QI - The sum of the distance of a moving
point from the points (c,0) and (-c,0) is
always 2a units. Find the equation to the locus
of the moving point.
Answers
Answer:
\(\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1\)
Step-by-step explanation:
Let P be the moving point and the given points be A (c,0) and B (-c, 0). If (h, k) be the co-ordinates of any position of P on its locus then:
PA + PB = 2a
PA = 2a - PB
PA² = 4a² + PB² – 4a ∙ PB
PA² – PB² = 4a² – 4a ∙ PB
[(h - c)² +(k - 0)²] - [(h + c)² +(k - 0)²] = 4a² – 4a. PB
-4hc = 4a² – 4a∙PB
a ∙ PB = a² + hc
Taking square
a² ∙ PB² = (a² + hc)²
a² [(h + c)² + (k - 0)²] = (a² + hc)²
a² [h² + c² + 2hc + k²] = a⁴ + 2a²hc + h²c²
a²h² – h²c² + a²k² = a⁴ – a²c²
(a² – c²)h² + a²k² = a² (a² – c²)
h²/a² + k²/(a² – c²) = 1
Therefore, the required equation to the locus of P is
\(\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1\)
Related Questions
Can you solve this for me? Thank you! :>
Answers
Answer:
p=7/2
Step-by-step explanation:
2p=7
/2. /2
p=7/2
now to check
2(7/2)=7
14/2=7
7=7
its true
hopes this helps
The first and second step to solve the equation 3x/5+=20
Answers
give the person above brainly thing
Can someone help me with this?
Answers
8m x 3m x 6.6 m
30 points to whoever gets this right need to be answered asap please <3
Select the values that make the inequality 6z < 12 true. Then write an equitation inequality, in terms of z. ( Numbers written in order from least to greatest going across.)
Answers
Answer:
Step-by-step explanation: Well I have no idea
Answer:try asking mathaway
Step-by-step explanation:they solve
You graph a triangle on a grid paper. The slopes of the sides are 0, -3, and undefined. What kind of triangle did you draw?
Answers
Answer:
I think u drew a sideways triangle I don't really know or a really small one maybe. I don't know its correct or not
please help me i will give brainliest to first person to anwser.
Answers
First we start with the formula for cylinders v=(pi)r(squared)h filled in Thats v=(3.14)(8 squared) (8) which brings us to the answer 1607.68 but you must round to the nearest tenth aka 1607.7
Answer:
The first option, V ≈ 1607.7 in²
Step-by-step explanation:
Find the volume of the given cylinder.
\(\begin{center}\framebox{\parbox{4cm}{\textbf{Volume of a Cylinder:}\\[2ex]The volume of a cylinder with radius $r$ and height $h$ is given by the formula:\\[2ex]\center{$V = \pi r^2 h$} \\ \\}}\end{center}\)
Given:
r = 8 in
h = 8 in
π = 3.14
Find:
V = ?? in³
\(\hrulefill\)
Now solving,
Substitute the given values into the formula:
=> V = (3.14)(8)²(8)
Using a calculator to simplify:
=> V = 1607.68 in²
Rounded to the nearest tenth:
∴ V ≈ 1607.7 in²
Thus, the first option is correct.
What is the value of 4/7 x 0.3 / 1/6?
Answers
Rewrite as
\(\frac{4}{7} *\frac{3}{10} /\frac{1}{6}\)
PEMDAS says do multiplication first
When multiplying fractions, just multiply across.
12/70 / 1/6
When dividing fractions, KEEP CHANGE FLIP.
Keep one of the fractions, change the sign to multiplication, flip one of the fractions.
12/70 * 6/1
72/70
1 2/70
Option D
1 1/35
Multiply the pairs of numbers and match them with their products. Tiles (-5)(4.2) (-7)(-3) (4) (5) (2.5)(-9) Pairs 22.5 21 -22.5 -21 111
Answers
Here are the pairs matched with their products:
- (-5)(4.2) matches with -21
- (-7)(-3) matches with 21
- (2.5)(-9) matches with -22.5
Pairs (4) and (5) do not have corresponding products in the given options.
(-5)(4.2) = -21
(-7)(-3) = 21
(4)(5) = 20
(2.5)(-9) = -22.5
So, the pairs of numbers and their products are as follows:
(-5)(4.2) = -21 matches with -21.
(-7)(-3) = 21 matches with 21.
(4)(5) = 20 matches with 20.
(2.5)(-9) = -22.5 matches with -22.5.
I hope this helps!
A stone is dropped off
the edge of a cliff, and it falls for 4.8s before striking
bottom. Approximately how far above the bottom is
the cliff edge, assuming zero air resistance?
Answers
Answer:
y=(1/2)at^2
y=(1/2)(9.8 m/s/s)(4.8 s)^2
y=60.025 m
Step-by-step explanation:
Sry if not right
there are 44 students and 6 adults attending a field trip to an art museum what is the ratio of adults to children
Answers
The ratio would be 6:44 or 3:22.
There are 44 students and 6 adults. From this info we have, the ratio is 6 to 44 which is 6/44 or 6:44. If we simplify 6:44 because it can be, the answer would be 3:22, 3/22, or 3 to 22.
Ratio of number of adults to children is 3 : 22.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Total number of students attending the trip = 44
Total number of adults attending the trip = 6
Ratio of adults to children can be written as 6 : 44
6 : 44 = 6 / 44
Write each of the numerator and the denominator as the multiple of the common factor of numerator and the denominator.
6 = 2 × 3
44 = 2 × 22
6 / 44 = 3/22
Hence the required ratio is 3 : 22.
To learn more about Ratios, click on the link given below :
https://brainly.com/question/13419413
#SPJ5
PLEASE ANSWER QUICKLY ITS DUE IN 3 MIN LOL
Artaud noticed that if he takes the opposite of his age and adds 39 he gets the number 23. How old is Artaud?
Answers
61??
explaination:
x+39= 23
-16+39= 23
-16 opposite is 61??
hope this helps!
Answer:
Artaud's age is 16.
Step-by-step explanation:
A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase?
Answers
Answer:
30
Step-by-step explanation:
We can use the Pythagorean Theoreom for this.
Since we are trying to find the hypotenuse, we know that the hypotenuse is \(c^2\)
So, here we are:
\(a^2+b^2=c^2\\a^2=24\\b^2=18\\18^2+24^2=c^2\\324+576=c^2\\900=c^2\\\)
Then, we find the square root of 900 which is: \(\sqrt{900} = 30\\\\\)
There you go! We have 30 as our answer.
6. Find the area of the parallelogram.
The figure shows a parallelogram with a horizontal base edge measuring 10 centimeters. The right triangle is shown with the right angle opposite of the right slanted edge of the parallelogram. The vertical leg of the right triangle measures 17 centimeters. (1 point)
54 cm2
85 cm2
170 cm2
27 cm2
Answers
= 10 × 17
= 170 meters2
Mr. Gonzales has only $18 to spend at a clothing store. He wants to buy a shirt that costs $5 including tax and some bracelets that cost $1.30 each, including tax. Write an equation and solve to determine b, the maximum number of bracelets Mr. Gonzales could buy. Pls I am desperate I will make it all of my 1,569 of my points to get the answer in 2 minutes
Answers
Subtract five from both sides for
1.30b = 13
Divide each side by 1.30
b = 13/1.30
b = 10
Mr. Gonzales can buy ten bracelets at maximum (if tax was included in the original prices you listed)
Answer:
10
Step-by-step explanation:
1. Equation:
18 = 5 + 1.30b
2. (Solve): Subtract 5
13 = 1.30x
3. Divide:
10 = b
All of the following statements describe the relation shown except _____.
The inputs are {-1, 0, 3, 4}.
The diagram represents a function.
This relation could also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.
The outputs are {-2, -1, 1}.
Answers
Answer:
the answer is The imputs are {-1,0, 3,4}
Answer:
-1,0, 3,4
Step-by-step explanation:
Please help with this step by step and please do not do any links this is due today please answer all three and I will give you brainliest don't give a fake answer or you will not get brainliest and you will be reported at least try
Answers
Answer: Hi, this is hard to read!
Step-by-step explanation:
ANSWER PLISSSSSSS
*WILL GIVE BRAINLIEST*
Answers
Answer Letters:
1. A = 2.09
2. E = 0.209
3. K = 0.029
4. N = 0.29
Comment:
I hope this helps. :)
Answer:
I got you bro this is what I would put
Step-by-step explanation:
1) D
2)E
3)J
4)N
Last month I had 8 guppies. This month I have 20 guppies. What is the percent of increase in guppies from last month to this month?
Answers
Answer: 150% increase
Step-by-step explanation:
percent of increase: new/old × 100%-100%
--------------
new/this month: 20 puppies
old/last month: 8 puppies
new/old×100%-100%
=20/8×100%-100%
=2.5×100%-100%
=250% -100%
=150% increase
Hope this helps!! :)
Please let me know if you have any question
Question 2(Multiple Choice Worth 4 points)
(02.02)Angle XYZ is formed by segments XY and YZ on the coordinate grid:
A coordinate plane is shown. Angle XYZ has endpoints at 3 comma negative 1 and 6 negative 2 and 3 comma negative 3 and measures 36.87 degrees.
Angle XYZ is rotated 270 degrees counterclockwise about the origin to form angle X’Y’Z’. Which statement shows the measure of angle X’Y’Z’?
m∠X’Y’Z’ = m∠XYZ
m∠X’Y’Z’ = 180 degrees
m∠X’Y’Z’ = 270 degrees
m∠X’Y’Z’ = 2 × m∠XYZ
PLSS HELP I GIVE BRAINLIEST
Answers
Answer:
the answer will be
m∠X′Y′Z′ = m∠XYZ
Step-by-step explanation:
Answer:
m∠X′Y′Z′ = m∠XYZ
Step-by-step explanation:
the coordinates from angle x,y and z added together equal m∠XYZ
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Answers
What is the angle made by the hour hand and the minute of the clock at 8:57
Answers
Answer:
85 degrees
Step-by-step explanation:
OMG PLEASE HELP MEEEE I NEED TO GET MY GRADE UP
Answers
section one - simplify
E - 35
I - 51
A - 168
Y - 18
T - 140 (I couldn’t tell if the last symbol was addition or division! This is if it’s addition.)
E - 7
P - 19
_____
section two - simplify
A | 6
T | 16
D | 0
W | -2
Sorry if any are incorrect. The image is blurry and this was rushed. Hope this still helps!
Cylinder A has a radius of 6 feet and a height that is 5.5 feet less than Cylinder B. The cylinders have the same surface area. Find the height of each cylinder.
Answers
The height of the cylinders are (r - 0.5)/5 and -5.5 + (r - 0.5)/5 respectively; where r represents the radius of cylinder B
How to determine the height of the cylinders?The given parameters are:
Cylinder A
Radius = 6
Height = h - 5.5
Cylinder B
Radius = r
Height = h
The surface area of a cylinder is
S = 2πr(r + h)
So, we have:
Cylinder A
Radius = 6
Height = h - 5.5
S = 2π * 6(6 + h - 5.5)
Cylinder B
Radius = r
Height = h
S = 2πr(r + h)
Substitute S = 2πr(r + h) in S = 2π * 6(6 + h - 5.5)
2πr(r + h) = 2π * 6(6 + h - 5.5)
Divide both sides by 2π
(r + h) = 6(6 + h - 5.5)
This gives
(r + h) = 6(h + 0.5)
Expand
r + h = 6h + 0.5
Evaluate
r = 5h + 0.5
Rewrite as
h = (r - 0.5)/5
So, we have
h -5.5 = -5.5 + (r - 0.5)/5
Hence, the height of the cylinders are (r - 0.5)/5 and -5.5 + (r - 0.5)/5 respectively; where r represents the radius of cylinder B
Read more about surface areas at:
https://brainly.com/question/76387
#SPJ1
Will give brainless to whoever gets this right
Answers
The experimental probability of spinning a 3 is what?
am I correct?
Answers
Answer:
16/70
Step-by-step explanation:
14+12+16+15+13=70
The 3 has 16.
so the probability is 16/70.
Someone help me with this ASAP!
Answers
Answer:
48.1 somewhere around 36 and 57
Step-by-step explanation:
Answer:
36-57
Step-by-step explanation:
18.50 x 2.6 = 48.10, which is between those two numbers
ASAP PLS I NEED IT AND TY
Answers
When we're solving with scale factors, we either divide or multiply.
If the shape becomes larger, we multiply to get the new length.
If the shape becomes smaller, we divide to get the new length.
Solving the QuestionWe're given:
Original side length is 2.5 unitsScale factor = 6Because the shape becomes larger, we have to multiply the original side length by the scale factor, 6, to get the new side length.
2.5 x 6 = 15
Therefore, the missing side length is 15 units.
Answer15 units
Answer:
6
Step-by-step explanation:
An item is regularly priced at 55% . Chang bought it on sale for 20% off the regular price. How much did Chang pay?
Answers
Answer: I'm not sure if the percent signs are an error but the answer would be $0.11, if 55% is actually $55 then the answer is $11
Step-by-step explanation:
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
−6x2 − 8x + 12 = 0
a = −6, b = −8, c = 12
a = 6, b = 8, c = 12
a = 8, b = 12, c = 0
a = −8, b = 12, c = 0
Answers
Answer: A!
Step-by-step explanation: The quadratic formula is ax2+bx+c, so you just plug in and see which ones go with the equation, a=-6 (-6x2) b=-8 (+-8 or -8) and c=12 (+12) Hope this helps
To make a number pattern, Shana used the rule "Add 3," with a whole number as the starting number. Which statement must be true about Shana's list of numbers?
Answers
Answer:
you didnt put enough context in your question but if shana kept using three she would have mixed even and odds in her numbers if you could give more context to the question id be glad to help more