship we get, h = 9
In the above question, a word problem is given with the following relations which are as
First we'll express the given word problem statements into mathematical equation expressions
Therefore, The difference of twice of h and 5 is as much as the sum of h and 4
It can be written as in mathematical equation form as
2h - 5 = h + 4
Now, we need to find the value of h by solving the above mathematical equation formed put of the given relationship
Here,
2h - 5 = h + 4
2h - h = 5 + 4
h = 9
Hence, The value of h by solving the given relationship we get, h = 9
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20 quarts=_ 20_×(1 quart) =_20_×(1\4 gallon) =_20/4_gallons =_5_gallons
Answers
From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/3x.
How to Determine the Value of a Given Function?For any given function, we can evaluate the function by plugging in the equation of each of the functions in the given expression.
Thus, we have the following given functions:
f(x) = x² + 5
g(x) = 3x
a. Find the value of the function for the expression (f + g)(x).
We are required here to add the expression for each of the functions, f(x) and g(x) together, which is:
(f + g)(x) = (x² + 5) + (3x)
(f + g)(x) = x² + 3x + 5
b. Evaluate (f - g)(x) by subtracting the function g(x) from f(x):
(f - g)(x) = (x² + 5) - (3x)
(f - g)(x) = x² - 3x + 5
c. Find (f * g)(x):
(f * g)(x) = (x² + 5) * (3x)
(f * g)(x) = x²(3x) + 5(3x)
(f * g)(x) = 3x³ + 15x
d. Find (f/g)(x):
(f/g)(x) = (x² + 5)/3x
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simply
i^3+i^20
show work
Answers
==================================================
Explanation:
Recall that
i = sqrt(-1)
Squaring both sides gets us
i^2 = -1
Now let's multiply both sides by i
i*i^2 = i*(-1)
i^3 = -i
Repeat the last step
i^3 = -i
i*i^3 = i*(-i)
i^4 = -i^2
i^4 = -(-1)
i^4 = 1
----------------------------
Here's a summary so far
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.
20/4 = 5 remainder 0
Therefore i^20 = i^0 = 1
Or we can think of it like this
i^20 = (i^4)^5 = 1^5 = 1
----------------------------
This means we can then say
i^3 + i^20 = -i + 1 = 1 - i
so, the order is i -1 -i 1.
if you have an exponent of 1, the answer is i.
if you have an exponent of 2, the answer is -1.
if you have an exponent of 3, the answer is -i.
if you have an exponent of 4, the answer is 1.
if you have an exponent of 5, the answer is i.
this repeats in this pattern. so one way to solve it is to count, or you can simply divide the exponent by 4.
if the answer has .25, it’s i.
if the answer has .50, it’s -1.
if the answer has .75, it’s -i.
if the answer has a whole nunber, any, such as 4 or 7, it’s 1.
3/4=.75. so i^3= -i.
20/4= 5. so i^20=1.
(-i) + (1) = 1-i
The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12
Answers
A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]hello I don't know if you can help me with this but I no am doing something wrong. because at the bottom its not spelling right
Answers
8. The difference of three and a number means x+3 or x-3 because in both equations you have three units plus or minus the number X.
10. '"4 times the sum of a number and three" means
[tex]4\cdot(x+3)=4x+12[/tex]Letter D
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion
Answers
The consumption is 355 billion .
Given,
In the question:
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.
Now, According to the question:
Based on the given condition,
Formulate;
Aggregate expenditure (consumption)= Output - Savings= Investment
370 - 15
Calculate the sum or difference
= 355billion
Hence, The consumption is 355 billion .
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p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
Answers
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]For the rotation 707°, find the coterminal angle from 0° ≤ 0 < 360°, thequadrant and the reference angle
Answers
Explanation
We are required to determine the coterminal, quadrant and reference angle of 707°.
This can be achieved as:
Therefore, the reference angle can be gotten as:
[tex]720\degree-707\degree=13\degree[/tex]Hence, the reference angle is 13°.
The angle lies in the fourth quadrant.
The cotermi
Chen is opening a new account with a $1,200 deposit. She will be keeping money in the account, compounded monthly for no more than 3 years. the formula gives the value, V, of the account as a function of time, t. Which is a reasonable domain of this function?V(t)= 1,200(1 + 0.02)^t/12A) 0< or equal to t < or equal to 36B) 0C) 0 < or equal to t < or equal to 1,273.45D) 1,200 < or equal to t < or equal to 1,273.45
Answers
The Solution:
Given the function:
[tex]V(t)=1200(1+0.02)^{\frac{t}{12}}[/tex]We are required to find a reasonable domain for the given function.
The domain of the function V(t) is the range of values for t.
The question says Chen is will continue to keep money in the account for not more than 3 years, but the interest will be compound monthly.
Recall:
1 year = 12 months
So,
3 years will be
[tex]12\times3=36\text{ months}[/tex]This means that the range of values for t is:
[tex]0\leq t\leq36[/tex]Therefore, the correct answer is [option A]
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges to rent trucks plus an additional fee of for each ton of sugar. The second company charges to rent trucks plus an additional fee of for each ton of sugar.For what amount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
Answers
step 1
Find the equation of the line First Company
y=100.25x+6,500
where
y is the total charge
x is the number of ton of sugar
Second Company
y=225.75x+4,492
Part a)
Equate both equations
100.25x+6.500=225.75x+4,492
solve for x
225.75x-100.25x=6,500-4,492
125.50x=2,008
x=16
answer part a is 16 tonPart b) For x=16 ton
substitute the value of x in any of the two equations (the result is the same)
y=100.25(16)+6,500
y=$8,104
answer Part b is $8,104You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
Answers
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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