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]
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Related Questions
Translate and solve. The quotient of m and 6/7 is 5/6
Answers
Answer:
m / 6/7 = 5/6
m = 35
Step-by-step explanation:
Answer:
m = 5/7Step-by-step explanation:
The quotient of m and 6/7 is 5/6:
m ÷ 6/7 = 5/6m = 5/6 × 6/7m = 5/7Solve the system of equations
X=11+y
2x+y=19
Answers
Answer:
Step-by-step explanation:
To solve this system of equations, let's first find the value y. We can replace the x in the second equation with 11 + y, since we are told in the first equation that x is equal to 11 + y. So, let's replace x:
2(11 + y) + y = 19
22 + 2y + y = 19
22 + 3y = 19
3y = -3
y = -1
And look at that - we've found our y-value! Now, we can replace the y in the first equation with -1 to find the value of x.
x = 11 + (-1)
x = 10
So, the solution to this system of equations is (10, -1). Hopefully that's helpful!
Last year, the ratio of the ages of Mel and her friend is 3:4. Next year, the ratio will be 4:5. Form two simultaneous equations using the information above, and solve them by using the elimination method. Hence find their ages now.
Answers
Answer:
Above is the answer, coupled with detailed step-by-step explanations. Thank you!
A car slows down at -5.00 m/s2 until it comes to a stop after traveling 15.0 m. How much time did it take to stop.
Answers
Answer:
2.45 seconds to the nearest hundredth.
Step-by-step explanation:
Acceleration a = -5, distance s = 15, time = ?.
Final velocity = v = 0.
We need to use the equations of motion under constant acceleration.
v^2 = u^2 + 2as where u is the initial velocity
0 = u^2 + 2*-5*15
u^2 = 150
so u = √150
Now we use v = u + at:
0 = √150 - 5t
t = √150/5
t = 2.45 seconds.
The domain of function f is (-00, 6) U (6,00). The value of the function approaches -o as x approaches -00, and approaches oo. Which function could be function ?
Answers
Answer:
a
Step-by-step explanation:
The function is [tex]F(x) = \dfrac{x+6}{x-6}[/tex]. Option C is correct.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The value of the function approaches -∞ as x approaches -∞ is,
[tex]F(x) = \dfrac{x+6}{x-6}[/tex]
The graph of the function is attached with the answer which is showing the approach of the function in the x-y plane.
Therefore, the function is [tex]F(x) = \dfrac{x+6}{x-6}[/tex]. Option C is correct.
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the triangle has a right angle at the middle letter.
In AABC, Ĉ = 40°, BC = 4 cm. Find AB.
Answers
.839=ab/4
Ab=3.36cm
BRO SOMEONE PLSS HELP ME
Write the inequality that represents the possible values for x
Answers
Answer:
6x + 12 < 10
Step-by-step explanation:
The side 10 is greater than 6x+12
If the measure of base angle ABC is 75 , what is m
Answers
The sum of the angles of any triangle is 180°.
75° + 75° + m<BAC = 180°
m<BAC = 180° - (75° + 75°) = 30°
|2x +4| = 12; =
Can someone else me solve this please
Answers
[tex]|2x+4| = 12\\\\\implies 2x +4 = 12 ~~ \text{or}~~ 2x +4 = -12\\\\\implies 2x = 8 ~~ \text{or}~~ 2x = -16\\\\\implies x = 4 ~~ \text{or} ~~ x = -8[/tex]
Can someone please explain this to me
Answers
Answer:
The answer is 4
Step-by-step explanation:
because add 4 then divided by 4
Samir sold 4 of his old Star Leaper video games at Trading Post Game Shop. Before he left, he spent $23.65 of his earnings on a controller. Samir had $6.35 remaining.
Which equation can you use to find the amount of money, v, Samir received for each video game? Also, can you solve for v?
Answers
The equation you can use to find the amount of money, v, Samir received for each video game is;
4v - 23.65 = 6.35 and v = $7.5
Algebraic word problemsSamir sold 4 oh his old star leaper video games.
He spent $23.65 of his earnings on a controller and has $6.35 left.If the amount received for each video game is v, the total cost of the 4 video games is; 4v
He spent $23.65 out of 4v and is left with $6.35Thus, this equation is;
4v - 23.65 = 6.35
Solving this gives;
v = $7.5
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5 What rate of interest is paid on a deposit of $2000 which earns $400
interest in 5 years?
Answers
Answer:
4%
Step-by-step explanation:
Given
I = 400P = 2000R = ?T = 5 yearsFormula
I = PRTSolving.
I = PRT400 = 2,000 × R × 5400 = 10,000 × R400 / 10,000 = R0.04 = RChange 0.04 to percent
0.04 × 100 = 4%Answer:
4%Solve for “x.”
9x = 912.6
Answers
Answer:
If it's not what You are looking for type in the equation solver your own ... is 12 percent of 912.6 - step by step solution || 2x-9=2x-9 || 2(x-3)=4(x+2) ...
Step-by-step explanation:
sorry if im wrong
Anna and Hannah are reading the same book. At the beginning of the month, Anna was on page 29 and Hannah was on page 7. Anna will read 9 pages per day and Hannah will read 11 pages per day. Let
A
A represent the page of the book that Anna is on at the end of
t
t days into the month, and let
H
H represent the page of the book that Hannah is on at the end of
t
t days into the month. Write an equation for each situation, in terms of
t
,
t, and determine whether Anna or Hannah is farther along in the book after 14 days.
Answers
Answer:
Hannah
Step-by-step explanation:
Anna: Page 29 + number of pages read t days into the month
number of pages read t days in the month = 9 t times = 9 * t
Anna: 29 + 9t
Hannah: 7 + 11t using the same logic
14 days in: t = 14
Anna: 29 + 9*14 = 155
Hannah: 7 + 11 * 14 = 161
Hannah is further along
The equations for Anna's progress A = 29 + 9t and Hannah's progress H = 7 + 11t show that after 14 days, Hannah is farther along in the book with page 161 compared to Anna's page 155.
How to Apply Algebraic Equation?The equation we would write for each situation in terms of t are explained below:
For Anna:
A = 29 + 9t
For Hannah:
H = 7 + 11t
After 14 days:
For Anna: A = 29 + 9 * 14 = 29 + 126 = 155
For Hannah: H = 7 + 11 * 14 = 7 + 154 = 161
After 14 days, Hannah is farther along in the book as she is on page 161 while Anna is on page 155.
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Which sign makes this number sentence true?
|-56|___ 1561
A)>
B)<
C)=
D) X
Answers
The absolute value of -56 is 56
the new sentence is 56____1561
A is not true because 56 is not bigger then 1561 if you count and put on number line
B is very true if you look at A. 56 is smaller than 1516
So, the answer is a
I hope this helped if it's wrong, plz blame me.
Ps.Brainlist would help a lot
Answer:
B
Step-by-step explanation:
The | | around -56 means absolute value or the total of the number, which in this case is 56, therefore 56 is less than 1561.
Solve for b.
2/3+5=20-b
Answers
emliy is thinking of a number which she calls n she find 1/4 of the number and then subtracts 3. write an expressions that represents emlily number.
Answers
Answer:
1/4 n - 3.
Hope this helps, sorry if it doesn't.
write a polynomial function in standard form with the given zeros x=1,-1,-2
Answers
Answer:
y = x³ +2x² -x -2
Step-by-step explanation:
A polynomial with root q has a factor (x -q). The factored form of the polynomial is ...
y = (x -1)(x +1)(x +2)
y = (x² -1)(x +2) . . . . . . partial simplification
y = x³ +2x² -x -2
How to solve this question?
Answers
Answer: -3
Step-by-step explanation:
The axis of symettry is basically what cuts the parabola perfectly in half. In this case draw a horizontal line right through -3 on the x-axis
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
A parabola's axis of symmetry is located at the line [tex]x=h[/tex] and essentially divides the parabola in half. The vertex is [tex](-3,4)[/tex] so the axis of symmetry is located at the line [tex]x=-3[/tex]
find mLABC
is from Big Ideas
Answers
Answer: 50
Step-by-step explanation: add DBC and ABD to get 50 ABC is 50
Use the information to answer the question.
A crew is loading crates onto a train. They can load 4 crates every 1.25 minutes. Each crate weighs 160 pounds.
C
=
At that rate, how many minutes would it take the crew to load crates with a total weight of 2400 pounds? Round the answer to the nearest
tenth. Enter the answer in the box.
minutes
Plz help me no links
Answers
Answer:
4.7
Step-by-step explanation:
2400/160 =15 crates
4/1.25=3.2 crates a minute
15/3.2=4.68 minutes
4.7 because it rounds up
To load 2400 pounds of crates crew will take around 4.69 minutes.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given,
Crew can load 4 crates every 1.25 minutes
4 creates ⇔ 1.25 minutes
Given,
1 crate = 160 pounds
So,
4 crate = 640 pounds
So,
640 pounds ⇔ 1.25 minutes
1 pound ⇔ 1.25/640 minutes
To load 2400 pounds
2400 pounds ⇔(1.25/640)2400 minutes
2400 pounds ⇔ 4.6875 minutes.
Hence " To load 2400 pounds of crates crew will take around 4.69 minutes".
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Which mathematical statement represents “17 more than a number is 26”?
17 greater-than 26
n + 17 = 26
17 less-than 26
26 + n = 17
Answers
Answer:
n + 17 = 26
Step-by-step explanation:
Let's replace the sentence with mathematical terms:
17 more than a number is 26
More than means addition. The answer will also be a sum.
17 + a number is 26
Since the number is not specified, it will be represented by a variable. In this instance, the variable is n.
17 + n is 26
The equal sign will replace the word "is".
17 + n = 26
Now, we can use the associative property of addition.
17 + n = 26 into n + 17 = 26
Which mathematical statement represents “17 more than a number is 26”?
Answer:
n + 17 = 26
Step-by-step explanation:
17 more than a number means that you are adding 17 to a number (n) to equal 26.
If you take 17 away from each side you get n = 9
9 + 17 = 26 is a true statement so the equation is correct.
Forty three fence posts are placed one yard apart. How many yards of fence is this?
Answers
Answer:
86
Step-by-step explanation:
43 x 2=86
If s(x)=x-7 and t(x)=4x^2-x+3, which expression is equivalent to (t x s) (x)
Answers
4x^3-x^2+3x-28x^2+7x-21
4x^3-29x^2+10x-21
Can someone please help me with number 49? :D ty!
Answers
Answer:
The answer is 4.5 cups I hope this helps :D
the distance between the points (-4, -3) and (-8, 6) to the nearest whole number.
Answers
Answer:
X1=-4,Y1=-3,X2=-8,Y2=6
=√(X2-X1)^2+(Y2-Y1)^2
=√(-8-(-4))^2+(6-(-3))^2
=√(-4)^2+(9)^2
=√(16+81)
=√97units
helpppppppppppppppppp
Answers
Answer:
IP information is attached to each packet, and this information helps routers to send packets to the right place. Every device or domain that connects to the Internet is assigned an IP address, and as packets are directed to the IP address attached to them, data arrives where it is needed.
Step-by-step explanation:
hope i helped!
#2: Find the value of X. (GEOMETRY)
I will give brainliest to BEST answer! fake answers will be reported.
refer to attachment!
Answers
===========================================================
Explanation:
Refer to the remote interior angle theorem (some books call it the exterior angle theorem). That says we can add the two interior angles and the sum is the exterior angle that is not adjacent to either interior angle.
(interiorAngle1) + (interiorAngle2) = exterior angle
(5x) + (2x+6) = 8x-11
7x+6 = 8x-11
6+11 = 8x-7x
17 = x
x = 17
----------------
Or the slightly longer method has you follow these steps:
y = missing interior angle in the upper right corner
The angle (8x-11) and angle y are supplementary
(8x-11) + (y) = 180
y = 180-(8x-11)
y = 180-8x+11
y = -8x+191
For any triangle, the three interior angles always add to 180
(angle1)+(angle2)+(angle3) = 180
(5x)+(2x+6)+(-8x+191) = 180
-x+197 = 180
-x = 180-197
-x = -17
x = 17
Pls help! Will mark Branliest!! 50 points for whoever answers!!!!!!
Answers
Answer: See below
Step-by-step explanation:
Isolate x for x-2y+2z=9
3x=9+2y
[tex]x=\frac{9+2y}{3}[/tex]....(1)
Substitute (1) into the 2nd equation
[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]
[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]
7y=-3
y=-3/7
Substitute y=-3/7
[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]
[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]
Isolate z by substituting it
[tex]3z+\frac{53}{7}=16[/tex]
[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]
[tex]z=\frac{59}{21}[/tex]
For x =9+2y/3 substitute z=59/21 and y=-3/7
[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]
[tex]x=\frac{19}{7}[/tex]
[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]
Answer:
(1, - 1, 3 )
Step-by-step explanation:
x - 2y + 2z = 9 → (1)
- x + 3y = - 4 → (2)
2x - 5y + 3z = 16 → (3)
Add (1) and (2) term by term to eliminate x
y + 2z = 5 → (4)
Multiply (2) by 2
- 2x + 6y = - 8 → (5)
Add (3) and (5) term by term to eliminate x
y + 3z = 8 → (6)
Subtract (6) from (4) term by term to eliminate y
- z = - 3 ( multiply both sides by - 1 )
z = 3
Substitute z = 3 into (4)
y + 2(3) = 5
y + 6 = 5 ( subtract 6 from both sides )
y = - 1
Substitute y = - 1, z = 3 into (1) and solve for x
x - 2(- 1) + 2(3) = 9
x + 2 + 6 = 9
x + 8 = 9 ( subtract 8 from both sides )
x = 1
solution is (1, - 1, 3 )
i don't know the answer to log4(x+6)=2
Answers
Answer:
10
Step-by-step explanation:
log4(x+6)=2
x+6=4²
x=4²-6
x=10
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
[tex]log_4(x+6)=2[/tex]
[tex]4^{log_4(x+6)}=4^2[/tex]
[tex]x+6=16[/tex]
[tex]x=10[/tex]
Remember that logarithmic functions are the inverses of exponential functions. Therefore, we raise the base of the logarithm to the logarithm to undo the operation.