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.
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Which equation represents this sentence?
6 times the difference of a number and 5 is equal to 36
5−6x=36
6(x−5)=36
6x−5=36
6(5−x)=36
The equation that represents this sentence "6 times the difference of a number and 5 is equal to 36" will be; 6(x - 5) = 36
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given a statement as "6 times the difference of a number and 5 is equal to 36"
Therefore, the 6 times means the multiplication.
Let the number be x then;
the difference of a number and 5 is equal to 36 means the subtraction that is;
(x - 5) = 36
Therefore, the equation becomes
6(x - 5) = 36
The equation that represents this sentence "6 times the difference of a number and 5 is equal to 36" will be; 6(x - 5) = 36
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need help with this :)))))))
Answer:
C
Step-by-step explanation:
For Triangles to be similar, there have to be a corresponding length and angle
In the previous year, at Hub Motors ltd, for a particular model of Mercedes, Nissan and Ford, one could purchase (in million shillings) all three cars for a total of Ksh 150. This year, due to inflation, the same cars would cost Ksh 161. The cost of the Mercedes increased by 8%, the Nissan by 6%, and the Ford by 12%. If the price of last year's Nissan was Ksh 7 less than the price of last year's Mercedes, Use matrix inverse to find the price of each of the three cars last year?
Answer:
Step-by-step explanation:
If 10 milligrams are contained in 2 milliters. how many milligrams are contained in 28 milliliters?
Answer:
28,000 milligrams is your answer
What decimal is 0.77 %
Answer:
0.0077
Step-by-step explanation:
What the answer is please
Answer:its the first one
Step-by-step explanation:
becuase it tells more explanation if you look at the answer or what im saying is problem to make it more simpler.
the x-coordinate is zero and the y-coordinate is positive choose the location
Answer:
(0,5)
Step-by-step explanation:
A positive number is a number higher than 0. The x-coordinate is the first number, and the y coordinate is the second number. Plug in any random positive y coordinate to get your point.
(x,y)
(0,1)
(0,2)
(0,3)
im giving brainliest to who ever needs it
Answer:
heck ya
Step-by-step explanation:
What is the probability of rolling a number greater than 7 on a 6-sided die rolled
68% of what number is 17
Answer:
25
Step-by-step explanation:
We can set up an equation and solve for x (68% of x is 17)
68%*x=17 perform the inverse operation and divide both sides by 68%
dividing both sides by 68% will isolate the x variable
68%*x/68%= 17/68%
x=17/68%
x=25
so, therefore,
68% of 25 is 17
Answer:
[tex]\displaystyle 11\frac{14}{25}[/tex]
Step-by-step explanation:
Whenever you take a percentage of something, you multiply. Turn 68% into a fraction and multiply by 17:
[tex]\displaystyle \frac{289}{25} = [\frac{17}{25}][17] \\ \\ \boxed{11\frac{14}{25}} = \frac{289}{25}[/tex]
I am joyous to assist you at any time.
the domain and range in this graph will be:
a. Domain : all real nums, Range : all real nums
b. Domain : - 4 Range: 2
c. domain: 2 range : 5
Answer:
a.
Step-by-step explanation:
this is a line going from -infinity to +infinity in x and in y direction.
for b or c to be right the function would have to be a single point, as nothing else is valid as value.
-
Find the equation of the line that
is parallel to y = 2x – 7 and
contains the point (-3,6).
Step-by-step explanation:
The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too
2) with the slope and the two points givens, you can find the equation
Y-Y1 = m( X-X1) , Y-6 = 2[(X-(-3)] ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7
Find the surface area of this cubiod
Answer:
surface area is 2(lb + bh + lh)
I think this is the right formula
Answer:
Total surface area = 62 cm^2.
Step-by-step explanation:
There are 2 faces each of area 2 * 3 = 6, = 12 cm^2.
There are 2 faces each of area 10, = 20 cm^2.
There are 2 faces each of area 15, = 30 cm^2.
12 + 20 + 30 = 62 cm^2.
does the graph represent a function?
Answer:
No
Step-by-step explanation:
fails the vertical line test, a test to see if a vertical line can touch 2 points on a graph at the same time.
I have more questions then this
Answer:1-1/3
2-16 in.
3-10.49
4-1/10
Step-by-step explanation:
i hope this helps
Find a formula for the inverse of the following function, if possible.
[tex]P(x) = 3\sqrt[3]{x} - 1[/tex]
[tex]P^{-1}(x) = \\\\[/tex]
or does not have an inverse function
to find the inverse of any expression, we start off by doing a quick variables switcheroo and then solve for "y", so let's do so
[tex]\stackrel{P(x)}{y}~~=~~3\sqrt[3]{x}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ =~~3\sqrt[3]{y}-1}\implies x+1 = 3\sqrt[3]{y}\\\\\\\cfrac{x + 1}{3}=\sqrt[3]{y}\implies \left( \cfrac{x + 1}{3} \right)^3 =y\implies \cfrac{(x+1)^3}{3^3}=y\implies \cfrac{(x+1)^3}{27}=\stackrel{\stackrel{y}{\downarrow }}{P^{-1}(x)}[/tex]
Help, please! You will be extremely smart if you answer this question, and if you do I will give brainliest. The test ends soon please help.
Answer:
B. y=6-1/3t
Step-by-step explanation:
If you graph this equation, it matches the given graph. Hope this helps :)
plz help on a timed test will pay 10 points and make brainlest
What other countries have set up early earthquake warning systems? Which of these countries are in the Ring of Fire? Why is it important for these Ring of Fire countries to have warning systems?
Answer:
Mexico, Japan, South Korea, Taiwan, and the United States, Chile, Japan, the US west coast; Chile, Japan, the US west coast; So all that is left for the people who live around the Ring of Fire is to be aware of the danger, perhaps to live further inland, build safer, earthquake-resistant housing, and for nations everywhere to improve oceanic and land-based early-warning systems to help minimize the risk to life
Step-by-step explanation:
What is 2+100009 it for my homework and I need it done today
Answer:
100011
Step-by-step explanation:
what is 1/2 divided by 75.096868
Answer:
Step-by-step explanation:
Let p=x^2+6. Which equation is equivalent to (x^2 + 6)^2 - 21 = 4x^2 + 24 in terms of p?
Answer:
p^2-4p-21=0
Step-by-step explanation:
Where you see (x^2 + 6) you put in p.
p 2 - 21 = 4 ( x 2 + 6 )
p 2 - 21 = 4p
p 2 - 4p - 21 = 0
:)
Evaluate the expression 5(7 − 4)2 ÷ 3 + 11
Answer:
21
Step-by-step explanation:
5(7-4)*2/3+11
5*3*2/3+11
15*2/3+11
30/3+11
10+11
21
Answer:
21
Step-by-step explanation:
Subtract 4 from 7
5 ⋅ 3 ⋅ 2 ÷ 3 + 11
Multiply 5 by 3.
15 ⋅ 2 ÷ 3 + 11
Multiply 15 by 2.
30 ÷ 3 + 11
Divide 30 by 3.
10 + 11
Add 10 and 11.
21
5. The price for
seedless oranges is $1.55 for the first
pound and $0.75 for each additional pound. Paul Paid $
5.35 to buy sour oranges.
How many pounds of seedless oranges did he buy?
Answer:
5 1/15 lb
Step-by-step explanation:
Equation:
5.35 = 1.55 + 0.75x [tex]\longmapsto\\[/tex] Subtract 1.55 from both sides
3.8 = 0.75x [tex]\longmapsto[/tex] Divide both sides by 0.75
5 1/15 lb
-Chetan K
f(x) = x^3 + 3x^2
What would the graph look like?
Answer: the answer is in the attachment.
Answer:
Hope this helps :)
Step-by-step explanation:
Darryl deposits $1,500 into a savings account that has a simple interest rate of 2.7%.
Lori deposits $1,400 into a savings account that has a simple interest rate of 3.8%.
If no other transactions are made, who will have more money in their account after 10 years? How much more?
Answer:
12
Step-by-step explanation:
Is 26% greater than 3/8?
Answer:
No. It is not greater than 3/8
Step-by-step explanation:
3/8 x 100
=> 300/8
=> 37.5
=> 26% < 37.5%
Therefore, 26% is not greater than 3/8 or 37.5
Hoped this helped.
In a 2004 poll of 500 cell phone users conducted by the Yankee Group, 20% indicated that they had received commercial messages or ads on their cell phones. Is there sufficient evidence to conclude that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of .13 reported for the previous year
Answer:44÷58+44
Step-by-step explanation:
list all the prime numbers between 90 and 100
Im pretty sure the only prime number in between 90 and 100 is 97
Solve the equation.
-9x + 1 = -x + 17
Step-by-step explanation:
-9x + 1 = -x + 17
collect like terms
-9x + x = 17-1
-8x = 16
divide both sides by -8
-8x/-8 = 16/8
x = 2
18
What is the value of y?
3
10
2y + 4
4
5
10 + 2x
6
From the principles of geometry, we can see that the value of y is 3.
Are the opposite sides of a rectangle equal?The lengths of the opposing sides in a rectangle are equal. A rectangle is a quadrilateral with four parallel opposed sides and four right angles (90-degree angles).
In specifically, a rectangle has two sets of equal-length opposite sides. In a rectangle, the lengths of the neighboring sides can vary, but the lengths of the opposing sides are always the same. This feature sets a rectangle apart from other quadrilaterals.
We know that;
10 = 2y + 4
10 - 4 = 2y
y = 6/2
y = 3
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