Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,0) of this point in which:
(a) r> 0, 2x <0 < 4x.
(b) r<0,0<0<2R.
(c) r> 0, -2x <0<0.
(10,pi/3)
Answers
Step 1: Plotting the Point
Make a polar coordinate system.
It looks like this ( look at the first photo)
Step 2: Graph the polar function
r=10.
Here since our first coordinate is 10, our radius of our point will be 10.
This basically means we will have a circle with a radius of 10. ( look at the second photo).
Step 3: Look for the angle pi/3,
So that how u graph polar coordinates.
Next, a polar form can have multiple representations.
a. Here we want a radius of to be positve, so our r will stay 10.
We want our angle to lie between 2 pi and 4 pi.
So we just add 2 pi to pi/3.
[tex] \frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3} [/tex]
So another angle is
[tex](10, \frac{7\pi}{3} )[/tex]
B. We want r to be negative so
[tex]10( - 1) = - 10[/tex]
And we want our angle to be in between 0 and 2 pi. so we add pi to our angle.
[tex] \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} [/tex]
So our new representation is
[tex]( - 10, \frac{4\pi}{3} )[/tex]
C. Finally, we want our r to be positvr and our angle to be negative and in between -2pi and 0.
So we just subtract 2 pi.
[tex] \frac{\pi}{3} - 2\pi = \frac{\pi}{3} - \frac{6\pi}{3} = - \frac{5\pi}{3} [/tex]
So our new representation is
[tex](10, - \frac{5\pi}{3}) [/tex]
Related Questions
54. Find [tex]y^{\prime}[/tex] if [tex]x^y=y^x\text{.}[/tex]
Answers
Step-by-step explanation:
Take the natural log of both sides:
[tex]ln ({x}^{y} ) = ln ({y}^{x} )[/tex]
Logarithm rules allow you to bring down the exponents:
[tex]yln(x) = xln(y)[/tex]
Now differentiate. We will have to implicitly differentiate 'y' since it is a function of 'x'. Both sides require the product rule:
[tex] \frac{dy}{dx} ln(x) + \frac{y}{x} = ln(y) + \frac{x}{y} \frac{dy}{dx} [/tex]
Isolate the terms that have y' since that is what we want:
[tex] \frac{dy}{dx} ln(x) - \frac{x}{y} \frac{dy}{dx}= ln(y) - \frac{y}{x} [/tex]
Factor out y' to get:
[tex] \frac{dy}{dx}( ln(x) - \frac{x}{y})= ln(y) - \frac{y}{x} [/tex]
Therefore:
[tex] \frac{dy}{dx} = \frac{ln(y) - \frac{y}{x} }{ln(x) - \frac{x}{y} } [/tex]
A grounds crew is marking out a circular logo at the center of a football field. The logo will
have a circumference of 141.3 feet. What will be the diameter length of the logo in yards?
Answers
Answer:
circumference of a circle formula is C=2*pi*r
Step-by-step explanation:
then
141.3 = 2*pi * r
solve for r
141.3/ (2*pi) = r
22.48859 feet
diameter is 2*r
2*22.48859= 44.9771 feet
divide by 3 because there are 3 feet in one yard
44.9771/3= 14.99239 yds.
it doesn't say to round off, but I would call this 15 yds.
Diameter is 15 yards ± .008 yds That's just about 1/4 of an inch
176.98 round to the nearest cent
Answers
Answer:
See answer(s) below
Step-by-step explanation:
$ 176.98 to nearest cent is $ 176.98
176.98 cents rounded to the nearest cent is 177 cents
Sarah can make 5 tables in 3 days, how many can she make in 21 days?
Answers
Answer
the answer is 105
Step-by-step explanation:
multiply 5 and 21
answer is 105
Step-by-step explanation:
multiply 5x21
Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval Then find all numbers c that satisfy the conclusion of the Mean Value Theorem: f(x) = 1/x on [1,3]
Answers
f(x) = 1/x and its derivative f '(x) = -1/x² are discontinuous only at x = 0; everywhere else it is defined and behaves nicely in the sense that f is
• continuous on the closed interval [1, 3], and
• differentiable on the open interval (1, 3)
and the MVT holds.
The theorem says there is some real number c between 1 and 3 such that
[tex]f'(c) = \dfrac{f(3) - f(1)}{3 - 1}[/tex]
Solve for this c :
[tex]-\dfrac1{c^2} = \dfrac{\frac13-\frac11}{3 - 1} \implies c^2 = 3 \implies \boxed{c = \sqrt3}[/tex]
What is the domain of the relation below?
Answers
Domain are the x values
{-4,-2,0,2}
Answer:
{-4, -2, 0, 2]
Step-by-step explanation:
THIS IS THE SET OF X-VALUES:
Domain is {-4, -2, 0, 2]
A litter of puppies has some male and
some female puppies. This can be
described with the following equation.
L = m + f
Solve the equation for the number of
female puppies, f.
Enter the variable that belongs in the green box.
f = [?] - [
Answers
L is in the green box
10. Find [tex]\frac{d^{2}}{d x^{2}}\int ^x_0\left(\int ^{\sin t}_1\sqrt{1+u^{4}}du\right)dt\text{.}[/tex]
Answers
Let g(t) denote the inner integral. By the fundamental theorem of calculus, the first derivative is
[tex]\displaystyle \frac{d}{dx} \int_0^x g(t) \, dt = g(x)[/tex]
Then using the FTC again, differentiating g gives
[tex]\displaystyle \frac{dg}{dx} = \frac{d}{dx} \int_1^{\sin(x)} \sqrt{1+u^4} \, du = \boxed{\cos(x) \sqrt{1+\sin^4(x)}}[/tex]
During a 6-week weight-loss regimen, Tony lost weight at a rate of 1.1 pounds per day. How much did he lose after 16 days? After weeks?
Answers
Answer:
After 16 days: 17.6 pounds
After 6 weeks: 46.2
Step-by-step explanation:
1.1 x 16 = 17.60
42 x 1.1 = 46.2 (6 weeks x 7 days a week = 42)
The weight loss after 16 days will be 17.6 pounds and after 6 weeks will be 46.2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that during a 6-week weight-loss regimen, Tony lost weight at a rate of 1.1 pounds per day.
The weight loss after 16 days will be calculated as,
1.1 x 16 = 17.60 pounds
The weight loss after 6 weeks will be calculated as,
42 x 1.1 = 46.2 (6 weeks x 7 days a week = 42)
Therefore, the weight loss after 16 days will be 17.6 pounds and after 6 weeks will be 46.2.
To know more about an expression follow
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Your brother is 1/3 your age. Your sister is 4 years older than your brother. Your sister is 9 years old. Write and solve an equation to find your age a.
what is the equation helppppp
Answers
Answer:
Your age(a) is 15 in this case.
If your brother is 1/3 of your age, that means multiply your brother's age by 3
Your sister is 9, and is 4 years older than your brother. In that case, we now know that your brother is 5
With that information, we can put this into a valid equation.
------------------------------------------------------------------------------------------------------------
turn 1/3 into a flipped fraction, 3/1 which is equal to 3
your brother's age is 5, so the first value would be 5
5 times 3 is 15, so that means a is 15
[tex]5 * 3/1 = 15[/tex]
Aman is adding -17 + 9. He wants to write -17 as the sum of two numbers so that one of the numbers, when added to 9, will equal 0.
Write integers in the blanks to show how Aman will solve this problem.
-17 + 9 = _____ + _____ + 9
-17 + 9 = _____ + 0
My question has been deleted because it was "incomplete." Look at photo please. Would really appreciate it, I just need the integers from the blanks above! Thank you!
Answers
Answer:
answer is ‘see analysis’
Step-by-step explanation:
A factory sells backpacks for $40.00 each. The cost to make
1 backpack is $10.00. In addition to the costs of making
backpacks, the factory has operating expenses of $12,000 per week. The factory's goal is to make a profit of at least $980
each week.
Which inequality represents the number of backpacks, x, that
need to be sold each week for the factory to meet this goal?
A. 30x + 12,000 < 980
B. 30x + 12,000 > 980
C. 30x - 12,000 < 980
D. 30x – 12,000 2 980
Answers
Answer:
it is a to my calculation
Step by step
What is the surface area of a rectangular prism with a height of 5 cm, length of 5.4 cm, and width of
2.4 cm?
The surface area is
Answers
=5.4*5*2.4= A=103.92cm²
The first image for the question and the other image for the example please I want the correct answer.
Answers
it is 2
Step-by-step explanation:
Answer:
the most appropriate answer will Be 2
Step-by-step explanation:
be happy
What is the measure of angle c?
Answers
Answer:
∠ c = 29°
Step-by-step explanation:
∠ b and 97° are vertically opposite angles and are congruent , so
∠ b = 97°
the 3 angles in the triangle sum to 180° , that is
54° + b + c = 180°
54° + 97° + c = 180°
151° + c = 180° ( subtract 151° from both sides )
c = 29°
Answer:
•SEE ABOVE ATTACHMENT•HOPE IT HELPS!
MARK AS BRAINLIAST.
Find the shaded area. Choose the letter for the best answer.
I’m checking if I’m correct
Answers
Answer:
H. 36 sq inches
Step-by-step explanation:
area of rectangle
= 4 x 6
= 24
area of triangle
= 1/2 x (10-6) x (4+2)
= 12
total shaded area
= 24 + 12
= 36 sq inches
so answer is H
hope this helps!
find the
Domain and sketch a
graph of
f (X) =2-0,4x
Answers
f(x)=x^2−2x+1
Yw and pls mark me brainiest
Answer:
-infty<xinfty
Step-by-step explanation:
Let f(x) = 6x^2 - 4x + 2. Find a constant c between 1 and 9 such that the average value of the function f(x) on the interval (1,9] is equal to fc).
A. 4.8735
B. 5.5402
C. 5.5721
D. -4.8735
E. 164
Answers
The value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.
What is mean value theorem?Mean value theorem is the theorem which is used to find the behavior of a function.
The function given as,
[tex]f(x) = 6x^2 - 4x + 2[/tex]
The value of function at 0,
[tex]f(0) = 6(0)^2 - 4(0) + 2\\f(0)=2[/tex]
Differentiate the given equation,
[tex]f(x)' = 6\times2x - 4\times1 + 0\\f(x)' = 12x - 4\\f(x)' = 12x -4[/tex]
If the constant c between 1 and 9 such that the average value of the function f(x) on the interval (1,9], then,
[tex]f(c)'=12c-4[/tex]
Using Lagrange's mean value theorem,
[tex]f(c)'=\dfrac{f(9)-f(1)}{9-1}\\12c-4=\dfrac{452-4}{9-1}\\12c=54+4\\c=\dfrac{60}{12}\\c=5[/tex]
Thus, the value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.
Learn more about the mean value theorem here;
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Answer:
5.5402
Step-by-step explanation:
First you need to find the average value of the function, you can use a calculator to do that, which you will find is 164.
The questions asks you to find a number between 1 and 9 so that f(c) (which is just f(x)) equals the average value of the function.
Since you already know the average value (164), you can set the equation equal to 164 and solve for x, which should give you 5.5402.
If you want more information: the function equals the average value, which is 164=6x^2-4x+2, is the equation you want to set up and solve for x.
You may get two answers and I can't explain why because I don't understand it that well, just use the one that is in the 1 to 9 range.
The second answer should be negative which is out of the 1 to 9 range, which leaves you with the other number that rounds up to 5.5402
I hope this helps any other struggling students
Do y’all know what the line on top mean?
Answers
Answer: hii
"Overbar (Vinculum)"Step-by-step explanation:
"a horizontal line written above a mathematical symbol to give it some special meaning."
" The vinculum can indicate a repeating decimal value: When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: ‾"
Hopefully this helps you!
- Matthew
Laura has 7 more than
triple the number of
pens Ann has. If Ann
has r
pens,
write an
expression for how
many pens Laura has.
Answers
Step 6. Check the answer in the problem and make sure it makes sense.
Yes, 75+0.25\left(500\right)=200.
Step 7. Write a sentence that answers the question. Sergio and Lizeth can travel 500 miles and still stay on budget.
Taleisha’s phone plan costs her ?28.80 a month plus ?0.20 per text message. How many text messages can she use and keep her monthly phone bill no more than ?50?
a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$3000 at the end of each year
Time
Rate
6% compounded annually
30 years
(round to the nearest dollar if needed)
Answers
Answer:
i think The final answer would be $3512.58
Step-by-step explanation:
help pls math is hard
Answers
x^2 + y^2 +2x+6y=26
what is the center
what is the radius
please show calculations/steps
Answers
Answer:
centre = (- 1, - 3 ) , radius = 6
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 2x + 6y = 26 ( collect x and y terms )
x² + 2x + y² + 6y = 26
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(3)y + 9 = 26 + 1 + 9
(x + 1)² + (y + 3)² = 36 ← in standard form
with centre = (- 1, - 3 ) and r = [tex]\sqrt{36}[/tex] = 6
[tex](x {}^{2} + 2x + 1) - 1 = (x + 1) {}^{2} - 1[/tex]
[tex](y {}^{2} + 6y + 9) - 9 = (y + 3) {}^{2} - 9[/tex]
[tex](x + 1) {}^{2} - 1 + (y + 3) {}^{2} - 9 = 26[/tex]
[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 26 + 10[/tex]
[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 36[/tex]
General form:[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
Center coordinates: I ( a , b ) I ( -1 , -3 )Radius:[tex]r {}^{2} = 36[/tex]
[tex]r = \sqrt{36} = 6[/tex]
Please help photo attached
Answers
Answer:
Your answer would be 2.
Step-by-step explanation:
If you divided 20 by 10 you get 2.
That's your answer.
Hope this helps.
The parent function f(x)= x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by
graph B and graph C.
Answers
Answer:
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Step-by-step explanation:
A square plot is 64 m^2 ..find its length..
Answers
Answer:
Length: 8 m
Explanation:
square area: length²
Here:area: 64So find Length:length² = 64length = ±√64length = ±8As length is positive, length = +8
Work out the sheet below
Answers
Answer:
32cm² is the area of face CFGD.
Step-by-step explanation:
Suppose the graph represents a map in which each grid unit equals 1 mile. If a school is located at B and a
library is located at N, what is the distance between the school and the library?
Answers
answer: 5 miles
Step-by-step explanation:
use the distance formula to solve this problem. plug in the two coordinates to solve this problem.
Select the correct answer.
A polygon is translated and then stretched vertically. Which statement is correct?
A.
The translation does not preserve side lengths and angles, but the vertical stretch preserves side lengths and angles of the preimage.
B.
Neither the translation nor the vertical stretch preserves side lengths and angles of the preimage.
C.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
D.
Both the translation and the vertical stretch preserve side lengths and angles of the preimage.
Answers
C: The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
How to explain translation of a polygon?When we talk about the concept of translation in transformations, it means that the side lengths remain the same. This means the object is just moved from one place to another and the lengths are preserved.
However, when we stretch the polygon, it means we are increasing or decreasing at least one side length.
Thus, we can conclude that The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
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find the vaule of 3x + 2 when 7 +x =5
Answers
Answer:
=> -4
Step-by-step explanation:
7 + x = 5
=> x = 5 - 7
=> x = -2
Putting the value of x = -2 in equation 3x + 2
=> 3(-2) + 2
=> -6 + 2
=> -4
Answer:
-4
Step-by-step explanation:
when 7 +x =5 solve for x by subtracting 7
x=5-7 =-2
3x+2 = substitute (-2) for x
3( )+2
3(-2)+2
-6+2=-4