Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, drepresents the distance from a star to the Sun. Using a technique called "stellar parallax," astronomers determined 0 is 0.00001389 degrees.
write an expression to calculate d for any star
Answers
By calculating the distance of a star to the Sun, astronomers can calculate the distance from Earth to the star.
[tex]\displaystyle \mathrm{The \ \mathbf{expression} \ to \ calculate \ \mathit{d} \ for \ any \ \mathbf{star} \ is; \ \underline{d \ is \ \frac{1 \, AU}{tan(\theta)}}}[/tex]Reasons
The given parameters are;
The distance from the star to the Sun = d
The angle formed by the ray to the Sun and the ray to Earth from the star, θ = 0.00001389 degrees
The average distance from Earth to the Sun = 1 AU
By trigonometric ratios, we have;
[tex]\displaystyle tan(\theta) = \mathbf{\frac{Opposite}{Adjacent}}[/tex]
Therefore;
[tex]\displaystyle tan(\theta) = \frac{1}{d}[/tex]
The expression to calculate for d for any star is therefore;
[tex]\displaystyle \underline{ d \ is \ \frac{1 \, AU}{tan(\theta) }}[/tex]The angle given for θ for the referenced star is θ = 0.00001389
Therefore;
[tex]\displaystyle d = \frac{1 \, AU}{tan(0.00001389^{\circ}) } \approx 4,124,966.13 \, AU[/tex]
Learn more about trigonometric ratio here:
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Related Questions
Anna and Sam each want to run for president of their school's student body council. In order
to do so, they must collect a certain number of signatures and get a nomination. So far, Anna
has 20 signatures, and Sam has 25. Anna is collecting signatures at an average rate of 6 per
day, whereas Sam is averaging 5 signatures every day. Assuming that their rate of collection
stays the same, eventually the two will have collected the same number of signatures. How
long will that take?
Time
elapsed
Write a system of equations, graph them, and type the solution.
Answers
Answer:
6x+20=5x+25
5 days
Step-by-step explanation:
Let x = the days that they have the same amount of signatures
We know Anna has 20 currently and gets 6 per day, so we can use y=mx+b to describe her linear relationship.
We also know that Sam has 25 and gets 5 per day, so we can again use y=mx+b to describe his linear relationship.
Since both equations equal the variable y, we can say they equal each other and set up 6x+20=5x+25.
Then you subtract 20 from both sides and subtract 5x, so you are left with x =5, or 5 days until they have the same amount of signatures
Hope this made sense :D
I need correct answer for this
Answers
Answer:
should be 82%
Step-by-step explanation:
Hope this helps!
Answer:
82%
Step-by-step explanation:
percents are out of 100, so its just multiplied by two
Please help me…………….
Answers
Answer:
Isosceles triangle.
Step-by-step explanation:
6 × 2 = ?
5 - 3 = ?
~~~~~~~~~~~
Hi i'm from Indonesian
Answers
Answer:
12
2
answer
hope it helps
Hazel bought 3/5 of a kilogram of clay for the students in her pottery class. She then divided the clay evenly into pieces that were 1/5 of a kilogram. Into how many pieces did Hazel divide the clay? Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
3
Step-by-step explanation:
3/5 kg of clay are divided into 1/5 a kilogram, so how many times is 1/5 in 3/5?
equation is
[tex]=\frac{3}{5} /\frac{1}{5}\\\\=\frac{3}{5}*\frac{5}{1} \\\\=\frac{15}{5} \\=3[/tex]
Solve: x ÷ 0.6 = 8.9
5.34
9.5
8.3
0.07
Answers
Answer:
5.34
Step-by-step explanation:
x = 8.9 X 0.6
x = 5.34
Your welcome :)
1. Which of the following is equivalent to x5/2?
1
(1)
5x
2
(3) Vr
2x
(2)
(4) Vx?
Answers
Given that the expression in the question is [tex]\displaystyle x^{\frac{5}{2} }[/tex], the equivalent expression
can be found using the rules of indices.
[tex]\displaystyle \underline{x^{\frac{5}{2} } \ is \ equivalent \ to \ x^2 \cdot\sqrt{x}}[/tex]Reasons:
The given expression is [tex]\displaystyle x^{\frac{5}{2} }[/tex]
Required:
To find the equivalent expression
Solution:
According to the rules of indices, we have;
[tex]a^{n + m} = a^n \times a^m[/tex]
[tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
Therefore, the above expression can be expanded as follows;
[tex]\displaystyle x^{\frac{5}{2} } = x ^{2.5} = \mathbf{x^{2 + 0.5}}[/tex]
[tex]\displaystyle x^{2 + 0.5} =\mathbf{ x^2 \times x^{0.5}}[/tex]
Which gives;
[tex]\displaystyle x^2 \times x^{0.5} = \mathbf{x^2 \times \sqrt{x}}[/tex]
Therefore;
[tex]\displaystyle x^{\frac{5}{2} } \equiv x^2 \cdot\sqrt{x}[/tex], which is the form [tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
[tex]\underline{An \ expression \ \mathbf{equivalent} \ to \ x^\frac{5}{2} \ is \ x^2 \cdot \sqrt{x}}[/tex]
Learn more about the rules of indices here:
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Whats the answer to this question?
Answers
Answer:
Try -4
Sorry if it's incorrect.
Step-by-step explanation:
Answer:
[3, -1]
Step-by-step explanation:
The computation is performed element by element, as you appear to have figured.
2f -g = 2[4, 1] -[5, 3] = [2·4 -5, 2·1 -3] = [8-5, 2-3]
2f -g = [3, -1]
f(x) = -x^3+8x^2-15x
Domain:
Range: R
Rel. Maximum: X=3
Rel. Minimum(s): X2
End Behavior:
As x, f(x)
As x, f(x)
Incr. Intervals:
Zeros
Decr. Intervals
Answers
That's all I got hope it helps
Solve for W
4w^2+9w= -2
Answers
Answer:
[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]
Step-by-step explanation:
[tex]4w^2+9w=-2[/tex]
[tex]4w^2+9w+2=0[/tex]
[tex]w^2+9w+8=0[/tex]
[tex](w+1)(w+8)=0[/tex]
[tex](4w+1)(w+2)=0[/tex]
[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]
Use an area model to find the quotient: 132 ÷ 3 = ________.
Answers
Answer:
44
Step-by-step explanation:
A local store buys used video games. For each game bought, they will pay $18 less than the original price paid for the game. Which expressions represent the total amount Jordan will receive if he sells n games that originally cost d dollars each? Select two options.
d (n minus 18)
n (d minus 18)
d + n minus 18
d n minus 18 n
18 n minus d n
Answers
Answer:
d
Step-by-step explanation:
I already did this before
Answer:
it B and D
Step-by-step explanation:
You use a juice mix to make orange juice.
You combine 12 ounces of the mix with 36 ounces of water.
What is a unit rate that describes your juice?
Mr. and Mrs. Ozawa are driving their family to a vacation spot 496 miles away. They want to get there in 8 hours. What is the average speed they need to drive?
Answers
Answer:
1. Ounces
2. 62 miles per hour
Step-by-step explanation:
1. 12 OUNCES and 36 OUNCES
2. 496/8 = 62 (check 62x8 = 496)
Calculate the distance between the points M=(-1, -2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answers
Answer:
nearest hundredth 8.944
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.944
I NEED HELP ASAP. PLEASE AND THANK YOU
Answers
Answer:
1, 2, and 5
Step-by-step explanation:
What are the steps to convert a number from standard notation to scientific notation
Answers
Answer:
Step-by-step explanation:
Let's take 4200 as an example.
To convert 4200 into scientific notation, follow these steps:
- Move the decimal 3 times to left in the number so that the resulting number, m = 4.2, is greater than or equal to 1 but less than 10
- Since we moved the decimal to the left the exponent n is positive
n = 3
- Write in the scientific notation form, m × 10^n
= 4.2 × 10^3
Therefore, the decimal number 4200 written in scientific notation is 4.2 × 10^3 and it has 2 significant figures.
Could anyone help out? It's 11pm and I have finals tmrw :/
For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). 3 P(x) = 5x? - 2x2 – 3x+ 3; - 4
Answers
There i hope it help
Stay safe and study hard
Find the solution set of each inequality below, and then determine which inequalities have the same
solution set as -(-8x – 3) < 23. Select all that apply.
A
1
(8x + 3) < -23
B
(10x =
- 20) >-44
1
(8x + 3) >-23
(10
(10x +20) >44
E
(8x + 3) < 23
F-crx
(10x +20) < -44
+
Answers
Answer:
(8x+3)<23 is the same as -(-8x-3)<23
Step-by-step explanation:
-(-8x-3)<23 Original equation
(8x+3)<23 [Remove the parentheses]
It is the same equation as the chosen answer: (8x+3)<23
Answer:
Choice E.
Step-by-step explanation:
-(-8x – 3) < 23
-8x - 3 > -23
-8x > -20
x < 20/8
x < 2.5.
E:-
(8x + 3) < 23
8x < 20
x < 2.5.
A patio measures 120 cm long and 70 cm wide. If a tile measures25 cm. How many tiles will be needed to cover the patio?
Answers
Answer:
So, multiply 120 by 70 cm for the area which is 8,400. Divide that by 25 cm which would be 336. That would be your final answer. (A tip for these problems is to draw it because it makes it easier sometimes.)
Thanks Mark As Brainlist
9+3x=18-6x find for x
Answers
Answer:
Hiya There!!!
_________________________
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
_________________________
“The harder you fall, the heavier your heart; the heavier your heart, the stronger you climb; the stronger you climb, the higher your pedestal.”
― Criss Jami, Killosophy
_________________________
Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!! ~Ashlynn
what comes after this:
2:4
4:8
8:10
_:_
Hint: Times two (x2) if you answer right then you shall get 30 points which is half of mine
You answer it you get 15 points so answer away
Answers
Answer:
16:20??
Lol I think it's wrong sorry.
Step-by-step explanation:
HELP ME PLEASE I DONT KNOW HOW TO DO THIS
Answers
Answer:
Step-by-step explanation:
x = 1 - 1
how to find the circumcenter of a triangle with given vertices
Answers
Answer:
What is the formula of area of Circumcircle?
Image result
We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.
Step-by-step explanation:
What starts with a p has a t in the middle and has an R at the end that has 12 letters that is for ur body
Note: its not any subject for school and its not anything for school so ignore the mathematics subject thing.
Answers
Answer:
Pronator??
Step-by-step explanation:
Find the area of each figure
Answers
Answer:
54
Step-by-step explanation:
.5*9*12
Explanation ~
B•h/2
9•12=108
108/2=54
:)
Factor 2x^2 - 4x - 30 =0 ( divide by 2 first!)
Answers
Answer:
Let's apply the quadratic formula:
⇒
x
=
−
4
±
√
4
2
−
4
(
2
)
(
−
30
)
2
(
2
)
⇒
x
=
−
4
±
√
16
+
240
4
⇒
x
=
−
4
±
√
256
4
⇒
x
=
−
4
±
16
4
⇒
x
=
−
1
±
4
⇒
x
=
−
5
,
3
Therefore, the solutions to the equation are
x
=
−
5
and
x
=
3
.
.
Step-by-step explanation:
Explanation:
All the terms in the equation are even, so we can divide by 2 immediately to make the numbers smaller.
2
x
2
+
4
x
−
30
=
0
x
2
+
2
x
−
15
=
0
Try to factor before we use loner methods of the quadratic formula or completing the square.
Find factors of 15 which subtract (because of -15) to give 2.
The signs will be different (because of -15), there must be more positives. (because of +2)
5 and 3 will work!
5
×
3
=
15
and
5
−
3
=
2
(
x
+
5
)
(
x
−
3
)
=
0
Putting each factor equal to 0 gives the solutions:
x
=
−
5
or
x
=
3
Answer:
(x+3)(x-5)
Step-by-step explanation:
2x²-4x-30 = 0
devide by 2
; x²-2x-15 = 0
(x+3)(x-5) = 0
please help me asap
ty
Answers
Answer:
y = -4x
Step-by-step explanation:
Subtract 8x both sides
2y = 0 + (-8x)
Divide by 2 both sides
y = -4x
A car travels 220 miles in 3 hours 20 minutes. What is its average speed?
Answers
Answer:
66 miles per hour
Step-by-step explanation:
average speed = distance / time
distance : 220 miles
time : 3 hours 20 minutes or 3.33 hours
220 miles / 3.33 hours = 66 miles per hour
How do I do this problem? We’ve been learning this recently and there’s a test we have on Thursday And I’m still not quite sure how to do these types of problems
Answers
Answer:
I have a test on thursday toooooooo
Step-by-step explanation:
what is 90 degrees plus 39 degrees plus 7x+16