Answers
Step-by-step explanation:
Let [tex]x = r\cos{\theta}[/tex] and [tex]y = r\sin{\theta}[/tex]. Substituting these into our equation, it becomes
[tex]\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1[/tex]
or
[tex]9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 225[/tex]
Let use the identity [tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex] to express the equation in terms of sine only:
[tex]9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 225[/tex]
which simplifies to
[tex]r^2(9 + 16\sin^2{\theta}) = 225[/tex]
Taking the square root and solving for r , we get the polar form of the equation as
[tex]r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}[/tex]
Answer:
x = r\cos{\theta}x=rcosθ and y = r\sin{\theta}y=rsinθ
\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1
25
r
2
cos
2
θ
+
9
r
2
sin
2
θ
=1
or
9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 2259r
2
cos
2
θ+25r
2
sin
2
θ=225
Let use the identity \cos^2{\theta} = 1 - \sin^2{\theta}cos
2
θ=1−sin
2
θ
9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 2259r
2
−9r
2
sin
2
θ+25sin
2
θ=225
which simplifies to
r^2(9 + 16\sin^2{\theta}) = 225r
2
(9+16sin
2
θ)=225
Taking the square root and solving for r ,
r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}r=
9+16sin
2
θ
15
Related Questions
Find the measurement of angle ABC
Answers
now that you have the complementary angle of 70/3 degrees, subtract 180-70/3 to get 156 2/3 degrees as your final answer
The bases of a prism are always
A. perpendicular
B. parallel
C. intersecting
D. rectangles
Answers
Answer:
D. rectangles
Step-by-step explanation:
Perpendicular is when they cross but the base isn't perpendicular
Parallel is when two lines never touch, but in the base of a prism there are lines that touch
Intersecting is when two or more lines meet and cross over each other
The area of a children square playground is 50m squared.
a. what is the exact length of the playground
2. pine logs 3m long are to be laid around the playground. How many logs will need to be bought?
Answers
Answer:
a. solution
Area = 50 m^2
Area of square = l^2
or, 50 m^2 = l^2
or, √50m^2 = l
or, 5√2 m= l
Hence, The exact length of the playground is 5√2 m.
Answers Please i gave the most amount of points i could!!!
Answers
Answer:
its c
Step-by-step explanation:
2. If 3x - y = 4, what is the value of 27^x/3^y
Answers
9514 1404 393
Answer:
81
Step-by-step explanation:
Rewriting the expression as powers of 3, we get ...
[tex]\dfrac{27^x}{3^y}=\dfrac{(3^3)^x}{3^y}=3^{3x-y}=3^4=\boxed{81}[/tex]
can anyone plz with steps (not for useless man )
Answers
[tex]\boxed{\sf \displaystyle{\lim_{x\to a}}(x^n)=a^n}[/tex]
[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}(\sqrt{3x}-\sqrt{x-5})[/tex]
[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}\sqrt{3x}-\displaystyle{\lim_{x\to \infty}}\sqrt{x-5}[/tex]
[tex]\\ \sf\longmapsto \infty^{\dfrac{1}{2}}-\sqrt{\infty-5}[/tex]
[tex]\\ \sf\longmapsto \infty-\sqrt{\infty}[/tex]
[tex]\\ \sf\longmapsto\infty-\infty[/tex]
[tex]\\ \sf\longmapsto\infty[/tex]
There are five boys to every three girls in an introductory chinese course. If there are 384 students enrolled in the course. how many are boys?
Answers
384\3 (girls) gives you 128 (girls)
384-128= 256
and to check yourself do 256+128
giving you 384
What would be the slope for a line passing through the two points below?
Point 1: (1, 0.1) Point 2: (7, 26.8)
Answers
Answer:
slope is 28.7/6
Step-by-step explanation:
m= y2-y1/x2-x1
subtitute value in formula:
m=28.8-0.1/7-1
m=28.7/6
Here are two triangles identical in size.10 cm.The two triangles are overlapped 3 cm 6 cm.What is the area of the blue triangle showing?
Pls I will give Brainliest
Sorry if the picture is too dark :(
Answers
Answer:
51 cm²
Step-by-step explanation:
Let's ASSUME that the vertical measurements are taken perpendicular to the roughly horizontal baselines.
The three yellow triangles are all similar
the upper small triangle has height 3 and base 6 cm. The ratio of the lengths is 6/3 = 2
This means the medium (overlapping) triangle has lengths 10 - 3 = 7 and 7(2) = 14 cm
Area of the large triangle is ½(14 + 6)(10) = 100 cm²
Area of the overlapping yellow triangle is ½(7)(14) = 49 cm²
Exposed area of the blue triangle is 100 - 49 = 51 cm²
Both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.
Based on the information given from statement, we can determine the missing length of the yellow triangle by means of simmilarity ratios, that is:
[tex]\frac{3\,cm}{6\,cm} = \frac{10\,cm}{x}[/tex] (1)
Where [tex]x[/tex] is the base of the yellow triangle, in centimeters.
Now we proceed to find the length base:
[tex]x = \frac{6\,cm}{3\,cm}\times 10\,cm[/tex]
[tex]x = 20\,cm[/tex]
The area of the triangle can be found by means of the following expression:
[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (2)
Where:
[tex]A[/tex] - Area of the yellow triangle, in square centimeters.[tex]b[/tex] - Base, in centimeters.[tex]h[/tex] - Height, in centimeters.If we know that [tex]b = 20\,cm[/tex] and [tex]h = 10\,cm[/tex], then the area of the triangle is:
[tex]A = \frac{1}{2}\cdot (20\,cm)\cdot (10\,cm)[/tex]
[tex]A = 100\,cm^{2}[/tex]
The area of the yellow triangle is 100 square centimeters and the area of the blue triangle is also 100 square centimeters due to congruency. The dimensions of the section of the yellow triangle overlapping the blue triangle are [tex]b = 14\,cm[/tex] and [tex]h = 7\,cm[/tex]. The area of this section is:
[tex]A' = \frac{1}{2}\cdot (14\,cm)\cdot (7\,cm)[/tex]
[tex]A' = 49\,cm^{2}[/tex]
And the area of the rest of the blue triangle is:
[tex]A'' = A - A'[/tex] (2)
[tex]A'' = 100\,cm^{2}-49\,cm^{2}[/tex]
[tex]A'' = 51\,cm^{2}[/tex]
In a nutshell, both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.
We kindly invite to check this question on triangles: https://brainly.com/question/23103213
3 laps 50 seconds 20% longer each lap
Answers
prove that the following arguments are valid by using formal proof. 1, if studies medicine be will get a good job,if they gets a good job,he will get a good wage,he did not get good wage therefore,he did not study medicine.
Answers
The argument; if he did not get a good wage, then he must not have studied medicine is valid.
What is valid proof?Let P represent "He studies medicine"
Let Q represent "He gets a good job"
Let R represent "He gets a good wage"
The argument can be written as:
P → Q
Q → R
¬R
∴ ¬P (conclusion: he did not study medicine)
Assume for contradiction that the argument is invalid:
P → Q
Q → R
¬R
P (assumption for contradiction: he studied medicine)
Use modus ponens to derive Q from (5) and (1):
Q (from 1 and 5 using MP)
Use modus ponens again to derive R from (6) and (2):
R (from 2 and 6 using MP)
This contradicts ¬R in (3), so our assumption in (5) must be false. Therefore, we can conclude that the argument is valid:
¬P (from contradiction of assumption in (5))
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George has $15. He tries to buy a movie ticket ($9.00), a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each) but he does not have enough money. Look at the numerical expression George used: 15-9+2.65+1.35+2(1.74)
Why does George need to fix the expression?
Answers
George needs to fix the expression because if you did the equation as is, it wouldn't subtract the added value from 15.
George always requires $1.48.
How to estimate the value of the expression?The order of operations exists as a law that tells the correct sequence of measures for considering a math expression. We can determine the mandate utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).
Given: George tries to purchase a movie ticket ($9.00), a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each)
9 + 2.65 + 1.35 + 1.74 + 1.74 = 16.48
Subtract 15 to 16.48
15 - 16.48 = 1.48
George always needs $1.48.
Therefore, the proper answer is $1.48.
To learn more about the PEMDAS refer to:
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please answer these
I need it rn
it's due to tommorow
Answers
2 3/4m for textbooks + 1 1/2m for Notebooks
2 3/4 + 11/2
11/4 + 3/2
11/4 + 6/4
17/4
4 1/4
Subtract5 1/2 - 4 1/4
11/2 - 17/4
22/4 - 17/4
5/4
1 1/4
Complete answer1 1/4 meters of plastic cover will be left
HOPE THIS HELPS. GOODLUCK:)
3)There are 9 colorful socks in a drawer: 3 green, 2
purple,
2 Navy, 1 yellow, and 1 pink. What's the
probability of picking a green putting it on and
then choosing a purple?
Answers
Answer:
1/24 chance
Step-by-step explanation:
To begin you would need to find the probability of picking a green sock which would be 3/9; and you could simplify this to 1/3.
After that you need to find the probability of picking a purple sock out of the 8 left, which would provide you with 1/8. To find the probability of both you would multiply 1/8 by 1/3 to find the combined probability which would leave you with 1/24.
brainliest to correct answer, please hurry
Answers
Start at 3, subtract 5 and you get -2
5x²+4x+3=0 solve for x
Answers
Answer:
[tex]{ \underline{ \sf{x \: is \: \: \{ \frac{ - 5 + i \sqrt{35} }{10} \} } \: \: and \: \: \{ \frac{ - 5 - i \sqrt{35} }{10} \}} }[/tex]
Step-by-step explanation:
[tex]5 {x}^{2} + 4x + 3 = 0 [/tex]
from quadratic formular:
[tex]{ \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }} [/tex]
general equation:
[tex] {ax}^{2} + bx + c = 0[/tex]
a is 5, b is 4 and c is 3:
substitute in formular:
[tex]{ \sf{x = \frac{ - 5± \sqrt{ {5}^{2} - (4 \times 5 \times 3) } }{(2 \times 5)} }} \\ \\ { \sf{x = \frac{ - 5± \sqrt{ - 35} }{10} }}[/tex]
but from complexes, i² = -1
[tex]{ \sf{x = \frac{ - 5± \sqrt{35 {i}^{2} } }{10} }} \\ \\ = { \sf{x = \frac{ - 5±i \sqrt{35} }{10} }}[/tex]
HELPPPP! PLEASEEEEE!
A mountain climber ascends a mountain to its peak. The peak is 10,740 ft above sea level. The climber then descends 400 ft to meet a fellow climber. Find the climber's elevation above sea level after meeting the other climber.
A. 10,740 ft above sea level.
B. 10.340 ft above sea level.
C. 11,140 ft above sea level.
D. 400 ft below sea level.
Answers
Answer:
10,340 ft
Step-by-step explanation:
the peak is 10,740 ft and since the climber is at the peak, that's their elevation.
he goes down 400 ft so its 10,470 - 400 which is 10,340
Answer:
B. 10,340
Step-by-step explanation:
The peak is 10,740, since they descend 400, it is subtraction. 10,740 - 400 is 10,340.
Which number should replace Z?
A 7
B 6
C 5
D 4
Answers
Answer:
2 sorry i don't know that's what answer i got
find the value of x.
Answers
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The parallel lines cut the transversals proportionally, so we have ...
(10 -x)/x = 3/2
2(10 -x) = 3x . . . . . . . multiply by 2x
20 -2x = 3x . . . . . . . eliminate parentheses
20 = 5x . . . . . . . . . . add 2x
4 = x . . . . . . . . . . . . divide by 5
I need to find all real values of x from this inequality x^2>2x-2 and also this question x^2>2x+2. I need the answer fast with working out pls
Answers
[tex]x^2\gt2x-2[/tex]
[tex]x^2-2x+2\gt0[/tex]
You are essentially asking at this point where is the quadratic function greater than 0. To get the interval find the roots. Between the roots the function is guaranteed to be LESS THAN zero. Everywhere else the function is greater than 0.
[tex]x^2-2x+2=0[/tex]
Use Vieta's rule to get the roots,
[tex](x-1)(x-1)=0[/tex]
Both roots are the same so no value is less than 0 which means all values except at the point of root are strictly greater, the point of root is at [tex]x_{1,2}=1[/tex] which means the set for which the quadratic function is greater than 0 is [tex]\mathbb{R}-\{1\}[/tex] "all real numbers except 1".
To convert this into interval notation use all numbers up to 1 but not including and all numbers after 1 but not including,
[tex](-\infty,1)\cup(1,\infty)[/tex]
Hope this helps :)
3. A clock is constructed using a regular polygon with 60 sides. The
polygon rotates every minute. How much has the polygon rotated
after 12 minutes? Explain your answer with words, a drawing or both-
Answers
We are required to find how much the polygon has rotated after 12 minutes
The number of times the polygon has rotated after 12 minutes is 72°
Number of sides of the polygon = 60
The polygon rotates every minute, that is
1 rotation = 1 minutes
12 rotation = 12 minutes
one rotation of the clock is 360°
Number of times the polygon has rotated after 12 minutes = one rotation of the clock / Number of sides of the polygon × number of minutes
= 360°/60 × 12
= 6 × 12
= 72°
Learn more about polygons and clock:
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For the second week of November, Eric White worked $41.75 hours. Eric earns $19 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the second week November (round your responses to the nearest cent if necessary):
Answers
Combine Like Terms
6. Which expression is equivalent to -2-(-15d)+(-11d)+2-6 ?
-4d+6
4d-6
4d+6
-26d-10
Answers
Answer:
4d - 6
Step-by-step explanation:
-2-(-15d)+(-11d)+2-6
-2 + 15d - 11d + 2 - 6
15d - 11d - 2 + 2 - 6
4d - 6
Imagine that you must cross the hallway staying an equal distance from each laser. Il you get closer to one laser than the other, it will blast you. Use a compass and straightedge to draw a safe path through the hallway.
Answers
Answer:
can you answer this first
The discussion is shown below:
what is data?In computing, data is information that has been translated into a form that is efficient for movement or processing.
A hall way with laser imagine that you must cross the hall way while staying at equal distance from each laser.
So, from the question we can consider the a point o which is in between laser 1 and laser 2.
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i need the answers for all three of those
Answers
1. -2
3. 4
Answer:
1) = -10
3) = 4
Step-by-step explanation:
Chow,...!
Suzie determined the range of a quadratic function to be y ≤ –5. Choose the correct interval notation.
Answers
The range of equation is
interval :(-5, ∞)interval :[-5, ∞)interval: (-∞, -5)interval: (-∞, -5]What is interval?A interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.
Given function : y ≤ –5
if, y > -5 then,
interval :(-5, ∞)
if y ≥ -5 then
interval :[-5, ∞)
if y < -5 then
interval: (-∞, -5)
if y ≤ -5 then
interval: (-∞, -5]
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What is a rational number between 1/3 and 1/9?
Answers
Answer:
1/4
Step-by-step explanation:
its 0.25 which is rational. and its between the two.
Find the sum
No links
Answers
⇛ -12 + 8
⇛ -4
[tex] \: [/tex]
Hey there!
The word “sum” simply means “to add” or “addition” in mathematical terms
So, we have to ADD -12 from 8 from each other.
Positives are on the RIGHT side of the number line whereas negatives are on the LEFT side of the number line
Start at -12 and go UP 8 spaces to the right.
-12 + 8
= -4
Answer: -4
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
please help , ill give brainliest
Answers
There are five boys to every three girls in an introductory chinese course. if there are 384 students enrolled in the course, how many are boys?
Answers
Answer:
There are 240 boys.
Step-by-step explanation:
There are five boys to every three girls in an introductory Chinese course. Given that there are 384 students enrolled in total, we want to determine the amount of students which are boys.
Let b represent the number of boys and g girls.
Since the ratio is 5:3, we can write that:
[tex]\displaystyle \frac{5}{3} = \frac{b}{g}[/tex]
And since the total number of students is 384:
[tex]b + g = 384[/tex]
From the first equation, cross-multiply:
[tex]5g = 3b[/tex]
Solve for g:
[tex]\displaystyle g = \frac{3}{5} b[/tex]
Substitute:
[tex]\displaystyle b + \left (\frac{3}{5} b\right) = 384[/tex]
Simplify:
[tex]\displaystyle \frac{8}{5} b = 384[/tex]
Solve for b:
[tex]\displaystyle b = \frac{5}{8}\left(384\right) = 240[/tex]
In conclusion, 240 of the total students are boys.