Answers
Answer:
1) The polar form of that equation will be r= √5cos(2θ)
2) i am stuck on this one (sorry)
Step-by-step explanation:
(i) We know that [tex]x = r\cos{\theta}\:\text{and}\:y = r\sin{\theta}.[/tex] So we can write the given equation as
[tex]r^2\cos^2\theta - r^2\sin^2\theta = 5[/tex]
[tex]\Rightarrow r^2(\cos^2\theta - \sin^2\theta) = 5[/tex]
[tex]r^2 = \dfrac{5}{(\cos^2\theta - \sin^2\theta)}[/tex]
[tex]\:\:\:\:\:=\dfrac{5}{\cos{2\theta}} = 5\sec{2\theta}[/tex]
(ii) Recall that
[tex]\cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}}[/tex]
[tex]\csc{\theta} = \dfrac{1}{\sin{\theta}}[/tex]
so we can write r as
[tex]r = 8\cot{\theta}\csc{\theta}[/tex]
[tex]\:\:\:\:= 8\left(\dfrac{\cos{\theta}}{\sin{\theta}}\right)\left(\dfrac{1}{\sin{\theta}}\right)[/tex]
[tex]\:\:\:\:= 8\left(\dfrac{x}{y}\right)\!\left(\dfrac{r}{y}\right) = \dfrac{8xr}{y^2}[/tex]
Upon simplification, we get
[tex]y^2 = 8x[/tex]
Related Questions
What is the value of the expression 4x^3 – 3x when x = 6?
Answers
4(6)^3 - 3(6)
4*(216)- 18
864 - 18
=846.
Hope it helped!
Find the supremum and infimum of each of the following sets of real numbers
S = {3x 2 − 10x + 3 < 0}
Answers
Answer:
[tex]\sup(S) = 3[/tex].
[tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Step-by-step explanation:
When factored, [tex]3\,x^{2} - 10\, x + 3[/tex] is equivalent to [tex](3\, x - 1)\, (x - 3)[/tex].
[tex]3\, x^{2} - 10\, x + 3 < 0[/tex] whenever [tex]\displaystyle x \in \left(\frac{1}{3},\, 3\right)[/tex].
Typically, the supremum and infimum of open intervals are the two endpoints. In this question, [tex]\sup(S) = 3[/tex] whereas [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Below is a proof of the claim that [tex]\sup(S) = 3[/tex]. The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar.
In simple words, the supremum of a set is the smallest upper bound of that set. (An upper bound of a set is greater than any element of the set.)
It is easy to see that [tex]3[/tex] is an upper bound of [tex]S[/tex]:
For any [tex]x > 3[/tex], [tex]3\,x^{2} - 10\, x + 3 > 0[/tex]. Hence, any number that's greater than [tex]3\![/tex] could not be a member [tex]S[/tex]. Conversely, [tex]3[/tex] would be greater than all elements of [tex]S\![/tex] and would thus be an upper bound of this set.To see that [tex]3[/tex] is the smallest upper bound of [tex]S[/tex], assume by contradiction that there exists some [tex]\epsilon > 0[/tex] for which [tex](3 - \epsilon)[/tex] (which is smaller than [tex]3\![/tex]) is also an upper bound of [tex]S\![/tex].
The next step is to show that [tex](3 - \epsilon)[/tex] could not be a lower bound of [tex]S[/tex].
There are two situations to consider:
The value of [tex]\epsilon[/tex] might be very large, such that [tex](3 - \epsilon)[/tex] is smaller than all elements of [tex]S[/tex].Otherwise, the value of [tex]\epsilon[/tex] ensures that [tex](3 - \epsilon) \in S[/tex].Either way, it would be necessary to find (or construct) an element [tex]z[/tex] of [tex]S[/tex] such that [tex]z > 3 - \epsilon[/tex].
For the first situation, it would be necessary that [tex]\displaystyle 3 - \epsilon \le \frac{1}{3}[/tex], such that [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex]. Let [tex]z := 1[/tex] (or any other number between [tex](1/3)[/tex] and [tex]3[/tex].)
Apparently [tex]\displaystyle 1 > \frac{1}{3} \ge (3 - \epsilon)[/tex]. At the same time, [tex]1 \in S[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex] when [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex].With the first situation [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex] accounted for, the second situation may assume that [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex].
Claim that [tex]\displaystyle z:= \left(3 - \frac{\epsilon}{2}\right)[/tex] (which is strictly greater than [tex](3 - \epsilon)[/tex]) is also an element of [tex]S[/tex].
To verify that [tex]z \in S[/tex], set [tex]x := z[/tex] and evaluate the expression: [tex]\begin{aligned} & 3\, z^{2} - 10\, z + 3 \\ =\; & 3\, \left(3 - \frac{\epsilon}{2}\right)^{2} - 10\, \left(3 - \frac{\epsilon}{2}\right) + 3 \\ = \; &3\, \left(9 - 3\, \epsilon - \frac{\epsilon^{2}}{4}\right) - 30 + 5\, \epsilon + 3 \\ =\; & 27 - 9\, \epsilon - \frac{3\, \epsilon^{2}}{4} - 30 + 5\, \epsilon + 3 \\ =\; & \frac{3}{4}\, \left(\epsilon\left(\frac{16}{3} - \epsilon\right)\right)\end{aligned}[/tex].This expression is smaller than [tex]0[/tex] whenever [tex]\displaystyle 0 < \epsilon < \frac{16}{3}[/tex]. The assumption for this situation [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex] ensures that [tex]\displaystyle 0 < \epsilon < \frac{16}{3}\![/tex] is indeed satisfied. Hence, [tex]\displaystyle 3\, z^{2} - 10\, z + 3 < 0[/tex], such that [tex]z \in S[/tex].At the same time, [tex]z > (3 - \epsilon)[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex].Either way, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex]. Contradiction.
Hence, [tex]3[/tex] is indeed the smallest upper bound of [tex]S[/tex]. By definition, [tex]\sup(S) = 3[/tex].
The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar and is omitted because of the character limit.
Consider f(x)=4x and g(x) = square root of x^2-1 and h(x)= square root of 16x-1
Answers
f(x) = 4x
g(x) =
[tex] \sqrt{x^{2} \: - \: 1 } [/tex]
h(x) =
[tex] \sqrt{16x \: - \: 1} [/tex]
We want to check if h(x) = g(f(x))
So g(f(x)) =
[tex] \sqrt{(4x) {}^{2} - \: 1} [/tex]
Simplified;
g(f(x)) =
[tex] \sqrt{16x {}^{2} \: - \: 1 } [/tex]
But h(x) =
[tex] \sqrt{16x \: - \: 1} [/tex]
Hence g(f(x)) is not equal to h(x)
In the coordinate plane, plot AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ given by the points A(−4, 5), B(−4, 8), C(2, −3), D(2, 0)
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The x-coordinate is the same in each pair of points, so the line segment will be a vertical line segment 3 units long.
i need help answering the question in the picture provided
Answers
answer:
(a).
Equation of circle is x² + y² - 25 = 0
(b).
(-5, 0) » yes
(√7, 1) » no
(-3, √21) » no
(0, 7) » no
Step-by-step explanation:
(a).
If centred at origin, centre is (0, 0)
General equation of circle:
[tex]{ \boxed{ \bf{ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}}}[/tex]
but g and f are 0:
[tex] {x}^{2} + {y}^{2} + c = 0 \\ but : \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = { - 25} [/tex]
If you were to take a longitudinal section from a long cylinder, what shape would you get? Question 23 options: A circle A parallelogram A square A rectangle
Answers
Answer:
A Rectangle
Step-by-step explanation:
A longitudinal section means that the plane slicing the cylinder is vertical, just as a latitudinal section means that the slice is horizontal.
When you think about it, a flat slice of a cylinder in the vertical direction is a rectangle.
If the cylinder is sliced along the length of the cylinder then the shape we get is a rectangle. Then the correct option is B.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
If you were to take a longitudinal section from a long cylinder.
Then the shape we get will be
If the cylinder is sliced along the length of the cylinder then the shape we get is a rectangle.
More about the cylinder link is given below.
https://brainly.com/question/3692256
Match the terms to their definition.
1. union
2. intersection
3. compound inequality
Hurry plz
Answers
Step-by-step explanation:
compound inequality: a statement formed by two.......
intersection: elements that are in both set A and B
union: elements that are in either set A or B
Select the correct answer.
Which statement best describes the zeros of the function () = (x-6)(X + 8x + 16)?
ОА.
The function has two distinct real zeros.
ОВ.
The function has three distinct real zeros.
OC. The function has one real zero and two complex zeros.
OD
The function has three complex zeros.
Answers
Answer:
So for the sequence to work, the 5,3=18 would have to be changed to 5,3=23 in which it now fits and works to solve for x which is 4. There was a pattern of the numbers 4 and 5 that surfaced as the difference between each pairings sum total. The difference between each sum was alternating between the numbers 4 and 5, which equal 9 when added together. Which also helped me to form a chart of sorts that makes sense. My answer is typed above, that is the most stable conclusion that I could come to to make sense of the pairings that were listed.
Answer: A (if i have well corrected)
Step-by-step explanation:
[tex]f(x)=(x-6)(x^2+8x+16)\ i\ suppose)\\\\f(x)=(x-6)(x+4)^2\\Sol=\{6;-4\}\\Answer \ A[/tex]
A property sells for $140,000 two years after it was purchased. If the annual appreciation rate is 6%, how much did the original buyer pay for it?
Answers
Answer:
$123,200
Step-by-step explanation:
0.06 x 2 = 0.12
140,000 x 0.12 = 16,800
140,000 - 16,800 = 123,200
The original buyer paid the amount of $123,200 for the property.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The property appreciated by 6% per year, so in two years it would have appreciated by 6% × 2 years = 12%.
Once we know the total appreciation, we can subtract that value from 100% to find the original purchase price as a percentage of the final sale price.
If the property appreciated by 12%, then the original purchase price must have been 100% - 12% = 88% of the final sale price.
Now, multiply the final sale price by the original purchase price as a percentage to find the original purchase price.
So, the original buyer paid the amount = 88% × $140,000 = $123,200
Therefore, the original purchase price was $123,200.
Learn more about the percentages here:
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√400=x² what is x? Thanks
Answers
Answer:
x=4.47213
I hope it's helps you
pls help with this problem
Answers
====================================================
Explanation:
Refer to the diagram below. The rectangle MATH has the diagonal MT that cuts the rectangle into two identical right triangles.
We then use the pythagorean theorem to find the length of the hypotenuse MT.
a^2 + b^2 = c^2
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
c^2 = 676
c = sqrt(676)
c = 26
Segment MT is 26 cm long.
This applies to the other diagonal AH as well.
A display case of glitter stickers are marked 15 for $2. If Cathy wants to buy 30 glitter stickers, how much will Cathy spend?
Answers
Answer:
$4, 15 x 2=30
2 x 2=4
Answer:
4 dollars
Step-by-step explanation:
We can write a ratio to solve
15 stickers 30 stickers
----------------- = -------------
2 dollars x stickers
Using cross products
15x = 2*30
15x = 60
Divide by 15
15x/15 = 60/15
x = 4
. Evaluate the expression below for x = 4. 6(x+8) (please
Answers
Answer:
D
Step-by-step explanation:
6(x + 8) = Plug in x with 4
6(4 + 8) =
6(12) =
72
6(4+8) (remember distributive property)
6(4) & 6(8)
24+48
=72
so that means the answer will be D. 72
5.
A bag contains three types of candy (gumdrops, jelly beans, and jawbreakers). If
chosen at random, the probability of getting a gumdrop is 1/6 and the probability
of getting a jellybean is 1/3 What is the probability of getting a jawbreaker?
Answers
Answer:
P) = 1/2 jawbreaker
simplified P) 3/6 = 1/2 jawbreaker
Which both mean the same, so show simplified if asked and either answer if not asked would be marked high.
as 2/6 + 1/3 = 3/6
1 - 3/6 = 3/6
= 1/2 are the workings.
Step-by-step explanation:
Jelly bean = 1/3 = 2/6
Gumdrop = 1/6
2/6 + 1/6 = 3/6 = the difference of 1
1-3/6 = 3/6
Therefore; P) = 3/6 jawbreaker
Calculate the distance between the points -8,2 and 3,2 on a coordinate plane
Answers
[tex]\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(3+8)^2+(2-2)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{11^2}[/tex]
[tex]\\ \rm\Rrightarrow 11[/tex]
please help meeee out
Answers
Answer:
between 15.5 and 16
Step-by-step explanation:
which std
jane bought two new skirts for school. one cost 15 less than twice the cost of the total cost for both skirts was 75, what was the cost of each skirt?
Answers
A multiple choice test contains 25 questions with 5 answer choices. What is the probability of correctly answering 8 questions if you guess randomly on each question?
Answers
Answer: 0.0623
Step-by-step explanation:
The probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
It is given that multiple choice test contains 25 questions with 5 answer choices.
To find probability of correctly answering.
What is probability?The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Given that:
The probability of each correct answer is [tex]p_{s}[/tex][tex]=\frac{1}{5}[/tex]
The probability of 8 successful answers in 25 independent trials for a binomial probability distribution is:
p(k|n)=[tex]\frac{n!}{(n-k)!*n!}[/tex][tex]p_{s}^{k} (1-p_{s})^{n-k} \\[/tex]
p(8|25)=[tex]\frac{25!}{(25-8)!*8!}[/tex][tex]{\frac{1}{5} }^{k} (1-1/5)^{25-8} \\[/tex]
p(8|25)=0.062348
So, the probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
Learn more about probability here:
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Name the two input device
Answers
Answer:
keyboard and mouse are two examples of input device
Answer:
keyboard and mouse
Step-by-step explanation:
If you like my answer than please mark me brainliest
the mean of seven numbers is 15. when three numbers are added, the mean of ten numbers becomes 12. find the mean of the three numbers.
Answers
Answer:
3 is the value I guess because with seven it becomes 15 where as with 10 it become 12 so there is 3 numbers gap
I don't know exactly so I just try
Answer:
13 is the answer
Step-by-step explanation:
15
Determine whether the ordered pairs (1,0) and 4,
(4:15)
are solutions of the following equation.
- 5x + 7y= -5
BRE
Is (1,0) a solution of - 5x + 7y = - 5?
O Yes
Ο Νο
(ANSWER QUICKLY)
Answers
Answer:
yes
Step-by-step explanation:
x = 1, y = 0
so,
-5×1 + 7×0 = -5
-5 + 0 = -5
-5 = -5
true, therefore (1, 0) is a solution (a point on the graph) of the equation.
I am not sure what the other pair should be.
The picture above is what I’m stuck on Algebra
Answers
Answer:
Inequality
2x > 14
Solution
x > 7
Step-by-step explanation:
Twice of a number = 2x or 2 * x
Is more than 14 = > 14
Put these 2 descriptions together
2x > 14
Then divide each side by the coefficient
2x / 2 = x > 14 / 2 = x > 7
Answer:
2x > 14
Any number above 7.
Step-by-step explanation:
"Twice a number (x) is more than 14." can be written as 2x > 14.
Breakdown:
2x > 14 for Twice a number (x) is more than 14.
2x > 14 for Twice a number (x) is more than 14.
2x > 14 for Twice a number (x) is more than 14.
The solution to the inequality is any number above 7.
round off 1,246,193 to the nearest thousands
Answers
Answer:
1,246,193 rounded to the nearest thousands is 1,246,000
Because the digit next to the thousands place (The hundreds place) is less that 5, it is 1 therefore you keep the digit the same in the thousands place and make the rest a 0.
Answer:
1,246,000
Step-by-step explanation:
1,246,193
The 6 is in the thousands place
We look at the hundreds place
1 is in the hundreds place, Since it is 4 or less, we leave the thousands place alone.
1,246,000
Can someone help me with this question? please
Answers
Answer:
6 cm3
Step-by-step explanation:
3 x 2 x 1 = 6
I need some help with the homework problem. I have a list of formulas, but can't seem to get it done.
[tex]\int\frac{9}{\sqrt{1+e^{2x}}} \, dx[/tex]
I started by taking the constant out and setting u = [tex]\sqrt{1+e^{2x\\}}[/tex]
After this I can't seem to progress.
Answers
After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives
[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]
Then taking differentials, you get
[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]
Replacing everything in the original integral then gives
[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]
Split up the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]
so that
[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]
A number is 10 more than another number. Twice the sum of the two numbers is 44. Find the two numbers.
Answers
Answer:
The two numbers are 6 and 16
Step-by-step explanation:
16+6=22
22+22=44
The numbers are 6 and 12.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number are x and y.
A number is 10 more than another number then
x + 10 = y...............(1)
and, Twice the sum of the two numbers is 44.
2(x+y)= 44...........(2)
Solving the above equation we get
x+ y= 22
y-10 + y = 22
2y = 32
y= 16
and, x= y-10 = 16-10= 6
Learn more about Algebra here:
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Gh bisects cf =2y-2 and cd =3y-11 find cd
Answers
Answer:CD is 4
Step-by-step explanation: ham
Whats the answer to it i can't figure it out
Answers
Answer:
-0.1
...............................
-0.1
Step-by-step explanation:
-1/7 = -0.142857
-0.1 = -0.10
-0.1 > -1/7
How do i express x^2-3x into the form of (x-m)^2+n.
I will give brainliest to first correct answer
Answers
Well this could be incredibly easy, by just saying [tex]m=0[/tex] and [tex]n=-3x[/tex].
This is a completely valid case but nevertheless seems too easy. The requirements are probably that n and m are integers or natural numbers but since that was not specified such probable requirement ought not to be followed.
Hope this helps :)
How can you rewrite simple rational expressions in different forms using long division?
(50 POINTS)PLEASE!!!!!
