Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 100. The comet follows a parabolic path with directrix x = 70 and vertex at (60, 0).
Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points)
Part B: Write the equation of the comet's path in standard form. Show your work. (4 points)
Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredth place. (4 points)
The equation of the circular orbit and the parabolic path of the comet are
given by the center, diameter, vertex, and directrix.
Part A: The equation of the planet's orbit is; x² + y² = 50²
Part B: The equation of the comet's orbit is; [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: The planet's orbit and the comet's path do not intersect.
Reasons:
Part A: The center of the orbit = The origin (0, 0)
The diameter of the orbit = 100
Therefore;
[tex]Radius \ of \ orbit = \dfrac{100}{2} = 50[/tex]
The radius of the planet's orbit, r = 50
The equation of a circle with center (h, k) is; (x - h)² + (y - k)² = r²
Therefore, the equation of the circle is (x - 0)² + (y - 0)² = r²
Which gives;
x² + y² = 50²
Part B: The directrix of the parabolic path is x = 70
The vertex = (60, 0)
Therefore, -p = 70
[tex]The \ equation \ is \ x = \dfrac{1}{4\cdot p} \cdot (y - k)^2 + h[/tex]
Which gives;
[tex]The \ equation \ is \ x = \dfrac{1}{4\times (-70)} \times (y - 0)^2 + 60 = -\dfrac{y^2}{280} + 60[/tex]
[tex]x = \mathbf{ -\dfrac{y^2}{280} + 60}[/tex]
The equation of the comet's path in standard form is [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: At the point where the path intersect, we have;
[tex]x^2 = \left( -\dfrac{y^2}{280} + 60 \right)^2[/tex]
Therefore;
[tex]\mathbf{\left( -\dfrac{y^2}{280} + 60 \right)^2} = 50^2 - y^2[/tex]
Let y² = a, we get;
[tex]\left( -\dfrac{a}{280} + 60 \right)^2 = 50^2 -a[/tex]
a ≈ -2015.693 and a ≈ -42784.31
y ≈ √(-2015.693) or y ≈ √-42784.31) (imaginary numbers)
The planet's orbit does not intersect the path of the comet.
Learn more here:
https://brainly.com/question/20743199
PLEASE HELP!!!!!!!!!!!!!!!!!
Answer:
7.11[tex]\leq[/tex]-7.1
Step-by-step explanation:
Answer:
Question 1- C. 7.11 > -7.1
Question 2- True
Question 3- -3 < -1 and -3 ≤ -1
Question 4- I don't know
Question 5- {3,4}
Step-by-step explanation:
I ran it through the calculator only on question 4 I didn't know the answer
-Rocketgamer360
Two polygons are similar. The corresponding angles of the polygons are- A congruent B proportional C regular D similar
9514 1404 393
Answer:
A congruent
Step-by-step explanation:
In similar polygons, corresponding sides are proportional, and corresponding angles are congruent.
Evaluate each expression.
12
N
3
(2511)
-
DONE
Answer:
1/5Step-by-step explanation:
[tex](25^{-3/2})^{1/3} = 25^{-3/2*1/3} = 25^{-1/2}=5^{-1/2*2}=5^{-1}=1/5[/tex]Let's evaluate the expression,
→ (25^-3/2)^1/3
→ 25^-3/2×1/3
→ 25^-3/6
→ 5^-1/2×2
→ 5^-1 {or} 1/5
Hence, the answer is 1/5.
What are the equivalent ratios to 6:5
Ratio of 6 to 5
A ratio of 6 to 5 can be written as 6 to 5, 6:5, or 6/5. Furthermore, 6 and 5 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on.
A ratio of 6 to 5 simply means that for every 6 of something, there are 5 of something else, with a total of 11
Below is a list of equivalent ratios of 6:5 that we created using our 6:5 ratio calculator above.
6:5
12:10
18:15
24:20
30:25
36:30
42:35
48:40
54:45
60:50
66:55
72:60
Which of these lenders will make a very short-term loan based on proof of
employment?
A. Title lender
B. Bank
C. Credit union
D. Payday lender
What is 6 3/4 percent of 800
Answer:
answer is 746.
have a nice day and do good in math
Admission to a baseball game is $2.50 for general admission and $5.00 for reserved seats. The receipts were $3667.50 for 1109 paid admissions. How many of each
ticket were sold? (Round to nearest integer if necessary.)
The general admission tickets sold are 1467 and the number of reserved seats tickets sold is 358.
Two equations would be derived from the question:
$2.50a + $5b = $3667.50 equation 1
a + b = 1109 equation 2
Where:
a - number of people for the general admission
b = number of people for the reserved seats
To determine the value of b, take the following steps:
Multiply equation 2 by 2.5
2.5a + 2.5b = 2772.50 equation 3
Subtract equation 3 from 2
2.5b = 895
Divide both sides by 2.5
b = 358
In order to determine the value of a, substitute for b in equation 2
358 + a = 1109
a = 1109 - 358 = 1467
To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults
Find the derivative of the function y = ln(3t+4)
Answer:
3 / (3t+4) is the answer
What is 3.59 rounded to the nearest whole number?
Answer:
its 4 ezy
Step-by-step explanation:
please mark as brainlists
Let f(x)=3x-8 and g(x)=x^2+4.
Find f(g(-2)).
Answer:
16Step-by-step explanation:
Given:
f(x) =3x - 8 and g(x) = x² + 4f(g(- 2)) = ?First find g(- 2):
g(- 2) = (-2)² + 4 = 4 + 4 = 8Find f(8):
f(8) = 3*8 - 8 = 24 - 8 = 16g(-2):-
[tex]\\ \sf\longmapsto (-2)^2+4[/tex]
[tex]\\ \sf\longmapsto 4+4[/tex]
[tex]\\ \sf\longmapsto 8[/tex]
Now
[tex]\\ \sf\longmapsto f(x)=3x-8[/tex]
[tex]\\ \sf\longmapsto f(g(-2))=f(8)[/tex]
[tex]\\ \sf\longmapsto 3(8)-8[/tex]
[tex]\\ \sf\longmapsto 24-8[/tex]
[tex]\\ \sf\longmapsto 16[/tex]
pls find prism if you find it your littearly a pro hacker
Answer:
24 cubic unitsStep-by-step explanation:
Given, in picture,It is a rectangular prism.
It's length in units = 4
It's breadth in units = 2
It's height in units = 3
Therefore,Volume of the given rectangular prism
= length × breadth × height
= 4 units × 2 units × 3 units
= 24 cubic units (Ans)
what is the additve inverse of 9/10
Answer is -9 litterly just take a postive and make it into a negative
Valentine's Day is coming up, so Sweet Dreams chocolate shop is ordering ribbon to decorate gift boxes. Small gift boxes use 20 inches of ribbon, while large ones use 30 inches. Sweet Dreams expects to sell 225 small boxes and 180 large boxes. If the ribbon they use is sold by the yard, how many yards of ribbon should they order?
Answer:
i think 9900
Step-by-step explanation:
225x20 = 4500
180x30 = 5400
5400+4500 = 9900
If a line l is perpendicular to a segment AB at point E and AE = EB how many points on line l are the same distance from point A as from point B
Answer:
101
Step-by-step explanation:
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
Answer:
58 2/3 fps
Step-by-step explanation:
To convert a speed value from miles per hour to feet per second, multiply it by 5280, then divide by 3600.
40 * 5280 = 211200
211200 / 3600 = 58.6666..... [58 2/3]
PLS HELP ASAP
x^2 - 4x-1=0
Solve using formula
2x ( x - 2x) = 1
2x= 1
x = 0.5
x-2x = 1
-x = 1
x = -1
Help me please ………..
Answer:
Step-by-step explanation:
Answer:
<QSR = 55°(180°-125°)
Step-by-step explanation:
therefore, p-8=55°
p=(55+8)° = 63°.
hope this helps you.
list all counting numbers which leave a remainder of 4 when divided by 22.
Answer:
0.1818
i hope it helped you :)
mark brainliest
$49.95 gloves 5 1/4 % markup
Answer:
1234567891011121314151617181920
third degree with zeros of − 3 −1 and 5 and a y-intercept of − 10
Answer:
What are you asking? Yeah I know that but what do you need to know?
Step-by-step explanation:
What is the solution of this system of equations?
x + 3y = 7
3x +2y = 0
A. (3,2)
B. (-2,3)
C. (2, -3)
D. (-3,2)
E. (-2,-3)
Answer:
B. (-2,3)
Explanation:
First, we'll turn both lines to slope-intercept form:
x + 3y = 7
Subtract x on both sides to get 3y = -x + 7, then divide 3 on both sides to get y = -1/3x + 7/3.
3x + 2y = 0
Subtract 3x on both sides to get 2y = -3x, then divide 2 on both sides to get y = -3/2x.
Now you can graph (I did it for you above⤴⤴⤴).
Hope this helps you :)
Find x.
Multiple choice.
8, 9, 10, 11
Answer:
Step-by-step explanation:
As RS is a straight line sin ∠RUT = sin ∠SUT
line UT bisects ∠RTS
Let θ be ∠UTR and ∠UTS
Law of sines
Left side triangle
3x/sinθ = 40/sinRUT
sinRUT = 40sinθ / 3x
Right side triangle
(x + 2) / sinθ = 16 / sinSUT
(x + 2) / sinθ = 16 / (40sinθ / 3x)
(x + 2)(40sinθ / 3x) = 16sinθ
(x + 2)(40sinθ) = 48xsinθ
40xsinθ + 80sinθ = 48xsinθ
40x + 80 = 48x
80 = 8x
x = 10
The Washington High key club is selling brownies and chocolate chip cookies to raise money. Their table only has room for 100 baked goods. Previous bake sells has taught them to plan to bake at most 30 brownies and at least 50 cookies. Write and graph a system of inequalities to represent the possible number of baked goods.
Step-by-step explanation:
Let x - brownies, y - cookies.
According to given w have following inequalities
Their table only has room for 100 baked goods:
x + y ≤ 100Plan to bake at most 30 brownies and at least 50 cookies:
x ≤ 30y ≥ 50See attached for the graphical solution
The solution is within the marked boundaries.
can someone heelp me
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{Guide}\downarrow\\\large\text{10's = X}\\\large\text{20's = XX}\\\large\text{30's = XXX}\\\large\text{40's = XL}\\\large\text{50's = L}\\\large\text{60's = LX }\\\large\text{70's = LXX}\\\large\text{80's = LXXX}\\\large\text{90's = IX}\\\large\text{100's = C}\\\large\text{200's = }CC \\\large\text{300's = CCC}\\\large\text{400's = CD}\\\large\text{500's = D}\\\large\text{600's = DC}\\\large\text{700's = DCC}\\\large\text{800's = DCCC}\\\large\text{900's = CM}\\\large\text{1,000's = M}[/tex]
[tex]\large\textsf{NOW THAT WE HAVE THAT GUIDE/INFORMATION OUT OF}\\\large\textsf{THE WAY, WE CAN ANSWER YOUR GIVEN QUESTION.}[/tex]
[tex]\huge\text{1,052 = \boxed{\rm{\bold{M}LII}}}\huge\checkmark\\\\\\\\\huge\text{450 = \boxed{\rm{\bold{CD}L}}}\huge\checkmark\\\\\\\huge\text{952 = \boxed{\rm{\bold{CM}LII}}}\huge\checkmark\\\\\\\huge\text{942 = \boxed{\rm{\bold{\bold{CM}}XLII}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Select the correct answer.
Which point is a reflection of T(-6.5, 1) across the x-axis and the y-axis?
A. point U
B. point V
C. point W
D. point X
Answer:
the answer is A. point U
or it's point W
What are the solutions of x2 - 2x + 10 = 0 ?
Answer:
Step-by-step explanation:
=
−
±
2
−
4
√
2
x
=
−
b
±
b
2
−
4
a
c
2
a
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
−
2
+
1
0
=
0
x
2
−
2
x
+
10
=
0
x2−2x+10=0
=
1
a
=
1
a=1
=
−
2
b
=
−
2
b=−2
=
1
0
c
=
10
c=10
=
−
(
−
2
)
±
(
−
2
)
2
−
4
⋅
1
⋅
1
0
√
2
⋅
1
x
Answer:
C. x=1+3i, x=1-3iStep-by-step explanation:
[tex]\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:10}}{2\cdot \:1} \\=\frac{-\left(-2\right)\pm \:6i}{2\cdot \:1}\\x_1=\frac{-\left(-2\right)+6i}{2\cdot \:1},\:x_2=\frac{-\left(-2\right)-6i}{2\cdot \:1}\\\frac{-\left(-2\right)+6i}{2\cdot \:1}\\ =\frac{2+6i}{2\cdot \:1}\\=\frac{2+6i}{2}\\=\frac{2\left(1+3i\right)}{2}\\1+3i\\\\\\frac{-\left(-2\right)-6i}{2\cdot \:1}\\=\frac{2-6i}{2\cdot \:1}\\=\frac{2-6i}{2}\\=\frac{2\left(1-3i\right)}{2}\\1-3i\\x=1+3i,\:x=1-3i[/tex]
The function c(h)= (20h)/(h^2+2) models the concentration of a medication in the bloodstream h hours after it’s injection into the muscle tissue.
-Does the graph have a vertical asymptote? If so, give the equation of the vertical asymptote and explain why this would be a concern or not. If the function does not have a vertical asymptote, explain why.
-Find the horizontal asymptote, what does it mean in the context of this problem?
-Does the function cross the horizontal asymptote? Does it make sense in the relation to this problem?
I have the answers, I just don’t understand how to explain them in the context of the problem.
Answer:
Step-by-step explanation:
What’s it’s answer I am wonder
geometry B: fill in the blank
Answer:
The circumference of a circle is the distance around the entire circle, while arc length, s, is the distance between two points on the circle.
C = 2πr = 2π( 5 ) = 10π ≈ 31.4 units
3.14 is an approximation for π.
s = θ/360° (C)
mAB = 60°/360° ( 31.4)
= 1/6(31.4) ≈5.2 units
help me please someone
=========================================================
Explanation:
Part A
Ignore the g(x) curve. We're looking for the intersection of the p(x) and f(x) curves. The two cross at (-3,-3) which is the solution to the system of these two equations. This point is on both p(x) and f(x) simultaneously. That means the coordinates of the point satisfy both p(x) and f(x) equations simultaneously.
------------------------
Part B
Pick any two points you want from the f(x) curve. You could pick the solution we mentioned, but I'll go for (0,0) and (2,2). When talking about a single curve, it has infinitely many solutions (as long as you pick a point on the curve).
------------------------
Part C
Ignore the f(x) curve. The graphs of p(x) and g(x) intersect when x = -6, which is the solution to the equation p(x) = g(x). We're only concerned about the x coordinate of the intersection.