the radius of Earth is 6400 km. the distance of the moon from the Earth's surface is 380000 km. find the radius of the moon which subtends an angle of 20'at the centre of the earth
Answers
Answer:
1100 km
Step-by-step explanation:
The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface. Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.
Draw circle representing the moon and earth. Draw tangent lines from the earth's center to the edge of the moon. The angle between these lines is the subtended angle. Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects. Notice this forms a right angle.
(See attached diagram)
Using trigonometry:
sin(θ/2) = r / (R + h)
r = (R + h) sin(θ/2)
Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:
r = (6400 + 380000) sin(1/6 °)
r = 1100
The moon's radius is 1100 km.
Related Questions
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9 - 1)(3)?
Answers
Answer:
(g − f) ( 3 ) = 23
Step-by-step explanation:
( g − f ) ( x ) = g ( x ) − f ( x )
= 6 x − ( 4 − x 2 )
= x 2 + 6 x − 4
to evaluate ( g - f ) ( 3 ) substitute x = 3 into ( g − f ) ( x )
( g − f ) = ( 3 ) 2 + ( 6 x 3 ) - 4 =23
For this case we have the following functions:
[tex]f (x) = 4-x ^ 2\\g (x) = 6x[/tex]
By definition we have to:
[tex](f-g) (x) = f (x) -g (x)\\(g-f) (x) = g (x) -f (x)[/tex]
Then, we find [tex](f-g) (x):[/tex]
[tex]f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4[/tex]
We evaluate the function in 3:
[tex](f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23[/tex]
Now we find[tex](g-f) (x):[/tex]
[tex]g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4[/tex]
We evaluate the function in 3
[tex](g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23[/tex]
Answer:
[tex](f-g) (3) = - 23\\(g-f) (3) = 23[/tex]
the sum of four consecutive odd integers is -72. What is the value of the four intergers
Answers
Answer:
let the integers be x, x+2, x+4 and x+6
therefore,
x + x+2 + x+4 + x+6 = -72
=> 4x + 12 = -72
=> 4x = -72 - 12
=> x = -84/4
=> x = -21
therefore the integers are: -21, -19, -17, -15
[tex]\huge\boxed{\text{-21, -19, -17, -15}}[/tex]
Represent this mathematically. [tex]x+(x+2)+(x+4)+(x+6)=-72[/tex]
Combine like terms. [tex]4x+12=-72[/tex]
Subtract 12 from both sides. [tex]4x=-84[/tex]
Divide both sides by 4. [tex]x=-21[/tex]
Find the numbers by adding 2 each time. [tex]-21, -19, -17, -15[/tex]
Francis teaches the piano. He charges each student an enrollment fee of $100 plus $15 per hour of piano lessons. The average cost of lessons for a
student per hour is $25
If h represents the number of hours a student spends in lessons, which equation can be used to find the value of h?
Answers
Answer:
The first one should be right. Since the teacher is charging $15 per hour of the piano lesson then it can't be any of the answers of $100h. The answer can't be C, the third one, since you're adding the enrollment fee to the cost of every piano lesson it would be wrong to subtract the $100. Hope that helps!
Step-by-step explanation:
The answer will the answer on the top $25=$100+$15h over h
Answer: The number of hours is 10 hours.
Step-by-step explanation:
Since we have given that
Average cost of lessons = $25
let h be the number of hours a student spends in lessons.
Since each student has fee of $100 plus $15 per hour.
So, According to question, it becomes,
[tex]25=\dfrac{100+15h}{h}\\\\25h=100+15h\\\\25h-15h=100\\\\10h=100\\\\h=\dfrac{100}{10}\\\\h=10[/tex]
Hence, the number of hours is 10 hours.
I need dire help, I'm almost done with summer school!
A store owner tracks the number of online orders she receives each week since the start of a new advertising campaign and graphs the data.
Use the graph to select the true statement about the function that models the given situation.
A. The function is linear and is growing by equal differences over equal intervals.
B. the function is exponential and is growing by equal percentages over equal intervals .
C. the function is exponential and is growing by equal differences over equal intervals
D. the function is linear and is growing by equal percentages over equal intervals
Answers
Answer:
A. The function is linear and is growing by equal differences over equal intervals.
Answer:
A. The function is linear and is growing by equal differences over equal intervals.
Step-by-step explanation:
As you can see in the graph, the function is linear since if draw a line that conects the dots, the graph would turnout linear, and as you can see it is growing 100 orders every 2 weeks, so it is growing by equal differences, over equal intervals.
hat is the approximate area of the circle shown below?
A. 60 in 2
B. 119 in 2
c. 4536 in 2
d. 1134 in 2
Help Me Please!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
d. 1134 inches squared
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi r^2[/tex]
where r is the radius.
You are given r=19 here so replace r in [tex]\pi r^2[/tex] with 19 giving us:
[tex]\pi (19)^2[/tex]
Then it is to the calculator we go:
1134 inches squared
10x^3 y^-5 z^-2 if x=3 y=2 and z=5 express your answer as a reduced fraction
Answers
Answer:
[tex]\large\boxed{\dfrac{27}{80}}[/tex]
Step-by-step explanation:
Put x = 3, y = 2 and z = 5 to the given expression [tex]10x^3y^{-5}z^{-2}[/tex]:
[tex]10(3^3)(2^{-5})(5^{-2})\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{10(27)}{(2^5)(5^2)}=\dfrac{270}{(32)(25)}=\dfrac{270}{800}=\dfrac{27}{80}[/tex]
A football team started at the line of scrimmage. On the first play of the drive, the team lost 4 yards. On the second play of the drive, the team gained 45 yards. Taylor calculated |–4 – 45| = |–49| = 49, and said that the team gained a total of 49 yards on the two plays. Which best describes Taylor’s error?
A. Taylor did not find the correct distance between –4 and 45.
B. Taylor did not make an error. The team gained a total of 49 yards on the two plays.
C. Taylor correctly found the distance between –4 and 45, but this number represents the team’s total loss, not the team’s total gain.
D. Taylor correctly found the distance between –4 and 45, but this number represents the total distance the team moved in both directions, not the team’s total gain.
Answers
Answer:
D. Taylor correctly found the distance between –4 and 45, but this number represents the total distance the team moved in both directions, not the team’s total gain.
Step-by-step explanation:
The team only ended up gaining the 45 yards on the second play and had gained -4 on the first play. 45-4≠49, but the total distance between -4 and 45 is 49.
Answer:
D.
Step-by-step explanation:
factor the trinomial below. 4x^2+23-6. which two binomials are factors of the trinomial
Answers
Answer:
4x - 1 and x + 6 are the factors of given Trinomial
Step-by-step explanation:
The given Trinomial is:
[tex]4x^{2}+23x-6[/tex]
We can factorize this trinomial by mid-term splitting. The mid-term(23x) can be split up in two terms (24x and -x) such that their sum is 23x and their product(-24x²) is equal to the product of other two terms (4x² and -6)
So, the above expression can be written as:
[tex]4x^{2}+23x-6\\\\ =4x^{2}+24x-x-6\\\\\text{Taking out commons, we get}\\\\=4x(x+6)-1(x+6)\\\\ =(4x-1)(x+6)[/tex]
Therefore, 4x - 1 and x + 6 are the factors of given Trinomial
Answer: 4x-1 and x+6
Step-by-step explanation: a p e x
Linda is twice the age of Vera.
Tanya is four less than four times the age of Linda.
Their total age is two more than nine times the age of Vera.
How old is Tanya?
Answers
Answer:
Tanya is 20 years old
Step-by-step explanation:
Let the age of Vera = x years
The age of Linda is twice the age of Vera = 2x years
Tanya is four less than four times the age of Linda = 4(2x)-4 = 8x-4
Total age of Vera, Linda and Tanya is:
x+2x+8x-4
Combine the like terms:
11x-4
But now their total age is two more than nine times the age of Vera:
11x-4 = 9x+2
Solve the expression
Combine the like terms:
11x-9x=2+4
2x=6
Divide both the sides by 2
2x/2 = 6/2
x= 3
Thus the age of Vera is 3 years.
The age of Linda is 2x= 2*3 = 6 years
The age of Tanya is 8x-4 = 8*3 - 4 = 24-4 = 20years....
What is the median of this data set?
22, 37, 49, 15, 82
O
<
A. 37
O B. 27
O C. 31
O D. 41
Answers
Answer:
A. 37
Step by step explanation:
The median is the middle value with high to low frequency and low to high frequency. How to determine the median is to sort the numbers from the smallest to the big number and the largest number to the smallest number, then count using two hands (one finger left hand and one finger right hand).
Method:
22, 37, 49, 15, 82 then sorted: 82, 49, 37, 22, 15 means the median is 37
-----------------------✨ Awesome ✨-----------------------The median of this data set is 49.
Option A is correct.
What is Median of the Data?The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. Given a small data set, count the number of data points (n) and arrange them in increasing order.
We have the data: 22, 37, 49, 15, 82
Now, arranging the data in Ascending order as
15, 22, 37, 49, 82
Now, the median is the middle term of the data.
Here there are 5 terms.
So, the median of data is 37.
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What is each power of i with its multiplicative inverse.
1. i
2. i ^2
3. i ^3
4. i ^4
Answers
Answer:
1) multiplicative inverse of i = -i
2) Multiplicative inverse of i^2 = -1
3) Multiplicative inverse of i^3 = i
4) Multiplicative inverse of i^4 = 1
Step-by-step explanation:
We have to find multiplicative inverse of each of the following.
1) i
The multiplicative inverse is 1/i
if i is in the denominator we find their conjugate
[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]
So, multiplicative inverse of i = -i
2) i^2
The multiplicative inverse is 1/i^2
We know that i^2 = -1
1/-1 = -1
so, Multiplicative inverse of i^2 = -1
3) i^3
The multiplicative inverse is 1/i^3
We know that i^2 = -1
and i^3 = i.i^2
[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]
so, Multiplicative inverse of i^3 = i
4) i^4
The multiplicative inverse is 1/i^4
We know that i^2 = -1
and i^4 = i^2.i^2
[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]
so, Multiplicative inverse of i^4 = 1
Find the missing value in the pair of similar polygons.
Answers
The scale factor is 2.25.
The segments shown below could form a triangle.
Answers
Answer:
True
Step-by-step explanation:
Answer:
The answer is false.
Step-by-step explanation:
Given line segments are :
AC = 9
CB = 8
AB = 17
As per the triangle inequality theorem the sum of any 2 sides should be greater than the third side. This should be true to all the three combinations.
[tex]AC+CB>AB[/tex] => [tex]9+8>17[/tex] => [tex]17>17[/tex] (not true)
[tex]AC+AB>CB[/tex] => [tex]9+17>8[/tex] => [tex]26>8[/tex] ( true)
[tex]AB+CB>AC[/tex] => [tex]17+8>9[/tex] => [tex]25>9[/tex] (true)
As we can see only two conditions are fulfilled not the third one, so the triangle cannot be formed.
The answer is false.
The perpendicular bisector of a chord...
Answers
Choices A and C are both true statements.
But C is trivial. It's CALLED a perpendicular "bisector" of the chord, so OF COURSE it bisects the chord ... otherwise it would be silly to CALL it a "bisector".
The choice that's surprising but true is A .
The perpendicular bisector of a chord passes through the center of the circle.
What is a chord?A chord in plane geometry is a line segment that connects two points on a curve. A line segment whose endpoints are on a circle is frequently described using this phrase. A cycle chord of a graph cycle is an edge that is not in and whose endpoints are in, according to graph theory, which also uses the phrase.
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The description below represents Function A and the table represents Function B:
Function A
The function is 2 more than 5 times x.
Function B
x y
−1 2
0 5
1 8
Which statement is correct about the slope and intercept of the two functions?
A) Their slopes are equal but y-intercepts are not equal.
B) Their slopes are not equal but y-intercepts are equal.
C) Both slopes and y-intercepts are equal.
D) Neither slopes nor y-intercepts are equal.
Answers
Answer:
D is correct
Step-by-step explanation:
Step 1 : Find equation of function A in y = mx + c
2 more than 5 times x
f(x) = 2 + 5x or y = 5x + 2
Step 2 : Identify slope and y-intercept of function A
y = mx + c
y = 2 + 5x
Slope = m = 5
Y-intercept = c = 2
Step 3 : Find the equation of function B in y = mx + c
From my understanding, the number given in the question are coordinates
(-1, 2) , (0, 5) , (1, 8)
Slope = y2-y1/x2-x1
Lets take two coordinates : (-1, 2) , (0, 5)
Slope = 5-2/0-(-1)
Slope = 3/1 = 3
For y-intercept
Lets take (1, 8)
y = mx + c
8 = 3(1) + c
c = 5
The equation is f(x) = 3x + 5 or y = 3x + 5
Step 4 : Lets write both equations with their slope and y-intercept and check with the statements
y = 5x + 2
y = 3x + 5
A) Their slopes are equal but y-intercepts are not equal. Incorrect
B) Their slopes are not equal but y-intercepts are equal. Incorrect
C) Both slopes and y-intercepts are equal. Incorrect
D) Neither slopes nor y-intercepts are equal. Correct
!!
The equation of a line is 3x + 8y - 16 = 0.
What is the slope and y-intercept?
slope =?
y intercept =?
Help confused !
Answers
3x+8y=16
8y=16-3x
Y= (16-3x)/8
Y= 2-3/8x
The y intercept is 2 and the slope is -3/8.
Hope this helps!
x³-64 in prime factored form
Answers
[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \qquad \qquad a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-64\implies x^3-4^3\implies (x-4)(x^2+4x+4^2)\implies (x-4)(x^2+4x+16)[/tex]
Amanda owns a clothing store that sells graphic t-shirts. n is the number of shirts she sells each month. the revenue function of her store is r = 15n. the cost function of her store is c = 9n + 450. using your calculator, what is the break-even point of amanda's store?
Answers
Answer:
The break- even point is attained when n=75
Step-by-step explanation:
The break-even point is defined as the point where revenue is equal to cost.
We take the equation for revenue r=15n, and set it equal to the equation c=9n+450
15n=9n+450
Subtract 9n from both sides:
6n=450
Divide both sides by 6.
6n/6=450/6
n=75
The break- even point is attained when n=75....
Final answer:
To determine Amanda's store's break-even point, set the revenue equal to the cost function and solve for n to find 75 shirts.
Explanation:
To find the break-even point of Amanda's store:
Set the revenue function equal to the cost function: 15n = 9n + 450
Solve for n: n = 75
Therefore, the break-even point is when Amanda sells 75 graphic t-shirts.
Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5 y = -3/4x - 3 y = -3/4x + 3 y = 4/3x + 2/3 y = 4/3x - 34/3
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope.
===========================================
We have the equation of the line: [tex]y=-\dfrac{3}{4}x-5[/tex]
The slope is [tex]m=-\dfrac{3}{4}[/tex].
Put the value of the slope and the coordinates of the point (4, -6) to an equation of a line:
[tex]-6=-\dfrac{3}{4}(4)+b[/tex]
[tex]-6=-3+b[/tex] add 3 to both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=-\dfrac{3}{4}x-3[/tex]
Ronalds furniture house is currently making 50 sofas in a day. How many sofas will be produced if prudction is to be increased by 150%
Answers
Answer:
125
Step-by-step explanation:
50 x 150% = 75
75 + 50 = 125
Answer:
125
Step-by-step explanation:
50 × 150% = 50 × 1.5 = 75
75 + 50 = 125
125 sofas is the answer
Evaluate the expression -66/(-3)+(-4)-(-5)
Answers
Answer:
-21
Step-by-step explanation:
For this case we must evaluate the following expression:
[tex]\frac {-66} {(- 3)} + (- 4) - (- 5) =[/tex]
We solve the division:
[tex]22 + (- 4) - (- 5) =[/tex]
We eliminate parentheses keeping in mind that:
[tex]+ * - = -\\- * - = +[/tex]
So:
[tex]22-4 + 5 =[/tex]
Different signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:
[tex]18 + 5 =\\23[/tex]
Answer:
23
rewrite square root of -49 -4 in complex number notation please help
Answers
Note that if [tex]i^2=-1[/tex] than [tex]i=\sqrt{-1}[/tex],
Also note that [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
So we have,
[tex]\sqrt{-49}=\sqrt{-1}\sqrt{49}=\boxed{7i}[/tex]
and,
[tex]\sqrt{-4}=\sqrt{-1}\sqrt{4}=\boxed{2i}[/tex]
Hope this helps.
r3t40
A train can hold 78 passengers. The train starts out empty and picks up one passenger at the first stop,2 passengers at the second stop,3 passengers at the third stop,and so forth. After how many stops will the train be full.
Answers
Answer:
After the 12th Stop
Step-by-step explanation:
2nd stop 1+2=3
3rd 3+3=6
4th 6+4=10
5th 10+5=15
6th 15+6=21
7th 21+7=28
8th 28+8=36
9th 36+9=45
10th 45+10=55
11th 55+11=66
12th 66+12=78
After the 12th stop.
The train will be full after 12 full stops. If we include the 13th stop, the train would exceed its capacity. Therefore, the train can handle 12 full stops if it picks one passenger at the first stop and increases the number of passengers picked by one at each stop.
Explanation:The problem you're describing is a summation problem in mathematics. You're incrementing the number of passengers at each stop starting at one and increasing by one each time. This can be summed up using the formula for the sum of the first n positive integers (including one), which is n*(n+1)/2. To find out after how many stops the train will be full, you'll need to solve this formula for n such that this sum is less than or equal to 78 (the capacity of the train). You can do this by substitution or by solving the quadratic equation, n² + n - 156 = 0. The result is roughly 12.421, which means that after 12 full stops, the train will have 78 passengers (since we can't have a fraction of a stop). After the 13th stop, the train will exceed its capacity.
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simplify -(x+5) + 3x completely
Answers
Answer:2x-5
Step-by-step explanation:-(x+5)+3x
-x-5+3x=(3x-x) -5
=2x-5
Y’all what do i write
Answers
Answer:
y = - 0.5x + 4
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-4}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - 0.5
Note the line crosses the y- axis at (0, 4) ⇒ c = 4
y = - 0.5x + 4 ← equation of boundary line
Answer:
y = -0.5 x + 4.
Step-by-step explanation:
Slope-intercept form of the equation of a line on a Cartesian Plane:
[tex]y = mx + b[/tex].
[tex]m[/tex] is the slope of the line.
If two different points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] on the line are given, the slope of the line will equal
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
For this line, the two points are:
[tex](4,2)[/tex], and [tex](0, 4)[/tex].As a result,
[tex]\displaystyle m = \frac{2 - 4}{4 - 0} = - \frac{1}{2}[/tex].
[tex]b[/tex] is the [tex]y[/tex]-coordinate (the second coordinate) of the point at the intersection of the line and the [tex]y[/tex]-axis (the vertical axis.) The [tex]x[/tex]-coordinate (the first coordinate) of that point shall equals [tex]0[/tex]. For this line, the coordinates of the intersection is [tex](0, 4)[/tex]. As a result, [tex]b = 4[/tex].
The slope-intercept form of the equation of this line will thus be
[tex]\displaystyle y = -\frac{1}{2}x + 4[/tex].
what is an irrational number that is between 5.2 and 5.5.
Answers
Answer:
The irrational number could be √30
Step-by-step explanation:
An irrational number is a number which can not be written as a ratio between two numbers and it can not be written as a simple fraction. In simple words we can not write it in p/q form.
Find an irrational number that is between 5.2 and 5.5.
Mostly irrational numbers are square root numbers.
So square the both numbers.
(5.2)^2 (5.5)^2.
27.04 , 30.25
It means that the number is between 27.04 and 30.25
We will pick number 30
Square root 30
√30 = 5.48
The irrational number could be √30
It is 5.48 to the hundredth....
I need help with #17 please and thank you!
Answers
The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –1 k = 1 k = 2.5
Answers
Answer:
k= - 2.5
Step-by-step explanation:
If the graph is the attached picture then according to this:
The graph is in V- shape. So if the corners of the graph are not at (0,0) than there must be a constant.
k is the constant which means that it is the amount the function is vertically shifted. The graph is shifted 2.5 units down, therefore the value of k is -2.5.
Thus option 1 is correct....
Which fraction is not equivalent to 5/6?
A-15/18
B-20/30
C-10/12
D-30/36
Answers
Answer: B. 20/30
Step-by-step explanation: 20/30 simplified to 2/3. Multiply each number by 2 to get 4/6. 4/6 is not the same number as 5/6.
Answer:
B. 20/30
Step-by-step explanation:
i need help with question 2. i think my answer is incorrect.
Answers
Answer:
395
You are 100% right! You go!
Step-by-step explanation:
We are given f(x)=5x^2-2x+8 and are asked to find the value of the function at x=9.
So replace x with (9):
f(9)=5(9)^2-2(9)+8
f(9)=5(81)-18+8 I did the exponent 9^2 and 2(9) in this step:
f(9)=405-18+8 I did 5(81) in this step
f(9)=405-10 I did -18+8 in this step
f(9)=395