Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
To convert from polar to Cartesian coordinates, recall that [tex](x,y)=(r\:cos\theta,r\:sin\theta)[/tex], thus, [tex](x,y)=(6\:cos\frac{5\pi}{6},6sin\frac{5\pi}{6})=(6(-\frac{\sqrt{3}}{2}),6(\frac{1}{2}))=(-3\sqrt{3},3)[/tex]
Therefore, C is the correct answer
Problem 2
Convert from polar to Cartesian coordinates:
[tex](x,y)=(-5\:cos\frac{2\pi}{3},-5\:sin\frac{2\pi}{3})=(-5(-\frac{1}{2}),-5(\frac{\sqrt{3}}{2}))=(\frac{5}{2},\frac{-5\sqrt{3}}{2})[/tex]
Therefore, U is the correct answer
Problem 3
Since [tex]r=\sqrt{x^2+y^2}[/tex], then [tex]r^2=x^2+y^2[/tex]. Don't also forget to use the substitution [tex]x=r\:cos\theta[/tex]:
[tex]x^2+y^2-7x=0\\\\r^2-7rcos\theta=0\\\\r(r-7cos\theta)=0\\\\r-7cos\theta=0\\\\r=7cos\theta[/tex]
Therefore, B is the correct answer
Problem 4
[tex]r=(tan\theta)(sec\theta)\\\\r=(\frac{sin\theta}{cos\theta})(\frac{1}{cos\theta})\\ \\\frac{r^2}{r}=(\frac{rsin\theta}{rcos\theta})(\frac{r}{rcos\theta})\\ \\\frac{x^2+y^2}{\sqrt{x^2+y^2}}=(\frac{y}{x})(\frac{\sqrt{x^2+y^2}}{x})\\ \\x^2+y^2=\frac{y(x^2+y^2)}{x^2}\\ \\1=\frac{y}{x^2}\\\\x^2=y[/tex]
Therefore, A is the correct answer
Related Questions
R\ {0}→→ Ris defined by Jff: 1 f(x)=x³-1/x³-1then show that 2 f(x) + f(1/x)=0.
Answers
[tex]\orange\bigstar \bold{ solution}[/tex]
[tex]\bold{f(x) = x³ - \frac{1}{x³ } }[/tex]
[tex]\bold{f ( \frac{1}{x} )= \frac{1}{x³} -x³ } [/tex]
[tex]\bold{f (x) + f (\frac{1}{x}) = (x³- \frac{1}{x³} ) + ( \frac{1}{x³} -x³)}[/tex]
[tex]\bold{ = 0 }[/tex]
AB= 7 and BC= 5. Find AC.
-
A) 9
B) 12
D) 8
C) 18
Answers
Answer:
B
Step-by-step explanation:
It would help if you can actually show the points
what should be the rate of interest to earn an 45000 as interest wale rupees 50000 easy in investment for 6 year
Answers
Answer:
5
Step-by-step explanation:
please help I will mark BRAINLIEST
Answers
Answer:
Your answer is t>28
Have a nice day!
mark as brainliest
Answer:
T>28
Step-by-step explanation:
Find the values of x for which the denominator is equal to zero for y=3x+5/x-6.
x = −5
x = 6
x = −6
none
Answers
Answer:
x=6 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width
Answers
Answer:
Length and width of rectangle is 24 and 8 inchesStep-by-step explanation:
Given:
Length of rectangle is three times the widthPerimeter of rectangle is 64 InchesTo Find:
Length and WidthSolution:
Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:
Perimeter of rectangle = 2(L + B)
→ 64 = 2(3x + x)
→ 64 = 2(4x)
→ 64/2 = 4x
→ 32 = 4x
→ 32/4 = x
→ 8 = x
Hence,
Length of the rectangle = 3x = 3(8) = 24 inchesWidth of the rectangle = x = 8 inchesAnswer:
Length = 24 inchesWidth = 8 inches⠀
Step-by-step explanation :
⠀
As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle is 8 inches .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 24 inches .⠀
Which angle is an x-intercept for the function y = cos(1)
A.0
B.2
C. £
D. 2£
Answers
Answer: C. [tex]\pi[/tex]
=======================================================
Explanation:
The x intercept always occurs when y = 0.
Use the unit circle to determine that [tex]\cos(\theta) = 0[/tex] when [tex]\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}[/tex]
So if [tex]x = \pi[/tex], then we have
[tex]y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\[/tex]
which shows us that [tex](\pi, 0)[/tex] is the location of one of the infinitely many x intercepts for this function.
what does Y=
what does z=
Answers
Answer:
Hope the picture will help you
Riley has completed 6 of the 30 pages she was assigned for homework. What percentage of her homework does Riley have left to complete?
Answers
Answer:
80 Percent
Step-by-step explanation:
Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent
Hopefully this helps - let me know if you have any questions!
trigonometric formulas
Answers
Answer:
all shown in the picture !
Step-by-step explanation:
also shown in the picture
An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant
rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and
then decelerates at a constant rate for 5 seconds until he stops.
a) What is the total distance that he ran?
[5]
Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She
however only accelerates for 10 seconds before running at a constant speed.
Answers
Answer:
probably 200
Step-by-step explanation:
or something like that
Briana has 3/4 pound of rabbit food. She feeds her rabbit 1/12 pound each day. How many days can Briana feed her rabbit with the food she has?
Answers
Hope this helps you!
find the area of circle o if DCBO is a rectangle and DB measure 10 units
Answers
Answer:
[tex]100\pi[/tex]
Step-by-step explanation:
Step 1: Identity the radius.
Since O is the center of the circle, and C and E lie on the circumference, OC and OE are the radii of the circle and thus,
OC=OE.
Step 2: Consider the rectangle.
All diagonals in a rectangle are congruent so this means
DB= OC ( OC is also a diagonal).
Thus, OC= 10 units.
Step 3: Analyze
So this means OE is also 10 units as well.
Since we know the length of the radius, Use the area of circle,
[tex]\pi {r}^{2} [/tex]
[tex]\pi( {10}^{2} ) = 100\pi[/tex]
So the area of a circle is 100 pi.
Answer:
314.2 square units
Step-by-step explanation:
The diagonals of a rectangle are the same length, so segment OC is the same length as segment DB: 10 units. OC is a radius of the circle, which means the circle's radius is 10 units.
The area of a circle is given by ...
A = πr²
A = π(10 units)² = 100π units²
A ≈ 314.2 units²
The area of circle O is about 314.2 square units.
a land mass is roughly in the shape of a rectangle whose perimeter is 1200 miles the width is 120 miles less than the length find the length and the width
PLEASE HELP ASAP!!! IM STUCK ON THIS
Answers
Answer:
Length: 360. Width: 240.
Step-by-step explanation:
360 * 2 = 720
240 * 2 = 480
720 + 480 = 1,200
Four divided by 1,000 rounded to the nearest whole number
Answers
Answer:
4 ÷ 1,000 = 0.004
Rounding up to 0 as the nearest whole number
Consider the function RX) = 3x + 1 and the graph of the function g(x) shown below.
у
4
6
4
2
X
-6 -4
- 2
12
4
6
-2
4
6
The graph g(x) is the graph of f(x) translated
✓ units
✓, and g(x) =
Answers
Step-by-step explanation:
f(x) goes through the point (0, 1).
g(x) goes through (2, 1) for the same y value.
that means g(x) is f(x) translated 2 units to the right.
but we could also look at the same x value (0).
then g(x) goes through (0, -5).
and that means g(x) is f(x) translated 6 units down.
since it is a line function, shifting it left/right or up/down makes no difference to the shape or position of the new curve itself.
as it looks like you don't have 6 in the drop-down menu, then 2 units (to the right) is the desired correct result.
that means g(x) = f(x-2) = 3(x-2) + 1 = 3x - 6 + 1 = 3x - 5
and that is what the graph is showing us.
How does Algebra act as a tool to improve communication
Answers
It is a tool as it represents the language of patterns.
It is also a means of working with abstract notions and then applying them, which frequently leads to the formation of generalisations and insights outside of the original context.
Please help Math-correct answers only!!
Have number with correct answers/letters!
Answers
I'll do the first three questions to get you started.
==========================================================
Question 1
x = horizontal component of the triangle
cos(angle) = adjacent/hypotenuse
cos(theta) = horizontal/hypotenuse
cos(40) = x/30
x = 30*cos(40)
x = 22.98133329 approximately
This is the horizontal force applies to the suitcase.
Work = force*displacement
Work = 22.98133329*120
Work = 2,757.7599948
Work = 2,758
Answer: 2,758 Nm (choice B)==========================================================
Question 2
Add the drone's relative air velocity and the wind velocity vectors.
v+w = (13i + 3j) + (-7i - 2j)
v+w = (13i-7i) + (3j-2j)
v+w = 6i + j
Answer: 6i + j (choice B)==========================================================
Question 3
Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.
sin(theta) = opposite/hypotenuse
sin(40) = x/200
x = 200*sin(40)
x = 128.557521937308
x = 128.558
Answer: 128.558 pounds (choice A)The sphere below has a radius of 25 cm.
O
25 cm
Work out the volume of the sphere.
Give your answer correct to 1 decimal place.
Volume of sphere= tr3
cm3
Answers
Answer:
65449.8 cm3
Step-by-step explanation:
We start with the volume formula for a sphere: 4/3 πr3
We start with subbing in 25 to r, then we cube 25, which is equal to 15625.
We multiply 4/3 and pi. And lastly we multiply what we got by 15625 and either round the answer or fphaving fixed your calculator.
I need help...you will be mark brainliest if it's right ty
Answers
Answer:
Median: 5
Interquartile range: 4
Have an amazing day!
Please rate and mark brainliest!!
is 1.3 greater than 1.52
Answers
find the value of x in the diagram
Answers
Answer: there is something off screen i cant see so i cant help you 183- what?
Step-by-step explanation:
3
0.33 points
Suppose you form 5-letter strings from the letters C,O, M, P, U, T, I, N, and G. What are the number of permutations as a ratio of factorials?
type your answer...
Answers
Using the permutation formula, it is found that it's number as a ratio of factorials is given by:
[tex]N = \frac{9!}{4!}[/tex]
The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, five letters will be chosen from a set of nine, hence:
[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
if you answer this question you will get 30 points
Answers
Answer:
2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:
1+1 is 2
How do you graph y=-1/3x
Answers
Step-by-step explanation:
it is negative so the slope must go downwards from left to right. since it is 1/3, for every 3 to the right, you go one down.
A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the
sphere which has a circumference of 489.84 yd. What is the surface area of the sphere? Use 3.14
for
The surface area of the sphere is about yd?.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
Answer:
76,400
Step-by-step explanation:
I think this is right, not sure though.
Surface area of sphere:
[tex]4\pi \times r {}^{2} [/tex]
Circumference :
[tex]2(\pi \times r)[/tex]
489.84 = 2 × 3.14 × r
2 × 3.14 = 6.28
489.84 = 6.28 × r
radius = 489.84 ÷ 6.28
R =78
Surface Area = 4 × 3.14 × (78)^2
Surface area = 76,415.04
= 76,400
What is the area?
2 yd
8 yd
5 yd
Answers
Answer:
28
Step-by-step explanation:
I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.
area of trapezoid = (base1 + base2)h/2
area = (2 yd + 5 yd)(8 yd)/2
area = 28 yd²
which of the following are polynomials
Answers
Answer:
I think so Option D is the correct answer
Vhat is the probability of flipping a coin 11 times and getting heads 3 times?
Found your answer to the nearest tenth of a percent.
Answers
Answer:
the answer should be 21 if it's there if I'm wrong let me know
26.95 divided by -5 1/2. can someone show me how to do it please?
Answers
Answer:
-4.9
Step-by-step explanation:
Since the number 26.95 has two decimal places, it can be turned into a whole number with a denominator having two zeroes; 100
2695
100
Then change -5 1/2 into an improper fraction; = -5 × 2 + 1
2
= -11/2
2695 ÷ ( -11 )
100 2
Reciprocate (put denominator as numerator and vice-versa ) the equation after the ÷ sign. After doing so, the ÷ sign changes to × sign.
Hence: 2695 × ( 2 )
100 -11
Then, cross multiply.
2695 ÷ ( -11 ) = -245100 ÷ 2 50
-245 ÷ 50
= -4.9
Answer: its -4.9
Step-by-step explanation: