Convert the equation to polar form. (Use variables r and as needed.)
x2 − y2 = 12
In converting to polar coordinates, we take
x = r cos(t)
y = r sin(t)
Then in the given equation,
x² - y² = 12
(r cos(t))² - (r sin(t))² = 12
r² cos²(t) - r² sin²(t) = 12
r² (cos²(t) - sin²(t)) = 12
r² cos(2t) = 12
r² = 12 sec(2t)
ChallengE
See attachment and answer :)
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
Answer :[tex]\displaystyle{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}[/tex]
Step-by-step-explanation:
We have given an expression.
We have to simplify the expression.
The given expression is
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16\:\times\:3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\pink{\sf\:\sqrt{a\:\times\:b}\:=\:\sqrt{a}\:\times\:\sqrt{b}\:}}\:\cdots\sf\:a\:,\:b\:\geq\:0}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16}\:\times\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\times\:4\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\blue{\sf\:\sqrt{\dfrac{a}{b}}\:=\:\dfrac{\sqrt{a}}{\sqrt{b}}\:}}\:\cdots\sf\:b\: > \:0}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{\sqrt{1}}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{1}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\sqrt{3}\:\times\:2\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\times\:2\:\sqrt{3}\:\times\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}} \\ \\\displaystyle{\implies\sf\:\dfrac{32\:\times\:3\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{8\:\times\:4\:\times\:3\:-\:5\:+\:(\:6\:\sqrt{3}\:\times\:2\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:6\:\times\:2\:\times\:\sqrt{3}\:\times\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:12\:\times\:3\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:12\:\times\:3}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:+\:12\:\times\:3\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:(\:8\:+\:3\:)\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:\times\:11\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{132\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}\:\times\:\dfrac{\sqrt{3}}{\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{2\:\times\:3}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{6}} \\ \\ \\ \displaystyle{\therefore\:\underline{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}}[/tex]
PLS HELP ON GEOMETRY: select all the true statements
Answer:
E
Step-by-step explanation:
What is an equation of the line that passes through the points (-4, -5) and (-2, -6)?
Answer: [tex]y=-\frac{1}{2}x-7[/tex]
Ok done. Thank to me :>
Hello can anyone help me with these problems please and ty
12. x= 4
13. x= 4
14. x= -1
Check the steps in the picture above
The area of any rectangular shape is given by the product of its width and length. If the area of a particular
rectangular garden is given by A = 15x°-35x and its width is given by 5x, then find an expression for the
garden's length.
The expression that can be used to find the
garden's length is l = 5x(x - 7) / 5x where l = (x - 7)
Given:
Area of a rectangle = 15x² - 35x
Width of the rectangle = 5x
Length of the rectangle = l
Area of the rectangle = length × width
15x² - 35x = l * 5x
Factor out the left hand side
5x(x - 7) = l * 5x
Divide both sides by 5x
5x(x - 7) / 5x = l
x - 7 = l
Therefore, the expression that can be used to find the garden's length is l = 5x(x - 7) / 5x
Learn more about area of a rectangle:
https://brainly.com/question/14137384
14 divided 4 and 7/8 written in simplest form
Answer:
7 and that is its simplest form
Step-by-step explanation:
thank me later
Answer:
4
Step-by-step explanation:
14 ÷ 4 = 3.5
3.5 and 7/8 = 4
I GIVE BRAINLEST !! PLS SLOLVE
Answer:
√6/2+1
Step-by-step explanation:
multiplying by √6/√6, we get √6(3+√6)/6=(3√6+6)/6=√6/2+1
The perimeter of the shape is
feet.
Answer:
This doens't realy make sense dude
help me with this question plz
Answer:
2
Step-by-step explanation:
you tell me true ya false
Type the correct answer in each box.
The slope of the line shown in the graph is ___, and the y-intercept of the line is ___.
Answer:
The slope (or gradient) is 0.6 and the y-intercept is 6.
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $1,000, annual interest: 6%, interest periods: 6, number of years: 14 more than the investment compounded annually.
After 14 years, the investment compounded periodically will be worth $ ____(Round to two decimal places as needed.)
After 14 years, the investment will be worth $ 2,306.72.
Given that an investment has a $ 1000 principal, 6% annual interest, 6 interest periods and 14 years of investment, to determine, after 14 years, how much the investment will be worth, the following calculation must be performed:
1000 x (1 + 0.06 / 6) ^ 14x6 = X 1000 x 1.01 ^ 84 = X 1000 x 2.3067 = X 2,306.72 = X
Therefore, after 14 years, the investment will be worth $ 2,306.72.
Learn more about maths in https://brainly.com/question/15603792
Find the missing side in the similar figures below
Answer:
e
Step-by-step explanation:
24*5/3=40
According to the website www.olx.uz, monthly rent for a two-bedroom apartment has a mean of
$250 and a standard deviation of $100 in the city of Andijan. The distribution of the monthly rent does not
follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample
of 40 two-bedroom apartments and finding the mean to be at least $275 per month?
Using the normal distribution and the central limit theorem, it is found that there is a 0.0571 = 5.71% probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of $250, hence [tex]\mu = 250[/tex].The standard deviation is of $100, hence [tex]\sigma = 100[/tex].The sample is of 40 apartments, hence [tex]n = 40, s = \frac{100}{\sqrt{40}}[/tex].The probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month is the p-value of Z when X = 275, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{275 - 250}{\frac{100}{\sqrt{40}}}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
1 - 0.9429 = 0.0571
0.0571 = 5.71% probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month.
You can learn more about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
need this soon please
Answer: pretty sure -7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
(-80) - (-10) is -79
-70 / (+10) = -7
been trying for an hour, need help
Answer:
[tex]\sqrt{\frac{5}{2} }[/tex]
Step-by-step explanation:
We know that this is a 45-45 triangle. Where there are two angles that are 45 degrees and the other angle is a right angle (90 degrees).
The sides are a, b (which equals a) and, c (which equals a*square root of 2).
In this triangle we are given c, and tasked at finding a. Since c= [tex]a*\sqrt{2}[/tex], then we know that, [tex]\sqrt{5}= a*\sqrt{2}[/tex]. Divide the equation by square root of 2 to find a. Which equals [tex]\sqrt{\frac{5}{2} }[/tex]
1985 x 99 I already know the answer: 196515
Answer:
196515
Step-by-step explanation:
Answer:
196515
Step-by-step explanation:
Suppose a 5-digit number is formed using the digits from 1 to 9 (without replacement). What is the probability that it will be an even number?
Answer:
First take 5 empty. Digits.The no of digits are 9 (1-9).The last no must be even so . The total no of even no’s . Are 4 (2,4,6,8)The probability of last digit is 4There are remaing 8 digits so. Place them where. U required. The probability are. 8, 7,6,5(no reputations)The final answer is 4*8*7*6*5=6720 waysAnswer:
0.444 (44.4%)
Step-by-step explanation:
All possible ending: 1,2,3,4,5,6,7,8,9 ... 9
ending with 2,4 6,8 to make even number: 4
___ ___ ___ ___ ___
even number : 8 * 7 * 6 * 5 * 4
All 5 digit without repeating: 8 * 7 * 6 * 5 * 9
possibility = (8*7*6*5*4) / (8*7*6*5*9)
= 4/9
= 0.444 (44.4%)
_______________________________________________
(4 * ₈P₄) / (9 * ₈P₄) = 4/9
Divide 7 divided by 3/5
Express your answer in simplest form.
Answer:
35/5
Step-by-step explanation:
7/1 divded by 3/5. flip 3/5 to its reciprocal so it becomes 5/3, then times 7/1 by 5/3
At the beginning of a basketball season, the Panthers won 20 games out of 80 games. At this rate, how many games will they win in a normal 100-game season?
games
During a Lynx basketball game, the ratio of baskets made to baskets attempted was 2 to 3. The Lynx made 88 baskets. How many baskets did they attempt?
1+3+5+...+X=441
X=?
Answer:
559
Step-by-step explanation:
PLS HELP HELLLLLOPPPPPP PLEASSSS BRO IM LITERALLY GONNA CRY
Answer:
F The last option
{ n = 7 h - 2}
{ n = 4 h - 2}
Step-by-step explanation: I HOPE THIS HELPS
Answer:
it's
n=2h+4
n=2h+7
(and vice versa)
The given represent 7 necklace and 4 necklace,that means add it to the no.of necklace they can make every hour and that is 2. So the correct equation is in the above answers.
Step-by-step explanation:
I hope it helps you a lot dude lovelots
#LEARN WITH BRAINLY
Need help asap! I would appreciate it soo much if your answered.
Answer:
Step-by-step explanation:
The point of closest approach is on a line perpendicular to the zip line
perpendicular lines have negative reciprocal slopes, so the perpendicular line has slope (8/3)
y = (8/3)x + b
adding our known point (3, 16)
16 = (8/3)3 + b
b = 8
y = (8/3)x + 8
now find where the two lines intersect by solving two equations with two unknowns
y = (-3/8)x + 8
as the two lines have a common y intercept of 8, that is the common point
(0, 8)
The distance from (0, 8) to (3, 16) is
d = √((3 - 0)² + (16 - 8)²) = √73 = 8.5440037453...
d = 8.5 ft
What is the value of x + y when x is the additive identity and y = 5?
O 5
O There is not enough information to determine the value.
O - 5
O 0
Answer:
-5.
Step-by-step explanation:
5 + -5 = 0, so i's -5.
what is the expression to 50 times the sum of 64 and 36
Answer:
50(64+36) this would be your answer
50 x (64+36)
Step-by-step explanation:
According to PEMDAS, you will have to solve 64 + 36 first, so you need to put them in the parenthesis. Next, simply multiply by 50.
WILL GIVE BRAINLIEST
Answer:
it is d
Step-by-step explanation:
Help help help math math
Answer:
25%
Step-by-step explanation:
multiply it by 100 over 1 then divide the top by the bottom.
2 2/7 multiplied by 5 1/6
Answer:
11 17/21
Step-by-step explanation:
Answer:
11 17/21
Step-by-step explanation:hope i helped
Find the slope of the line below:
Answer:
[tex]\bold{m=-\frac{2}{5}}[/tex]
Step-by-step explanation:
Slope
First, we have to find two points that hit the graph at the right place:
[tex](0,4)[/tex]
[tex](10,0)[/tex]
Then, we plug the value into the slope formula:
[tex]\sf{Slope\:formula:\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{0-4}{10-10}[/tex]
Now, we can solve:
[tex]\frac{0-4}{10-0}\\\\=\frac{-4}{10}\\\\\bold{m=-\frac{2}{5}}[/tex]
Therefore, the slope of the line is [tex]-\frac{2}{5}[/tex]