Answer:
There are two alternatives: (i) Polar coordinate system (a.k.a. Circular coordinate system), (ii) Elliptic coordinate system.
Step-by-step explanation:
There are two alternative ways of describing the location of points on a plane:
(i) Polar coordinate system (a.k.a. Circular coordinate system).
(ii) Elliptic coordinate system.
Now we proceed to explain briefly the characteristic of each option:
Polar coordinate system: [tex](r, \theta)[/tex]
Where:
[tex]r[/tex] - Distance of the point with respect to origin.
[tex]\theta[/tex] - Direction of the vector between origin and point with respect to the +x semiaxis, in sexagesimal degrees.
The formulae for each component in terms of Cartesian coordinates are described below:
[tex]r = \sqrt{x^{2}+y^{2}}[/tex] (1)
[tex]\theta = \tan^{-1} \frac{y}{x}[/tex] (2)
Elliptic coordinate system: [tex](\mu, \nu)[/tex]
Where [tex]\mu[/tex] and [tex]\nu[/tex] are elliptical coordinates.
The formulae for each component in terms of Cartesian coordinates are described below:
[tex]x = a\cdot \cosh \mu \cdot \cos \nu[/tex] (3)
[tex]y = a \cdot \sinh \mu \cdot \sin \nu[/tex] (4)
Where [tex]a[/tex] is the distance between origin and any of the foci along the x axis.
show that the the product of the first two numbers 28,48 of that stem is equal to the product of their LCM and HCF
Answer:
HCF is 4
LCM is 336
Step-by-step explanation:
2/28 , 48
2/14 , 24
2/7 , 12
2/7 , 6
3/7 , 3
7/7 , 1
1 , 1
HCF is 2 × 2 =4
LCM is 2 × 2 × 2 × 2 × 3 × 7 = 336
18. fine two consecutive odd integers whose sum is 36.
Answer:
17 and 19
Step-by-step explanation:
Let n denote the first odd integer.
If the two integers are consecutive and odd, then the second number is n+2.
Hence, n+n+2=36
=2n=34
Divide both sides by 2
=n=17
Therefore, the numbers are 17 and 19.
Bret wants to take an advert out in a newspaper. The page has a length of 36cm. An advert will take 1/3 of the length of the page. Bret says the advert needs to be 11cm in length. Is Bret correct? Show your working out and state a clear answer.
Answer:
I don't think so
Step-by-step explanation:
the length of the newspaper page=36cm
the advert will take 1/3 of the page=1/3*36=12
so the advert takes12 cm and he says it has to be 11 cm which is not right .
I hope this helps
A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is –16 ft/s2, what is the maximum height reached by the firework?
Answer:
h = 256 feet
Step-by-step explanation:
Given that,
The initial velocity of firework, v = 128 ft/s
The acceleration due to gravity is-16 ft/s².
We need to find the maximum height reached by the firework.
The equation for the firework is :
[tex]h(t) = -16t^2 + 128t[/tex]
To find the vertex's x-coordinate, we can use
[tex]t=\dfrac{-b}{2a}\\\\t=\dfrac{-128}{2\times (-16)}\\\\t=4\ s[/tex]
Put all the values in the expression for h (t).
[tex]h(t) = -16(4)^2 + 128(4)\\\\h(t)=256\ ft[/tex]
So, the maximum height reached by the firework is 256 feet.
I need help to find Y =
Answer:
3
Step-by-step explanation:
Last one thanks to whoever helps
Answer:
see below
Step-by-step explanation:
take f(x)=5x-6, which is y=5x-6
switch the y for x and x for y and you get
x=5y-6
then add 6 on both sides and you get
x+6=5y
now divide both sides by 5 and you get
y=(x+6)/5
which is the inverse of the original function
Answer:
Solution given:
f(x)=5x-6
let f(x)=y
we get
y=5x-6
Interchanging role of x and y
x=5y-6
x+6=5y
y=[tex]\bold{\frac{x+6}{5}}[/tex]
so
f-¹=[tex]\bold{\frac{x+6}{5}}[/tex]
shown
2400meters = kilometers
Answer:
2.4.....................
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of h is different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted left 3 units.
B.
The graph of h is the graph of g vertically shifted down 3 units.
C.
The graph of h is the graph of g horizontally shifted right 3 units.
D.
The graph of h is the graph of g vertically shifted up 3 units.
Answer:
C
Step-by-step explanation:
Given f(x) then f(x + a) is f(x) translated horizontally
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Given that h(x) = g(x - 3) , then
The graph of h(x) is the graph of g(x) horizontally shifted 3 units right
Answer:
C
Step-by-step explanation: I took the test
CAN SOMEONE HELP PLEASE
Answer:
72
The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.
Answered by GAUTHMATH
Please help me with this problem
Answer:
4x² - 5x - 8 = 0
Step-by-step explanation:
Standard form of a quadratic: ax² + bx + c
Move all terms to one side and sort them based on the level of degree:
[tex]4x^2-9x-8=-4x\\4x^2-9x+4x-8=0\\4x^2-5x-8=0[/tex]
Answer:
4x^2 -5x-8 =0
Step-by-step explanation:
ax^2 + bx + c = 0 is the standard form
4x^2 -9x-8 =-4x
Add 4x to each side
4x^2 -9x+4x-8 =-4x+4x
4x^2 -5x-8 =0
sin 0= 20/29. Find tan 0.
Answer: D) 20/21
Explanation:
Recall that sin(theta) = opposite/hypotenuse.
sin(theta) = 20/29 tells us that 20 is the vertical side while 29 is the hypotenuse. Note how the vertical side is opposite the reference angle theta.
Use these two sides to find that the missing side is 21. You'll need the pythagorean theorem a^2+b^2 = c^2.
Once you determine that the adjacent side is 21 units long, we can then say,
tan(theta) = opposite/adjacent = 20/21
Answer:
D. 20/21
Step-by-step explanation:
3. Create and write a real-world situation that could be represented by the equation below:
5x + 15 = 45
Answer:
You ordered 5 tickets for a show on line...
The cost was $5 a ticket Plus a one time ordering fee of $15.
you total cost was $45 ....
Solving for x will determine the cost of one ticket
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a taxi charges $5 a mile plus $15 "pull fee" ...
you ride cost a total of $45 ... x is the number of miles that you got driven
Step-by-step explanation:
You rent a car for a down payment of $15 and $5 is charged per mile driven. The total charge is therefore, $45. In essence, x is the no. of miles driven.
According to the question;
We are required to create a real-world problem that could be represented by the equation; 5x + 15 = 45.In essence, x is the no. of miles driven in this scenario.
By solving for x in 5x + 15 = 45, we may determine the no. of miles driven.
Read more:
https://brainly.com/question/2319353
= X
20
100
60
Please help me
Answer:
x = 100
Step-by-step explanation:
(100-40)/2
= 60/2
= 30
So it's 100
Answered by GAUTHMATH
answer to this problem?
Answer:
The p is 4
Step-by-step explanation:
Find the equation of the linear function represented by the table below in slope-intercept form.
Help plzz will give brainiest
Answer:
y = 2x+4
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 12-6)/(4-1)
= 6/3
= 2
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Using a point from the table
10 = 2(3)+b
10 = 6+b
10-6 = b
4=b
y = 2x+4
c. The sum of two number is 59. If the Smaller number is less than the bigger one by 7,find the number.
Step-by-step explanation:
Hi there!
According to the question;
The sum of two number is 59. And the Smaller number is less than the bigger one by 7,
Let the bigger number be "X" then smaller number will be x-7.
Then;
x + (x-7) = 59
2x = 59+7
X = 66/2
Therefore, the bigger number (X) is 33 and smaller number (x-7) is 26.
Hope it helps!
Which value is the closet approximation of the square root of 27
A 4.5
B 5
C 5.5
D 5.9
Determine whether each of the following products is rational or irrational.
Expression
Rational
Irrational
77-18
-7,49
5
2
./II
Answer:
-irrational
-rational
-rational
-irrational
__________________________________________________________quick and easy way is to see if the squares are perfect squares, like square root seven is irrational, so the answer is irrational. square root 9 is 3, which is rational, so its rational.
brainliest is appreciated :)
Match each equation with its solution
PLEASE HELPP ASAP!
Answer:
-5x = 26 is 5.2
x/2 = 4 is -8
3/2x=6 is 4
x/-7.2=4 is 28.8
factor 25-4z^2
im having trouble with a question
Answer:
(5-2z)(5+2z)
Step-by-step explanation:
25 -4z^2
Rewriting
5^2 - (2z)^2
This is the difference of squares a^2 - b^2 = (a-b)(a+b)
(5-2z)(5+2z)
given the functions f(x)=3/2 and g(x)=7/3x-8/3, find(f*g)(x)
Answer:
pagal man
Step-by-step explanation:
tumko Answer Nahi Aata Padhte Likhte Nahi hoo kya
Find the volume of this cone.
Use 3 for T.
12ft
12
5ft
V = Tr?
V [?]ft3
V
Answer:
V = 180 ft^3
Step-by-step explanation:
The volume of a cone is found by
V = 1/3 pi r^2 h where r is the radius and h is the height
The diameter is 12 so the radius is 1/2 the diameter or 1/2(12) = 6
The height is 5 and we are using 3 for pi
V = 1/3 (3) *6^2 *5
V = 180 ft^3
Is 2.73234(34 repeating) rational or irrational?
It's rational because of the repeating digits.
We have
x = 2.732343434…
Then
1,000x = 2,732.343434…
and
100,000x = 273,234.343434…
Subtracting these makes the fractional part go away, leaving you with
100,000x - 1,000x = 273,234.343434… - 2,732.343434…
100,000x - 1,000x = 273,234 - 2,732
99,000x = 270,502
x = 270,502/99,000 = 135,251/49,500
which is clearly a rational number.
3x (x - 2) = x^2 - 4
Answer:
x = 1, x = 2
Step-by-step explanation:
Given
3x(x - 2) = x² - 4 ← distribute parenthesis on left side
3x² - 6x = x² - 4 ( subtract x² - 4 from both sides )
2x² - 6x + 4 = 0 ( divide through by 2
x² - 3x + 2 = 0 ← in standard form
Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (- 3)
The factors are - 1 and - 2 , since
- 1 × - 2 = + 2 and - 1 - 2 = - 3 , then
(x - 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
Find the value of x. Round
the nearest tenth.
Step-by-step explanation:
here's the answer to your question
Which number sentence is true? A. 12 < |-12| B. |-12| < |-48| C. |-48| < |48| D. |12| > |-48|
Step-by-step explanation:
B ) |-12| < |-48|
because the signs are not taken on to consideration if we write in |
so hence B is right option
MARK AS BRAINLIST IF IT IS USEFUL
help pls I need answer to question (e)
Answer:
I assume you'd already figured out the other questions so you just don't understand the question E
Step-by-step explanation:
The product of the first 2 numbers its stating is -28 and 48, and it's asking if the product (multiply -28 by 48 to get the product) is equal to the HCF and LCM you got in the previous answer.
Hey guys ♡
hw r u all doin
pls solve this question for me ⤵️
(m-1)/2 - (m-2)/3 = ( m - 4 )/7
Answer:
m = - 31
Step-by-step explanation:
Given
[tex]\frac{m-1}{2}[/tex] - [tex]\frac{m-2}{3}[/tex] = [tex]\frac{m-4}{7}[/tex]
Multiply through by 42 , the LCM of 2, 3 and 7 , to clear the fractions
21(m - 1) - 14(m - 2) = 6(m - 4) ← distribute parenthesis
21m - 21 - 14m + 28 = 6m - 24
7m + 7 = 6m - 24 ( subtract 6m from both sides )
m + 7 = - 24 ( subtract 7 from both sides )
m = - 31
Kevin says that lines p and m will eventually intersect. Lines A and B intersect. Plane A contains lines p, m, and n. Line n is horizontal on the plane. Lines p and m are both going in the same direction and are identical. Plane B contains vertical line l which forms a right angle with line n. Is Kevin correct?
Answer:
No, because they are parallel.
Step-by-step explanation:
The lines [tex]p[/tex] and [tex]m[/tex] will not intersect, so Kevin is not correct.
It is given that planes A and B intersects. The plane A contains the line p, m and n on its plane. The lines p and m are parallel to each other. They are identical and move in the same direction.
Since the line p and m are parallel, they will not meet each other at any point because parallel lines does not intersect or meet at a point, they run parallelly along each other.
So, line p and m will not intersect.
Thus the answer is " No, because they are parallel."
Answer:
Step-by-step explanation:
no, because they are parrallel.
9. The ticket at right has a perimeter of 42 cm.
a) Calculate the unknown side length.
A = 42 - 11 x 2 = 20 / 4 = 5
b) Olivia wishes to decorate the ticket by placing a
gold line along the slanted sides. How long is the line on each ticket?
A =
c) A bottle of gold ink will supply enough ink to draw 20 m of line. How many bottles of ink should be purchased if 200 tickets are to be decorated?
A =
Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.
I've added the image of the ticket as an attachment.
(a) The missing side length
From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.
So, we have:
[tex]Perimeter =2\times 11 + 4 \times L[/tex]
This gives
[tex]2\times11 + 4 \times L = 42[/tex]
[tex]22 + 4 \times L = 42[/tex]
Collect like terms
[tex]4 \times L = 42-22[/tex]
[tex]4 \times L = 20[/tex]
Divide both sides by 4
[tex]L =5cm[/tex]
(b) The length of the gold lines
There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).
So, the length of the gold line is:
[tex]Gold = 4 \times L[/tex]
[tex]Gold = 4 \times 5cm[/tex]
[tex]Gold = 20cm[/tex]
(c) The number of gold ink bottles.
[tex]n = 200[/tex] --- number of tickets
The length of all gold line in the 200 tickets is:
[tex]Length = 200 \times Gold[/tex]
[tex]Length = 200 \times 20cm[/tex]
[tex]Length = 4000 cm[/tex]
[tex]Length = 4000 \times 0.01m[/tex] ---- convert to meters
[tex]Length = 40m[/tex]
Given that:
[tex]Bottle = 20m[/tex] --- 1 bottle for 20 m
The number of bottles (n) is:
[tex]n = \frac{Length}{Bottles}[/tex]
[tex]n = \frac{40m}{20m}[/tex]
[tex]n = 2[/tex]
Hence, 2 bottles of gold ink are enough.
Read more about perimeters at:
https://brainly.com/question/6465134
