45 Points!
The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below.
A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and
the Sun.
Answers
Answer:
by using pythagoras theorem
Step-by-step explanation:
the distance between sun and moon is hypoteneous
the distance between earth and sun is perpndicular
and distance between earth and moon is base
we can use,
tanx°=distance betwwen earth and sun/ distance betweenearth and moon
or,
sinx°= distance between earth and sun/ distance between sun and moon
we can use other formulas also same as above 2 examples
Hope ithelps
Answer:
The scientist can use trigonometry to figure out the distance between the Moon and Sun. More specifically, using sine (sin).
Step-by-step explanation:
Label the triangle first.
- x should be theta
- y would be opposite (o) as it is across/opposite from the side where x is
- the distance between the sun and moon would be hypotenuse (h), as it's opposite of the right angle.
The calculation that has o and h in it's formula is sine. The formula looks like :
Sin(Ф) = [tex]\frac{o}{h}[/tex]
To solve for the distance between the Sun and Moon, we plug it into the formula and solve
Sin(x) = [tex]\frac{d}{y}[/tex]
- where d is the distance between the Sun and Moon
hope this helps !! :D
Related Questions
I’m having trouble figuring out how to find the limit of this function algebraically.
Answers
Answer:
Step-by-step explanation:
A circular disc has circumference 250 cm.
Calculate the radius of the disc.
Answers
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=250 \end{cases}\implies 250=2\pi r\implies \cfrac{250}{2\pi }=r\implies \stackrel{cm}{39.79}\approx r[/tex]
The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
Answers
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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Serenity earned a grade of 39% on her multiple choice science final that had a total of
200 problems. How many problems on the final exam did Serenity answer correctly?
Answers
Answer:
78
Step-by-step explanation:
The number of correct problems is found by multiplying the percentage that were correct by the total number of problems.
__
number correct = fraction correct × number of problems
number correct = 0.39 × 200 = 78
Serenity answered 78 problems correctly.
_____
Additional comment
The symbol % is fully equivalent to /100. That is 39% = 39/100 = 0.39 (pronounced "thirty-nine hundredths"). Using a percent symbol is just another way to write a fraction.
find the area and the circumference of a circle with the diameter 6 yards
Answers
Answer:
area = 28.27
circumference = 18.85
Step-by-step explanation:
Using the formulas for area,
A = πr^2
d = 2r
Solving for area,
A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²
Using the formulas for circumference,
C = 2 πr
d = 2r
Solving for circumference,
C = πd = π × 6 ≈ 18.85yd
Julian calculates the volume of a rectangular prism with the dimensions 3/4ft by 4 feet by 1/2 ft. His work is shown here.
What error did Julian make?
He multiplied the numerators incorrectly.
He multiplied the denominators incorrectly.
He simplified 12/6 incorrectly.
He wrote 4 as a fraction incorrectly.
Answers
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
V=LWH
we have
L=3/4 ft
W=5/1 ft
H=1/2
substitute
V=(3/4)(5/1)(1/2)= 3x5x1= 15
₋₋₋₋₋₋₋₋ ₋₋₋₋ ft³
4x1x2= 8
therefore
He multiplied the denominators incorrectly
A point that is exterior to an angle is found on the acute side of the angle. true of false?
Answers
A point that is exterior to an angle is found on the acute side of the angle which is true.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the sum of the exterior angle and interior angle is equal to 180 degrees.
"If one of the exterior angles is an acute angle, then the corresponding interior angle is an obtuse angle."
A point that is exterior to an angle is found on the acute side of the angle which is true.
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What are the domain and range of the function f(x)=x²-2x² -4?
Answers
Answer:
The domain is -∞, ∞
The range is -∞, -4
Step-by-step explanation:
The domain is the data in a set representing the possible real numbers for a function.
The range is the range that this function's result is likely to be in.
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.
please help
Answers
The height and the base area of both the design must be equal. Then the correct option is A.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.
Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.
The figure shows both designs.
The volume of the cylinder will be given as
V = πr² h
If the volume of the oblique cylinder and right cylinder is the same.
Then the height of both the designs must be equal and the base area of both the design must be equal.
Then the correct option is A.
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Answer:
D
Step-by-step explanation:
did the test on edmentum
If a fission reaction yields 4.50×10^9 kJ of energy, then how much mass was lost?
1.50×10^−6 kg
5.00×10^−2 kg
5.00×10^−5 kg
1.50×10^−3 kg
Answers
Answer:
(c) 5.00×10^-5 kg
Step-by-step explanation:
The mass and energy are related by Einstein's formula E = mc².
__
Solving for mass in kg, we find it to be ...
m = E/c² . . . . . . . . where E is in joules, and c is in meters/second
m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg
The lost mass was about 5.00×10^-5 kg.
Answer:
5.00×10^−5 kg
Step-by-step explanation:
I took the test and it was correct! PLEASE LIKE and have a wonderful day!
I need help please anyone ?!!!
Answers
What is the y-intercept for this function?
a
(0, −3)
b
(3, 0)
c
(−9, 0)
d
(0, −9)
Answers
Answer:
d
Step-by-step explanation:
the y- intercept is the point on the y- axis where the graph crosses
the graph crosses the y- axis at point (0, - 9 )
then y- intercept = (0, - 9 )
What is the greatest common factor of 20 and 10?
Answers
Answer:
Step-by-step explanation:
The factors common to 20 and 10 are 1, 5 and 10. The largest of these is 10. That's the GCF of 20 and 10.
If a cylinder has a volume of 120 cm3 and a cone has a volume of 360 cm3, is it possible that the two cones have congruent bases and congruent heights?
Answers
No, the cone and the cylinder can't have congruent heights and bases.
is it possible that the two cones have congruent bases and congruent heights?
The volume of a cylinder of radius R and height H is:
V = pi*R^2*H
And for a cone of radius R and height H is:
V = pi*R^2*H/3
So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.
Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.
This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.
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Please help!!
Explain the difference between using the cosine ratio to solve for a missing angle in a right
triangle versus using the secant ratio. You must use complete sentences and any evidence
needed (such as an example) to prove your point of view.
Answers
In trigonometry, secant in a right triangle, is the reciprocal of the cosine of an angle symbol: sec while cosine is in a right triangle, is the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.
The cosine of an angle is the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle. The cosine of ∠A will be abbreviated as cos ∠A
The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .
Answer:
Step-by-step explanation:
Suppose a right triangle ABC in which
BC=3 units and AC=5 unit and angle B=90 degree
Let x be the missing angle of right triangle
We know that
Hence, there is no difference between using cosine ratio to solve for a missing angle in a right triangle versus using the secant ratio.
Given that the quadrilateral is a parallelogram, find the values of x, y and z.
Answers
Answer:
x=9
y=4
z=4
Step-by-step explanation:
9x-13=7x+5
9x-7x=5+13
2x=18
x=18/2=9
3y=12
y=12/3=4
11z-41=5z-17
11z-5z=-17+41
6z=24
z=24/6=4
A triangle has vertices at (2, 3), (-4, 5), and (-3, 4). What are the coordinates of the vertices
of the image after the translation (x, y) (x + 1, y - 3)?
Answers
[tex](2,3) \longrightarrow (2+1, 3-3)=\boxed{(3,0)}\\(-4,5) \longrightarrow (-4+1, 5-3)=\boxed{(-3, 2)}\\(-3,4) \longrightarrow (-3+1, 4-3)=\boxed{(-2, 1)}[/tex]
An auto weighing 2,000 pounds is on a street inclined at 10° with the horizontal. Find the force necessary to prevent the car from rolling down the hill. (Round your answer to the nearest whole number.)
347 pounds
14,397 pounds
2,462 pounds
Answers
Force (F) = WSin(angle)
F = 2000×Sin(10)
Therefore, F = 347lb.
12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)
Answers
Step-by-Step Explanation:
=> y = -2x + 13 (Eq. 1)
=> 4x + 8y = 20 (Eq. 2)
Substitute value of ‘y’ from Eq. 1 in 2 :-
4x + 8y = 20
4x + 8(-2x + 13) = 20
4x + -16x + 104 = 20
-12x + 104 = 20
-12x = 20 - 104
-12x = -84
12x = 84
x = 84/12
=> x = 7
Substitute value of ‘x’ in Eq. 1 :-
y = -2x + 13
y = -2(7) + 13
y = -14 + 13
=> y = -1
Therefore, x = 7, y = -1 which can be written in an ordered pair as (7,-1).
i needs help with it please
Answers
The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
Meaning of congruent trianglesA triangle can be defined as a plain shape that has three sides and three angles.
Congruent triangles are triangles that satisfy one or more congruence postulates or laws. The triangles could either be similar based on their angles or sides or angles and side being similar.
In conclusion, The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
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Graph f(x)=2^x what is the answer?
Answers
Graph is in attached image.
EASY POINTS
What is the slope-intercept equation of this line?
Answers
Answer:
B
Step-by-step explanation:
The y-intercept is 8
The slope is -2x
Therefore the slope-intercept is y = -2x + 8
This figure is a square, with side lengths as shown.
415 mm
What are the perimeter and the area of the square?
80
200
400
8√5 16√5
32√5
The perimeter of the square is,
The area of the square is_
millimeters.
square millimeters
Answers
The perimeter and area of the square are 16√5 mm and 80 mm²
How to find perimeter and area of a square?Perimeter of a square = 4L
where
l = lengthTherefore,
Perimeter of a square = 4 × 4√5
Perimeter of a square = 16√5 mm
Area of a square = l²
Area of a square = (4√5)²
Area of a square = 16 × 5
Area of a square = 80 mm²
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PLEASE HELP!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!
Classify the expression by the number of terms.
5y^2-8+6y^4
Answers
Answer:
5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.
Step-by-step explanation: Also pls answer by question
Lila invested 10000 in one of long life insurance company annuity contracts. When issued, the contract was paying a 5 percent rate of return
Answers
The kind of annuity does Lila own is: variable immediate annuity.
What is variable immediate annuity?Variable immediate annuity can be defined as the type of annuity that vary or fluctuate based on the type of investment you choose or pick.
In this type of annuity the payment you will receive will not be fixed reason being that payments that will made to you will always increase or decrease.
Therefore the kind of annuity does Lila own is: variable immediate annuity.
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9 less than the sum of x and y
Answers
If we need to turn this into a mathematical expression:
Answer: (x + y) - 9
Step-by-step explanation:
9 less than the sum of x and y
(the sum of x and y) - 9
(x + y) - 9
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What is the median of the data set?
16, 21, 28, 30, 40, 45, 54, 58
A. 58
Β. 35
C. 10
D. 19
Answers
Answer:
I think 10 is the answer it's not sure.
please help! acellus
find the missing side of this right triangle.
30
3
x
x= [?]
Answers
Answer:
The number that belongs in the green box is equal to 909.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
a = 30
b = 3
c = x
Step 2: Find x
Let's solve for the general equation that allows us to find the hypotenuse:
[Pythagorean Theorem] Square root both sides [Equality Property]:[tex]\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}[/tex]
Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:
[Equation] Substitute in variables:[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}[/tex]Evaluate:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}[/tex]
∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.
___
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___
Topic: Trigonometry
EGG DROP The physics class is holding an egg drop competition. The formula h= −16t2+h0 can be used to approximate the number of seconds, t, it will take for the eggs to reach height, h, from an initial height of h0 in feet.
Find the time it takes an egg to reach the ground if it is dropped from an initial height of 40 feet. Round to the nearest hundredth, if necessary.
Answers
By solving a quadratic equation we will see that the egg will hit the ground after 1.58 seconds.
How long will take the egg to reach the ground?
Here we know that the initial height of the egg is 40ft, so the equation for the height will be:
[tex]h(t) = -16*t^2 + 40[/tex]
The egg will hit the ground when h(t) = 0, so we need to solve the quadratic equation:
[tex]h(t) = -16*t^2 + 40 = 0\\\\16t^2 = 40\\\\t^2 = 40/16\\\\t = \sqrt{40/16} = 1.58[/tex]
This means that the egg will hit the ground after 1.58 seconds.
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the width of a rectangular prism is 7cm, height is 5cm and length is 13 cm. find the volume
Answers
7 x 5 x 13 = 455
The volume of the given rectangular prism.
Solution:[tex]\huge\boxed{Formula: lwh}[/tex]
To find the the volume we'll have to multiply the height, width and length.
[tex]V=\: 13×7×5 [/tex]
[tex]\large\boxed{V= \:455\: {cm}^{3}}[/tex]
Therefore, the volume of the given rectangular prism is 455 cubic centimeters.