Identify the equations of ellipses whose major axis lengths are twice their minor axis lengths.
Answers
Answer:
If its set up like
1 2
3 4
5 6
the answer is 1,2,4,6
Step-by-step explanation:
i hope my math on desmos was right xD
The equations of ellipses[tex]2x^{2} +8y^{2} -12x+16y-174=0[/tex], [tex]4x^{2} +y^{2} +16x+4y+4=0[/tex],[tex]3x^{2}+12y^{2} +18x-24y-69=0[/tex] and [tex]x^{2} +9y^{2} -2x+18y-71=0[/tex] having the major axis lengths are twice their minor axis length.
Equations of ellipse
[tex]\frac{(x-h)^{2} }{a^{2} } +\frac{(y-k)^{2} }{b^{2} } =1[/tex] (for horizontal major axis ,a>b)
[tex]\frac{(x-h)^{2} }{b^{2} } +\frac{(y-k)^{2} }{b^{2} }=1[/tex] ( for vertical major axis, b>a))
Where, (h, k) is the center of ellipse.
What is major axis of an ellipse?The major axis of an ellipse is its longest diameter(a line that runs through the center and both foci, with ends at the two most widely separated points on perimeter).
Formula for calculating the length of major axislength of major axis = 2a (where a is the length of semi major axis)
What is minor axis of an ellipse?The minor axis of an ellipse is the line that contains the shorter of the two line segments about which the ellipse is symmetrical.
Formula for calculating the length of minor axislength of minor axis = 2b (where b is the length of semi minor axis)
According to the given question
we have, the equations of ellipses
A) [tex](4x^{2} +32x)+(25y^{2} -250y)+589=0[/tex]
[tex]4(x^{2} +8x)+25(y^{2} -10y)+589=0[/tex]
[tex]4(x^{2} +8x+b^{2} )-4b^{2} +25(y^{2} -10y+b^{2} )-25b^{2} +589=0[/tex]
[tex]4(x^{2} +8x+4^{2})-4(4^{2})+25(y^{2} -10y+b^{2} )-25(5^{2} ) +589=0[/tex]
[tex]4(x+4)^{2}+25((y-5)^{2} )-100=0[/tex]
[tex]4(x+4)^{2} +25(y-5)^{2} =100[/tex]
dividing both the sides by 100
[tex]4\frac{(x+4)^{2} }{100} +25\frac{(y-5)^{2} }{100} =1[/tex]
[tex]\frac{(x+4)^{2} }{25} +\frac{(y-5)^{2} }{4} =1[/tex]
[tex]\frac{(x+4)^{2} }{5^{2} } +\frac{((y-5)^{2} }{2^{2} }=1[/tex]
here, h=-4 and k=5
major axis =2a=2×5=10
minor axis=2b=2×2=4
⇒ the length of major axis is not twice the length of minor axis.
Similarly, we will do for the other equations
B).
[tex]2x^{2} +8y^{2} -12x+16y-174=0\\\frac{(x-3)^{2} }{10^{2} } +\frac{(y+1)^{2} }{5^{2} } =1[/tex]
here, h=3 and k=-1
major axis:2a=2×10=20
minor axis:2b=2×5=10
⇒ length of major axis is twice the length of minor axis.
C).
[tex]4x^{2} +y^{2} +16x+4y+4=0[/tex]
[tex]\frac{(x+2)^{2} }{2^{2} } +\frac{(y+2)^{2} }{4^{2} } =1[/tex]
here, h=-2 and k= -2
major axis: 2b=2×4=8
minor axis: 2a= 2×2=4
⇒ the length of the major axis is twice of the length of minor axis.
D).
[tex]x^{2} +4y^{2} +6x-8y-23=0[/tex]
[tex]\frac{(x+3)^{2} }{6^{2} } +\frac{(y-1)^{2} }{3^{2} } =1[/tex]
here, h=-3 and k=1
major axis: 2a=2×6=12
minor axis: 2b= 2×3=6
⇒ the length of major axis is twice of the length of minor axis.
E).
[tex]16x^{2} +y^{2} -64x+8y+16=0[/tex]
⇒[tex]\frac{(x-2)^{2} }{2^{2} } +\frac{(y+4)^{2} }{2^{2}} =1[/tex]
here, h=2 and k=-4
major axis: 2a= 4
minor axis :2b=4
⇒ the length of major axis is not the twice of minor axis.
F)
[tex]x^{2} +9y^{2} -2x+18y-71=0[/tex]
⇒[tex]\frac{(x-1)^{2} }{9^{2} } + \frac{(y+1)^{2} }{3^{2} } =1[/tex]
here, h=1, and k=-1
major axis: 2a= 18
minor axis: 2b = 9
⇒ the length of major axis is twice to the length of minor axis.
Learn more about the major and minor axis of the ellipse here:
https://brainly.com/question/14180045
#SPJ2
Related Questions
The ages of eight different students in a college math class were used to make the box plot shown above. Which of the following numbers below is the median of the ages?
A. 21.5
B. 20.5
C. 22.5
D. 24.5
Answers
Bc if u go to college and take a more advanced math and your 18-19 when u graduate high school and people may take a break or look for a job then apply then u would be around 21.5
Which of the following statistics measures the variability of a distribution?
A) Mean
B) Median
C) Mode
D) Range
Answers
Answer:
B
Step-by-step explanation:
B is the answer .
Answer:
[tex]\huge{\textbf{\textsf{{\color{skyblue}{An}}{\blue{sw}}{\red{er}}{\color{red}{:}}}}}[/tex]
[tex]{\boxed{\boxed{\tt { D. \ Range}}}} \ [/tex]
Step-by-step explanation:
The mean, median and mode are central tendency measures. Statisticians use range to describe the amount of variability or spread in a set of data.
⋆┈┈｡ﾟ❃ུ۪❀ུ۪❁ུ۪❃ུ۪❀ུ۪ﾟ｡┈┈⋆
Use the Figure to find the measure of the angle. Explain your Reasoning.
Plz Help
Answers
Step-by-step explanation:
look at the picture i have sent
If you were the number keep 660 times how many times will you likely roll a two or five
Answers
Answer:
220
Step-by-step explanation:
a dice has 6 sides
660 divided by 6 = 110
you asked for 2 numbers so
110 times 2 = 220
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2475 . What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?
Answers
Answer:
1st: 105/h
2nd: 95/h
Step-by-step explanation:
10A+15B=2475 (1)
A+B=200 |*10 => 10A+10B=2000 (2)
From (1) - (2), we have 5B=475, so B=95
then A+95=200 so A is 105
Solve this problem...!
Answers
Answer:
a) 66 degrees
b) 32 degrees
Step-by-step explanation:
a) 90+24
=114
180-114
=66 degrees
b) 180-51= 129
x= 129+19
148
180-148
= 32
mark me brainliestt :)) i worked hard
A line goes through the points (0, -2) and (5, 18). What is the slope of the line?
Answers
Answer:
[tex]\displaystyle m = 4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (0, -2)
Point (5, 18)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{18--2}{5-0}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{20}{5}[/tex][Fraction] Divide: [tex]\displaystyle m = 4[/tex]EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answers
Answer:A..the diagonal bisect perpendicular one other.Since bisectors divide the diagonals equally in two parts.
.
Answer:
D
Step-by-step explanation:
I'm not smart :)
Consider the following functions. (See attachment)
Find the area of the region.
Answers
Answer:
Area: [tex]\displaystyle \frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationGraphing FunctionsExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Area - Integrals
Area under a curveArea between 2 curvesIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify functions
[tex]\displaystyle f(x) = \sqrt[3]{x - 9}[/tex]
[tex]\displaystyle g(x) = x - 9[/tex]
Step 2: Identify Info
Graph the functions - See Attachment
[1st Integral] Bounds: [8, 9], g(x) top function/f(x) bottom function
[2nd Integral] Bounds: [9, 10], f(x) top function/g(x) bottom function
Step 3: Find Area Pt. 1
Set up integrals [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^9_8 {[(x - 9) - \sqrt[3]{x - 9}]} \, dx + \int\limits^{10}_9 {[\sqrt[3]{x - 9} - (x - 9)]} \, dx[/tex]Rewrite integrals [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^9_8 {(x - 9)} \, dx - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \int\limits^{10}_9 {(x - 9)} \, dx[/tex]Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = (x^2 - 9x) \bigg| \limits^9_8 - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - (x^2 - 9x) \bigg| \limits^9_8[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = \frac{-1}{2} - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \frac{1}{2}[/tex]Subtract: [tex]\displaystyle A = -\int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - 1[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle A = -\int\limits^9_8 {(x - 9)^{\frac{1}{3}}} \, dx + \int\limits^{10}_9 {(x - 9)^{\frac{1}{3}}} \, dx - 1[/tex]Step 4: Identify Variables
Identify variables for u-substitution.
u = x - 9
du = dx
Step 5: Find Area Pt. 2
[Integrals] U-Substitution: [tex]\displaystyle A = -\int\limits^0_{-1} {u^{\frac{1}{3}}} \, du + \int\limits^1_0 {u^{\frac{1}{3}}} \, du - 1[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = -(\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^0_{-1} + (\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^1_0 - 1[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = -(\frac{-3}{4}) + \frac{3}{4} - 1[/tex]Simplify: [tex]\displaystyle A = \frac{1}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integrals - Area between 2 curves
Book: College Calculus 10e
2+2=?
i dont remember this, its too complex for me someone help asap
Answers
ahem ahem
2+2=69
it's 4 thanks for the points
Fill in the blank. Using the number line below, the plotted number is when rounded to the nearest ten.
Answers
2sqroot97x
Which value of x makes the expression above equivalent to 20 sqroot97? pls provide a step by step explanation (:
Answers
Answer:
A
Step-by-step explanation:
Need help on this one plz
Answers
Answer:
3 15/18
Step-by-step explanation:
well, 4 5/18 can't take away 8/18 with the fraction itself. so, you take 5 from 8 and get -3. then, take one whole number away and subtract the 18 from 3 (this was the negative 3) and you have the answer. so to conclude it 5 cant take away 8 so its like carrying. you take one whole number that is 18/18 and you subtract the 18 from 3.
Can someone do 11-12?
Answers
find the solution set of 1/3x-4≤ 2+x
Answers
1/3x*3-4*3≤ 2*3+x*3
x-12≤6+3x
-12-6≤3x-x
-18/2≤2x/2
-9≤x
OR
1÷3x-4≤ 2+x
x-12≤6+3x
-12-6≤3x-x
-18/2≤2x/2
-9≤x
Answer:
[-9 ≤ x] or [x ≥ -9]
Step-by-step explanation:
QUESTION :-
Find the solution set of → [tex]\frac{1}{3} x - 4 \leq 2+ x[/tex]
SOLUTION :-
Simplify the L.H.S.[tex]=> \frac{x-12}{3} \leq x + 2[/tex]
Multiply both the sides by 3[tex]=> \frac{x - 12}{3} \times 3 \leq 3(x + 2)[/tex]
[tex]=> x - 12 \leq 3x +6[/tex]
Substract 'x' from both the sides[tex]=> x - 12 - x \leq 3x + 6 -x[/tex]
[tex]=> -12 \leq 2x + 6[/tex]
Substract 6 from both the sides.[tex]=> -12 - 6 \leq 2x + 6 - 6[/tex]
[tex]=> -18 \leq 2x[/tex]
Divide both the sides by 2.[tex]=> \frac{-18}{2} \leq \frac{2x}{2}[/tex]
[tex]=> -9 \leq x[/tex] or [tex]x \geq -9[/tex]
Work out the size or angle X
Answers
Answer:
180-132
Step-by-step explanation:
the entire angle should sum to 180
Answer:
48 °
Step-by-step explanation:
132° + x° = 180° (Linear pair)
∴ x° = 180° - 132°
∴ x° = 48°
Hope this helps :) !!!
The base of a rectangular prism has a base of 15 square cm. The height of the prism is 5 cm. What is the volume of the rectangular prism?
Answers
Step-by-step explanation:
eyeyeyeyeyyeyeyeyeeyeyeueueuryryru
Which statement about 214° is correct?
O A. tan 214° < 0
O B. sin 214° < 0
O C. cos 214° > 0
Answers
Answer:
B.
Step-by-step explanation:
214 degree terminates in the 3rd quadrant.
Sine and cosines are both negative there.
This means that sin(214)<0 and cos(214)<0.
If sine and cosine are both negative and since tangent is the quotient of them, then tangent is positive, or tan(214)>0.
Which graph shows a dilation?
Answers
Answer:
Hello! Mizuki here to answer!
The correct answer would be the first option!
Step-by-step explanation:
Remember, dilation is when a shape gets bigger/smaller.
In this case, the first option would be the only dilation.
Find the area of the circle.
Use 3.14 for pi
d = 10 cm
A = [?] cm2
A=Pi r2
Answers
Step-by-step explanation:
the only thing youre missing is
radius = diameter / 2
Answer:
78.54 cm squared
Step-by-step explanation:
A=πr^2
Since they only give the diameter, divide the diameter by 2
π*25 = 78.54
Have a good day :)
A bucket holds 243.5 oz of water. The bucket loses 0.5 oz of water per second. In how many seconds will the bucket be 40% full?
Answers
1250
€ 125oo
Q8 A taxi company charges £5 standing charge and £1.50 per mile for a journey.
A man travels in a taxi for 12.2 miles.
What is the cost of his journey?
Show your working
Answers
Answer:
£23.30
Step-by-step explanation:
First, find the cost from traveling 12.2 miles. Since the cost is £1.50 per mile, multiply 12.2 by 1.5:
12.2(1.5)
= 18.3
Add the standing charge to this:
18.3 + 5
= 23.3
So, the cost of his journey is £23.30
Alberto ran at a speed of 3 m/hr. After he ran 6 miles, Omar ran in the same direction with a speed of 4.6 m/hr.
How many hours will it take Omar to catch up to Alberto.
Answers
Answer:
1.3 Hours (1 Hour and 18 Minutes)
Step-by-step explanation:
It took Alberto 2 hours because he ran 3 miles an hour and the total distance he ran was 6 miles.
Now, you have to divide 6 (Alberto's distance) by 4.6 (Omar's rate) and you get 1.3043.
Round the answer to get 1.3
Answer: jjijmjn
Step-by-step explanation:
"HOT PIZZA" is offering 20% discount on all its pizza
Ali bought a pizza for £5.60 what was the original price
Answers
Answer:
Original price was £7.00
Step-by-step explanation:
20% discount means that ali is paying 80% of the full price
.8p = 5.60
Divide both siides by .8
p = 7
Original price was £7.00
Use the change of base formula and a calculator to approximate each logarithm. Round to
three decimal places.
log14 (16)
Answers
Answer:
[tex]1.051[/tex]
Step-by-step explanation:
The change of base formula is given by [tex]\log_a b=\frac{\log b}{\log a}[/tex]
Substituting given values, we have:
[tex]\log_{14} 16=\frac{\log 16}{\log 14}\approx \boxed{1.051}[/tex]
Tom is tiling a wall.
He needs to buy at least 100 tiles. The tiles are sold in large packs and small packs.
Large pack = 40 tiles £18
Small pack = 28 tiles £14
Special offer = 25% reduction when you buy 3 or more large packs.
Work out the cheapest cost for Tom to buy the packs of tiles he needs.
Answer £
Answers
Answer:
The correct answer is - £ 40.5 for 3 large packs.
Step-by-step explanation:
Given:
Large pack = 40 tiles £18
Small pack = 28 tiles £14
Special offer = 25% reduction when you buy 3 or more large packs.
Solution:
Following combinations are possible for tom to get the tiles he needs:
1. 3 large packs
40*3 = 120 tiles with 25% discount
cost = 18*3 - 0.25*18*3 = 40.5
2. 4 small packs
28*4 = 112 tiles
cost = 14*4 = 56
3. 2 large packs and 1 small pack
40*2 + 28 = 108 tiles
cost = 18*2 + 14 = 50
4. 1 large pack and 3 small packs
40 + 28*3 = 124 tiles
cost = 18 + 14*3 = 60
Thus, the correct answer is - 1st case with three large packs.
Let f(x) = x – 5 and g(x) = 3x – 7. Find f(x) + g(x).
Show your work
Answers
Answer:
4x+2
Step-by-step explanation:
When you try to evaluate the expression f(x) + g(x). You just evaluate the problem x-5+3x-7.
When it as been evaluated you will get 4x+2
Kira tutors history. For each hour that she tutors, she earns 30 dollars. Her earnings, E (in dollars), after tutoring for h hours is given by the following.
E = 30h
How much does Kira earn if she tutors for 5 hours?
Answers
Answer:
E = 30h = 30(5) = 150 dollars
Step-by-step explanation:
....
Is it bad that I immediately thought Light Yagami?
Answer:
Kira earns 30×5:$150if she tutors for 5 hours.
Please help! I will give Brainliest!
Answers
Answer:
p(not L) = 7/8, 0.875, 87.5%
Step-by-step explanation:
8 letters in total
7 are not L
p(not L) = 7/8, 0.875, 87.5%
In the diagram, the sum of the values of r and z is 116.
bo/20
xo
What is the value, in degrees, of y?
Enter a number in the space provided.
Answers
Answer: 122 degrees
Step-by-step explanation:
Don’t feel like explaining.