Does anyone know how to solve this?
Answer:
A point in polar coordinates is written as (R, θ)
If we want to transform this point to rectangular coordinates, we get:
x = R*cos(θ)
y = R*sin(θ)
Now we can remember that the sine and cosine functions have a period of 2*pi, then:
cos(θ) = cos(θ + 2*pi)
or:
cos(θ) = cos(θ + 2*pi + 2*pi)
and so on.
Then the point (R, θ) is the same as (R, θ + 2*pi) and (R, θ + k*(2*pi))
where k can be any integer number.
Then if we have a point in polar coordinates:
(-4, -5*π/3)
Then another two polar representations of this point are:
(-4, -5*π/3 + 2*π) = (-4, -5*π/3 + 6*π/3) = (-4, π/3)
Now we can not add 2*π (nor subtract) because we would have an angle outside the range [-2*π, 2*π]
For example, if we have:
(-4, π/3 + 2*π) = (-4, 7*π/3)
And we can not change the value of the radius and get the coordinates for the same point.
So another representation could be something like:
(-8/2, π/3)
Where i just wrote -4 in another way.
Now, a really important point.
When working with polar coordinates, we always use R as a positive number (here you can see that R is negative) so this is not the standard notation for the polar representation of a point.
A cookie jar starts off with 32 cookies in it, and
each day 2 cookies are eaten. After a certain
number of days, there are 14 cookies left in the jar.
Which of the following equations represents the
day, d, when there are 14 cookies in the jar?
Answer:
9 days
Step-by-step explanation:
32-2-2-2-2-2-2-2-2-2 = 14
The equation that represents the day, d, when there are 14 cookies in the jar will be 14 = 32 - 2d, and that day will be on the 9th day.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given,
Initial cookie = 32
Since each day 2 cookies are eaten so after "d" days the total eaten cookies will be 2d.
Remaining cookies = initial cookies - eaten cookies
Remaining cookies = 32 - 2d
The day when 14 cookies remain will be,
14 = 32 - 2d
2d = 32 - 14
d = 9
Hence "The equation that represents the day, d, when there are 14 cookies in the jar will be 14 = 32 - 2d, and that day will be on the 9th day".
For more about the equation,
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The perimeter of a rectangular atrium is 300 yards. The length of the garden is ninety-six yards more than the width. Find the length and the width
Answer:The perimeter of a rectangular atrium is 27 yards in width and 123 yards in length.
Step-by-step explanation:
Step 1
The perimeter of a rectangular atrium is given as 2( l+b)
The perimeter of a rectangular atrium is 300 yards.
Let the width be represented as x
such that the
The length of the garden which is ninety-six yards more than the width is expressed as x+ 96
and the expression to solve for length and width will now be
Step 2
Perimeter = 2(l+b) = 2l + 2b
300=2( x+96) + 2 x
300= 2x+ 192 + 2x
300= 192+ 4x
300-192=4x
108=4x
x=108/4
x=27
width = 27 yards
length = x+ 96= 27 +96=123 yards
Determine the sine, cosine, and tangent of angle THETA. Check tje appropriate solution for each.
Step-by-step explanation:
c²=a²+b²
a²=c²-b²
a²= 15²-9²=225-81=144
a=√144=12
sinΩ=a/c=12/15=4/5
cosΩ=b/c=9/15=3/5
tanΩ=a/b=12/9=4/3
If sin (x) =2/5 and tan(x) > 0, what is sin(2x)?
Answer:
sin2x = [tex]\frac{4\sqrt{21} }{25}[/tex]
Step-by-step explanation:
Given sinx = [tex]\frac{2}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
Then the third side, the adjacent is found using Pythagoras' identity, that is
adj² + opp² = hyp²
adj² + 2² = 5²
adj² + 4 = 25 ( subtract 4 from both sides )
adj² = 21 ( take the square root of both sides )
adj = [tex]\sqrt{21}[/tex] , then
cosx = [tex]\frac{adj}{hyp}[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]
Using the double angle identity
sin2x = 2sinxcosx
= 2 × [tex]\frac{2}{5}[/tex] × [tex]\frac{\sqrt{21} }{5}[/tex]
= [tex]\frac{4\sqrt{21} }{25}[/tex]
The Hiking Club is taking another trip. The hike leader's watch shows that they gained
296 feet in altitude from their starting position. Their altitude is now 285 feet, but there is
no record of their starting altitude,
Which equation represents this situation?
A: x + 285 = 296
B: x - 296 = -285
C: x + 296 = 285
D: x- 285 = - 296
Anyone available I been trying to get the answer for this assignment :(
Answer:
c
Step-by-step explanation:
they started at x added 296 and now are at 285
Answer:
-987
Step-by-step explanation:
Taylor is decorating for a party. She cuts 5 equal-length streamers from a strip of yellow paper that is 9 feet long. How long is each streamer in fraction form?
Answer: 1 4/5 feet
Step-by-step explanation:
Length of the strip of yellow paper = 9 feet.
Number of streamers that were cut = 5
Length of each streamer will then be:
= Length of the strip of yellow paper = 9 feet / Number of streamers that were cut
= 9 feet / 5
= 1 4/5 feet
24. Morgan and Natalie's heights can be
compared using a scale of 1.5 inch :2.5
inches. If Morgan is 36 inches tall, find Natalie's
height. Give your answer in feet.
Marsha went shopping at Best Buy and spent $75.25. If the sales tax was 8.75%, how much was her total bill?
Answer:
The answer is 81.834375
Step-by-step explanation:
Hope this helps
Answer:
$81.83
Step-by-step explanation:
Amount spent: £75.25
Sales tax: 8.75%
1% of 75.25 = 0.7525
0.7525 x 8.75 = 6.584375
75.25 + 6.584375 = 81.834375
As this question involves money it needs to be rounded to 2 decimal places:
$81.83
Can any one help me out
Answer: A
Step-by-step explanation:
Answer: (-7,3)
Step-by-step explanation:
A
What type of answer would you expect from the problem below? Explain why you expect that type of answer.
5/6 + 9.25
A) Rational; Both numbers can be written as fractions, so the answer will be a fraction, which is a rational number.
B) Irrational; Both numbers can be written as fractions, so the answer will be a fraction, which is an irrational number.
C) Rational; One number is a fraction and the other is a decimal, so they are not like terms and cannot be combined.
Answer:A
Step-by-step explanation:
Edge 2020
Help please............................
Answer:
C
Step-by-step explanation:
m∠7=m∠3
3x-10=2x+5
x=15
m∠3=2(15)+5
=35
m∠1=m∠3 (vert. opp. ∠)
= 35
is y = -x a proportional relationship
Answer:
For any proportional relationship, k=yx (such as a line that passes through the origin). Find the equation of the line by solving for y in the constant of proportionality equation. This equation y=kx is another representation of a proportional relationship.
Step-by-step explanation:
Answer:
Yes kdsjsbahajajsjsbsbsbsnsn
Will give Brainly! Please help!
Answer:
The answer is option c.
Hope this helps!
Graph the image of rectangle STUV after a reflection over the line y= –x
Answer:
U (7,1)
T (10,1)
V (7,9)
S (10,9)
Step-by-step explanation:
The image of the rectangle STUV after a reflection over the line y= –x is attached below.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The coordinates of the points in the graph are S(-9,-10) , T(-1,-110) , U(-1,-7) , V(-9,-7)
We have to graph the image of the rectangle STUV after a reflection over the line y= –x
The points obtained after graphing ate,
U (7,1)
T (10,1)
V (7,9)
S (10,9)
Thus, the image of the rectangle STUV after a reflection over the line y= –x is attached below.
Learn more about the geometric transformation here:
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4(x + 3) = 3(3x - 1)
Answer:
Either 4x+12 ≠ 9x-3 OR x = 3
Hope this helps!! (Please mark Brainliest if possible!!)
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
[tex]4(x+3)=3(3x-1)[/tex]
Distribute 4 and 3 into the parentheses
[tex]4x+12=9x-3[/tex]
Combine like terms; subtract both sides by 12
[tex]4x+12-12=9x-3-12\\4x=9x-15[/tex]
Combine like terms; subtract both sides by 9x
[tex]4x-9x=9x-15-9x\\-5x=-15[/tex]
Divide both sides by -5 to isolate x
[tex]\frac{-5x}{-5} =\frac{-15}{-5} \\x=3[/tex]
I hope this helps!
A rectangle has a perimeter of 124 units. If the length is 5 more than 2 times the width, what is the width.
Answer:
19 units
Step-by-step explanation:
Perimeter of the rectangle = 124 units
width = x units
length = 5 + 2x units
The perimeter of a rectangle is given by;
P = 2(l + b)
Substituting values;
124 = 2[(5 + 2x) + x]
124 = 2[5 + 3x]
124 = 10 + 6x
124 - 10 = 6x
114 =6x
x= 114/6
x = 19
width = 19 units
el area de un rectangulo es 84 cm cuadrados si la base mide 9 cm cuanto mide la altura y cual es su perimetro?
Mind lending me a hand
Answer:
54
Step-by-step explanation:
55 + 74 + 78 + z + z + 45 = 360
252 + 2z = 360
2z = 108
z = 54
Answer: 288
Step-by-step explanation:
78+74+55=207
The degree of a pentagon is 540°
so 540-207=333
so z has to be 333 but the question says +45 and that would make 333 become 378 and we need to get exactly to 333 so the answer cant be 333 but a number that 45 can be added to ,to make 333 for example 54+45=99 so 54 isnt the answer,next is 144+45 which is 189 that doesnt equall 333 so that isnt the answer either lastly is 288+45 which is 333 Thats the answer ...
The polynomial
[tex] { - 3x}^{2} + 400x[/tex]
represents the budget surplus of the town of Alphaville for the year 2010. Alphaville's surplus in 2011 can be modeled by
[tex] { - 1.5x}^{2} + 300x[/tex]
If x represents the yearly tax revenue in thousands, enter a polynomial for how much Alphaville's budget surplus increased from 2010 to 2011. If Alphaville took in $450,000 in tax revenue in 2011, what was the budget surplus that year?
The surplus increased by __________
Alphaville's budget surplus was $_____ thousand, or$ ______ million
Answer:
Answer:
Question 1: Budget Surplus Increase = 12x(exponent 2) - 200x
Question 2: Budget surplus in 2011 = $3.04 * 10 (exponent 12)
Step-by-step explanation:
Question 1
Budget surplus in 2010 =
Budget surplus in 2011 =
Increase in buget surplus = Budget surplus in 2011 - Budget surplus in 2010
Question 2
2011 yearly tax revenue, x = $450,000
Budget surplus in 2011 =
Budget surplus in 2011 ≅ $
Step-by-step explanation:
please help. i will give brainliest
the question is in the picture below
A) There is an asymptote at y = 70.
B) The y-intercept is located at (0, 70).
C) There is an asymptote at x = 0.
D) The x-intercept is located at (70, 0).
Answer:
B. The y-intercept is located at (0,70)
Step-by-step explanation:
This is because 70 is on the y part of table. Hope this helps!
The amount paid for different weights of oranges at a farmer's market are shown below (A) is the relationship between the price and the weight of the oranges proportional?
The amount paid for different weights of oranges at a farmer's market are shown below (A) is the relationship between the price and the weight of the oranges proportional?
Oranges (lb) Price ($)
2--------- $3
3--------- $4.50
5--------- $7.50
Answer:
proportional relationship. Exist
Step-by-step explanation:
To check for propottionality:
2 = 3k
Solve for k = constant of proportionality
2/3 = 3k/3
2/3 = k
Quantity at price = 4.50
Price * k = quantity
4.50 * 2/3 = 3
Quantity at price = 7.50
Price * k = quantity
7.50 * 2/3 = 5
Hence, proportional relationship. Exist
2−4(5p+1) Simplify to create an equivalent expression.
Answer:
2-20p-4 = -20p-2
Step-by-step explanation:
Answer:
- 20p - 2
Step-by-step explanation:
Given
2 - 4(5p + 1) ← distribute parenthesis
= 2 - 20p - 4 ← collect like terms
= - 20p - 2
How do I solve? Or what is the answer for this?
Notice that the square root is accompanied with ^2 and can be simplified:
This works because 4x^4 = (2x^2)^2
[tex]\sqrt{(2x^{2})^{2} * (256y^{8})^{2} }[/tex]
Remove the square root:
[tex]2x^{2} (256y^{8} )[/tex]
Calculate the product:
[tex]512x^{2} y^{8}[/tex]
This is your answer after simplification.
What’s the radius of a circle with the circumference of 37.68 feet
Answer:
r≈6ft
Step-by-step explanation:
Using the formula
C=2πr
Solving forr
r=C
2π=37.68
2·π≈5.99696ft
pls mark as brainliest
What do you notice about the area of the base in each prism
Answer:
The area's are the same
Step-by-step explanation:
Both base's areas are 30.
3c+2d=-24 and 2c+5d= -38
Answer:
c=-4, d=-6
Step-by-step explanation:
The pool is partially filled with water. The volume of the water in the pool is 45 ft3. How deep is the
water?
A.)0.5 ft
B.)1.5 ft
C.)2.5 ft
D.)3.5 ft
C.)2.5 ft
it's just a guess
Guy please help me out so this is the question 3. Last Sunday, the temperature at 8:00 a.m. was -3०C. Between 8:00 a.m and 1:00 p.m., the temperature rose by 5०C. By 6:00 p.m. the temperature was 2०C colder than it was at 1:00p.m. Then, the temperature dropped 3०C each hour between 6:00 p.m. to 10:00 p.m. What was the temperature at 10:00 p.m.? I got the answer -1 is that correct?
Answer:
ayuda necesito lo mismo
Step-by-step explanation:
por favor algún voluntario
Answer:
-9C
Step-by-step explanation:
-3+5-2-3(3)=-9C
i think you made a mistake on "it got colder by 2C." If temperatures get colder, they drop, meaning you subtract it.
also, it said between the hours of 6-10pm, which is three hours, the temperature drops each hour by 3C. so, you multiply 3 to -3, and come up with -9
In UVW, u = 190 cm, v = 380 cm and w=560 cm. Find the measure of ZW to the
nearest 10th of a degree
Answer:
157.2
Step-by-step explanation:
Delta math
Answer: 157.2 degrees
Step-by-step explanation: Use law of cosines