1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ratling [72]
2 years ago
6

Part 3: Write the equation of and graph an ellipse.

Mathematics
1 answer:
tensa zangetsu [6.8K]2 years ago
8 0

Answer:

Step-by-step explanation:

The center is halfway between vertices, at (4, -6).

It is also halfway between foci.

:::::

The vertices are vertically aligned, so the parabola is vertical.

General equation for a vertical ellipse:

 (y-k)²/a² + (x-h)²/b² = 1

with

 center (h,k)

 vertices (h,k±a)

 co-vertices (h±b,k)

 foci (h,k±c), c² = a²-b²

Apply your data and solve for h, k, a, and b.

center (h,k) = (4, -6)

h = 4

k = -6

vertices (4,-6±a) = (4,-6±9)

a = 9

foci (4,-6±c) = (4,-6±5√2)

b² = a² - c² = 9² - (5√2)² = 31

b = √31

The equation becomes

 (y+6)²/81 + (x-4)²/31 = 1

:::::

length of major axis = 2a = 18

length of minor axis = 2b = 2√31

You might be interested in
The graph below describes the journey of a train between two cities.
Veseljchak [2.6K]

Answer:

[A] Acceleration in first 15 min = 200  km/h²

[B] Distance between two cities = 125 km

[C] Average Speed of journey =  62.5  km/hr

Step-by-step explanation:

To Solve:

Acceleration in first 15 min

Distance between two cities  

Average speed of journey

Solve:

[A] Work out the acceleration, in km/h?, in the first 15 mins.

Each horizontal block is 1/8 hr = 7.5 min

Each vertical block is 10 km/hr

Time                     Velocity  km/hr

0 Min  ( 0 hr)            0

15 Min (1/4 hr)           50

45 Min (3/4 hr)         50

60 MIn  ( 1 hr)            100

90 Min  ( 3/2 hr)        100

120 Min ( 2hr)            0

Acceleration in first 15 min  (1/4 hr)  =  (50 - 0)/(1/4 - 0)  = 50/(1/4)

= 200  km/h²

Hence, Answer for [A] = 200  km/h²

[B] Work out the distance between the two cities. $60 Velocity (in km/h)

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

Distance between two cities = 125 km

[C] Work out the average speed of the train during 20 the journey.

Average Speed of journey = 125/2  = 62.5  km/hr

[RevyBreeze]

5 0
2 years ago
Which is the solution to (8.5 x 103)(2 x 105) expressed in scientific notation?
kenny6666 [7]

We have been given an expression (8.5\times 10^3)(2\times 10^5). We are asked to find the solution to our given expression expressed as scientific notation.

Let us simplify our given expression.

Using exponent property a^m\cdot a^n=a^{m+n}, we will get:

8.5\times 2\times 10^3\times 10^5

17\times 10^{3+5}

17\times 10^{8}

Now to write our answer in scientific notation, we need our 1st multiple between 1 and 10. So we will rewrite our expression as:

1.7\times 10\times 10^{8}

1.7\times 10^{1+8}

1.7\times 10^{9}

Therefore, our required solution would be 1.7\times 10^{9}.

8 0
2 years ago
If you improve your credit score to good and paid $1500 on your $12,465 purchase how much interest could you save in the first m
Gennadij [26K]

Answer:

Step-by-step explanation:

The amount your credit score improves depends a lot on how high your utilization was in the first place. If you're already close to maxing out your credit cards, your credit score could jump 10 points or more when you pay off credit card balances completely.

8 0
2 years ago
In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.<br><br><br> NOT A RIGHT TRIANGLE
Damm [24]

Answer:

c = 13.2

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

# Side a is opposite to ∠A

# Side b is opposite to ∠B

# Side c is opposite to ∠C

- The sine rule is:

# \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}

* Lets solve the problem

- In Δ ABC

∵ m∠A = 16°

∵ m∠B = 49°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 16° + 49° + m∠C = 180°

∴ 65° + m∠C = 180° ⇒ subtract 65° from both sides

∴ m∠C = 115°

- Lets use the sine rule to find c

∵ a = 4 and m∠A = 16°

∵ m∠C = 115°

∵ \frac{4}{sin(16)}=\frac{c}{sin(115)}

- By using cross multiplication

∴ c sin(16) = 4 sin(115) ⇒ divide both sides by sin(16)

∴ c=\frac{4(sin115)}{sin16}=13.2

* c = 13.2

8 0
2 years ago
ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (2, 2
r-ruslan [8.4K]
The answer is 4 units. The distance between the two points of B and C is equals 6-4=2, because the y is the same. According to the question, the BC is equals 0.5*B'C'. So the length of B'C' is 2/0.5=4 units.
3 0
3 years ago
Read 2 more answers
Other questions:
  • Hassem and his family cut an apple pie into 5 equal slices and a blueberry pie into 10 equal slices. They ate 3/5 of the apple p
    8·2 answers
  • Select true or false to tell whether the following conditional pq is true or false. Use the truth table if needed.
    5·1 answer
  • What is the value of 2x + 11y when x = 4 and y = 2?
    8·2 answers
  • Terry is 5 1/3 ft her brother is 3/5 the height of tanning how tall is Tammy's brother
    8·1 answer
  • Please help! I have an answer but idk if it's right so please check and tell me if I made any mistakes! Thank you!
    13·1 answer
  • In ΔKLM, m = 5.3 inches, ∠K=21° and ∠L=88°. Find the length of k, to the nearest 10th of an inch.
    11·1 answer
  • Simplify the expression<br>​
    11·2 answers
  • Simplify the following expres<br> (- 4xy-2) - 5<br> (xy-2)-1
    9·2 answers
  • Natalie walked 3/5 mile in 1/2 hour. How fast did she walk, in miles per hour
    13·2 answers
  • 1/3 divided by 1/8<br> a, 1/24<br> b. 3/8<br> C. 2 and 2/3<br> d. 24
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!