Please help!!!


A shooting star forms a right triangle with the Earth and the Sun, as shown below: A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg 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 Sun and the shooting star. (10 points)

 Please Help!!!A Shooting Star Forms A Right Triangle With The Earth And The Sun, As Shown Below: A Right

Answers

Answer 1

Answer:

 - The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

 You can observe in the figure attached that  "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°,  the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

 This is:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC[/tex]

Therefore, the scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] , and solve for the distance between the Sun and the shooting star "AC":

[tex]cos(x\°)=\frac{y}{AC}[/tex]

[tex]AC=\frac{y}{cos(x\°)}[/tex]

Answer 2

The scientist can use the two measurements by applying the knowledge of trigonometry, particularly Cosine (cos).

[tex]cos x = \frac{adjacent (y)}{hypotenuse (AC)}[/tex]

AC = [tex]\frac{y}{cos x}[/tex]

where the distance between the shooting star and the sun is AC

and the distance between Earth and Sun is BC = y

the right angled triangle has three sides

Hypotenuse (hyp): longest sideOpposite (opp): the side facing the angle of interestAdjacent (adj): the remaining side

cosine (θ) = [tex]\frac{adj}{hyp}[/tex]

sine (θ) = [tex]\frac{opp}{hyp}[/tex]

tan (θ) = [tex]\frac{opp}{adj}[/tex]

where (θ) =  angle of interest

What is trigonometry?

This is the branch of mathematics that is concerned with angles of triangles as well as the length of it's sides.

Read more on trigonometry: https://brainly.com/question/24349828


Related Questions

what is x in -2-3x=19

Answers

Answer:

x=-7

Step-by-step explanation:

Since you are solving for x, you need to work backwards. Add 2 to both sides: -2 and 2 cancel out, and 19 plus 2 is 21. Isolate the x by dividing both sides by -3. -3 cancels out, and 21 divided by -3 is -7.

Answer:

-7

Step-by-step explanation

−2−3x=19

−2+−3x=19

−3x−2=19

Step 2: Add 2 to both sides.

−3x−2+2=19+2

−3x=21

Step 3: Divide both sides by -3.

−3x

−3

=

21

−3

x=−7

Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?

Answers

Answer:

Step-by-step explanation:

You don't say whether this is compound interest or simple interest.

I will assume it's compounding that interests you.

The appropriate formula is

A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount.  Thus:

A = $1000·(1 + 0.05)^t, or  A = $1000·(1.05)^t

Please note:  There were apparently possible answer choices.  Next time, please be sure to list such choices.  Thank you.

Final answer:

The equation modeling the value of an investment, V, after t years, for an initial investment of $1,000 at a 5% annual interest rate is V = 1000(1 + 0.05)^t, incorporating the principles of compounding interest.

Explanation:

The question asks about the equation modeling the value of an investment, V, after t years, given an initial investment of $1,000 at a 5% annual interest rate. Using the formula for the future value of a single sum, V = P(1 + r)^t, where P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), and t is the number of years, we can determine that the equation modeling the value of the investment is V = 1000(1 + 0.05)^t. This formula is applied to calculate the future value of the investment, taking into account the compounding interest over a period t years.

Which choice is equivalent to the expression below? square root of negative 20​

Answers

Answer:

B

Step-by-step explanation:

The expression can be written as

[tex]\sqrt{-20}[/tex]

The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression

[tex]2i\sqrt{5}[/tex]

Answer:

Correct option is:

B

Step-by-step explanation:

We have to find a expression which is similar to:

[tex]\sqrt{-20}[/tex]

Now we start solving

[tex]\sqrt{-20}[/tex] could also be written as:

[tex]\sqrt{-2\times 2\times 5}[/tex]

When we take - sign out of the square root it becomes i

i.e. [tex]\sqrt{-1}=i[/tex]

And there are two 2's inside the square root when we take square root it becomes 2

Hence, [tex]\sqrt{-20}=2i\sqrt{5}[/tex]

Hence, Correct option is:

B

Quadrilateral ABCD is inscribed in a circle with m<A = (x2)°, m<B = (7x - 10)°,
and
m<C = (3x)°.
What is m<D?

Answers

Answer:

106°

Step-by-step explanation:

A quadrilateral inside a circle is a cyclic quadrilateral.

It means that the angles opposite are supplementary (add up to 180).

If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.

Since we know A and C, we can write:

A + C = 180

x^2 + 3x = 180

x^2 +3x - 180 = 0

(x+15)(x-12) = 0

x= -15, or x = 12

Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.

Now finding B:

B = 7x - 10

B = 7(12) - 10

B = 74

We also know that B + D = 180, so:

B + D = 180

74 + D = 180

D = 180 - 74 = 106

The formula gives the height of an object in free fall at time t and acceleration g.

[tex]h = \frac{1}{2}gt^{2} [/tex]

Solve for t.
[tex]t = (2gh)^{2} [/tex]
[tex]t = 2 \sqrt{gh} [/tex]
[tex]t = \frac{ \sqrt{gh} }{2} [/tex]
[tex]t = \frac{ \sqrt{2hg} }{g} [/tex]

Answers

t must equal √2h/g but I don't see that in the choices above

Answer:

t=2hg√g

Step-by-step explanation:

took the test!

what’s the MAD of 7 20 9 35 12 15 7 10 20 25

Answers

Answer:

Population size:10

Mean (μ): 16

Mean Absolute Deviation (MAD): 7.2

Step-by-step explanation:

Mean absolute deviation (MAD) Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. ... Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.

ABC or d? I really need help and CANNOT get this wrong

Answers

Answer:

1.A. X6Y5

Step-by-step explanation:

Remove the Parenthesis calculate the product

#2 I have no clue on that one.

So sorry but I simply forgot to answer your questions.

The answer to question 1 is A.

The answer to question 2 is D.

There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel are added to the mound. Two orders of 900 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,500 pounds of gravel. Write the equation that best describes the situation.

Answers

Answer:

The equation that best describes the situation is:

[tex]g +400 -1800 = 1,500[/tex]

Step-by-step explanation:

The initial amount of gravel is g.

[tex]g[/tex]

Then we know that 400 pounds are added

[tex]g +400[/tex]

Two orders of 900 pounds are sold and the gravel is removed from the mound. This is:

[tex]g +400 -2 * 900[/tex]

[tex]g +400 -1800[/tex]

At the end of the day, the mound has 1,500 pounds of serious. This is:

[tex]g +400 -1800 = 1,500[/tex]

The equation that best describes the situation is:

[tex]g +400 -1800 = 1,500[/tex]

And

[tex]g= 1500 +1800 - 400\\\\g=2900[/tex]

The equation that best describes the given situation is[tex]\rm g + 400 - (2\times 900) = 1500[/tex]  and this can be determined by forming the linear equation with the help of given data.

Given :

Throughout the day, 400 pounds of gravel are added to the mound.Two orders of 900 pounds are sold and the gravel is removed from the mound.At the end of the day, the mound has 1,500 pounds of gravel.

Let the initial amount of gravel be 'g'. Then after the addition of 400 pounds of gravel, the total gravel becomes:

= g + 400

Given that two orders of 900 pounds are sold and the gravel is removed from the mound so, the total gravel now becomes:

[tex]\rm = g + 400 - (2\times 900)[/tex]

= g + 400 - 1800

= g - 1400

At the end of the day, the mound has 1,500 pounds of gravel, that is:

g - 1400 = 1500

g = 1500 + 1400

g = 2900

Therefore, the equation that best describe the given situation is:

g + 400 - 1800 = 1500

For more information, refer to the link given below:

https://brainly.com/question/19770987

What is the volume of the pyramid 7x7x8

Answers

Answer:

The volume of the pyramid is [tex]130\frac{2}{3}\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

Find the area of the base B

In this problem we have a square base

[tex]B=7^{2} =49\ units^{2}[/tex]

we have

[tex]H=8\ units[/tex]

substitute

[tex]V=\frac{1}{3}(49)(8)=\frac{392}{3}\ units^{3}[/tex]

Convert to mixed number

[tex]\frac{392}{3}=\frac{390}{3}+\frac{2}{3}=130\frac{2}{3}\ units^{3}[/tex]

you do length x width x be aight divided by 3 to get 392/3

A dog on intravenous fluids has received 40% of the 1000 mL initially in the i.v. bag. How many mL has it received?

Answers

Answer:

The dog should receive 400 mL of the i.v. bag.

Step-by-step explanation:

40% x 1000 = 400

Answer:

The dog received 400mL

Step-by-step explanation:

Givens

A dog received 40% of 100 mL of intravenous fluids.

To know how many mL the dog received, we just need to find the 40% of 100 mL.

We know that 40% equals 0.40, then we multiply it

[tex]0.40(1000mL)=400mL[/tex]

Therefore, the dog received 400mL

need helpppppp thank you!!

Answers

Answer:

I would say 50%

Step-by-step explanation:

The answer is 50%. Hope that helps!

Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?

Answers

Answer:

Step-by-step explanation: a is adjacent, b is opposite, c is the hypotenuse

Answer:

D

Step-by-step explanation:

Help me please will give 14 points

Answers

First, set up a proportional fraction.

[tex]\frac{5 sec}{30 gallons}[/tex] = [tex]\frac{x sec}{1gallon}[/tex]

Cross multiply

5 * 1 = 5

30 * x = 30x

So,

30x = 5

Divide 5 by 30

x = 5 / 30

x = 1 / 6 or 0.17

Do the same thing to find for 17 gallons.

30x = 85

x = 85 / 30

x = 17 / 6 or 2.8

Find all solutions of the equation in the interval [0, 2 pi) 2 cos0-1=0

Answers

Answer:

θ = π/3, 5π/3

Step-by-step explanation:

2 cos θ - 1 = 0

2 cos θ = 1

cos θ = 1/2

θ = π/3, 5π/3

ANSWER

EXPLANATION

The given trigonometric equation is:

[tex]2 \cos( \theta) - 1 = 0[/tex]

[tex] \implies \: 2 \cos( \theta) = 1[/tex]

[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]

The cosine ratio is positive in the first and fourth quadrants.

In the first quadrant,

[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]

[tex]\theta = \frac{\pi}{3} [/tex]

In the fourth quadrant,

[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]

[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]

[tex]\theta = \frac{5\pi}{3} [/tex]

Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:

[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]

What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46?

Answers

Answer:

z = 19

Step-by-step explanation:

Given

2(4z - 9 - 7) = 166 - 46 ← simplify both sides

2(4z - 16) = 120 ← distribute parenthesis on left side

8z - 32 = 120 ( add 32 to both sides )

8z = 152 ( divide both sides by 8 )

z = 19

Answer:

z = 19.

Step-by-step explanation:

2(4z − 9 − 7) = 166 − 46

 2(4z − 9 − 7) = 120

Divide both sides by 2:

4z − 9 − 7 = 60

4z = 76

z = 19.

Plz help me with this

Answers

Answer:  D) at least 6mm

Step-by-step explanation:

95% confidence is 2 standard deviations.

5mm + 2(0.5) = 5 + 1 = 6

The oysters must be at least 6 mm

the diameter of a bicycle wheel is 0.7 meters. find the number of complete revolutions made by the wheel if the bicycle travels 440 meters. use 22/7 as an approximation for [tex]\pi[/tex]

Answers

Final answer:

To calculate the number of complete revolutions a bicycle wheel makes after traveling 440 meters, we find the wheel's circumference using its diameter and then divide the travel distance by the circumference. With a diameter of 0.7 meters and using 22/7 as an approximation for π, the wheel's circumference is 2.2 meters. The wheel makes 200 complete revolutions to cover 440 meters.

Explanation:

Finding the Number of Complete Revolutions

To find the number of complete revolutions made by a bicycle wheel when the bicycle travels a certain distance, we firstly need to calculate the circumference of the wheel. The circumference 'C' of a circle can be found using the formula C = πd, where π (Pi) is a constant (approximately 22/7 or 3.14) and 'd' is the diameter of the circle. In this case, we are given that the diameter of the bicycle wheel is 0.7 meters.

Using the approximation for π of 22/7 and the given diameter, the circumference is: C = π × d = (22/7) × 0.7 meters = 2.2 meters.

To find the number of complete revolutions 'N', we divide the total distance the bicycle travels by the circumference of the wheel: N = total distance / circumference = 440 meters / 2.2 meters. So, the number of complete revolutions the wheel makes is 200.

Suppose you deal three cards from a regular deck of 52 cards. What is the probability that they will all be jacks?

Answers

Answer:

Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Step-by-step explanation:

It is given that you deal three cards from a regular deck which contains 52 cards.

We are to find the probability of getting all three Jack cards.

We know that there are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

3 chances of jacks out of 52 cards

A roll of fabric was 120 inches long. A customer bought 2 feet of the fabric.
How many feet of fabric were remaining?
(Hint: 1 foot = 12 inches)
OA. 12
OB. 7
OC. 118
OD.8

Answers

the correct answer is OB. 7.


A tourist has planned a trip to cover the distance of 640 miles, driving at some constant speed. However, when he already covered a quarter of the distance, he took a rest for 1.2 hours. Then, in order to arrive at the destination on time, he increased the speed by 20 mph. How long, actually, the trip lasted?

Answers

Answer:

The trip lasted for a total of 8 hours.

Step-by-step explanation:

Distance planned = S = 640 miles

Constant speed = V

Thus the time to be taken would be = T = V/S

We have an equation 640 = VT ----- eq (a)

Time For First Quarter = T/4

speed = V

Distance = 640/4 = 160

After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.

So, the remaining distance = 640 - 160 = 480 miles.

Speed = V + 20 mph

Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours

We have an equation for remaining distance s = vt

=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)

using eq (a), we have V = 640/T. Putting it in eq (b), we have:

[tex]480 = (\frac{640}{T} + 20)(3\frac{T}{4} - 1.2)\\480 = 480 - \frac{768}{T}  + 15T - 24\\=> 15T - \frac{768}{T} -24 = 0\\=> 15T^{2} - 24T - 768 = 0\\[/tex]

Solving the equation, we get T = 8 or T = -32/5(which is not possible.

So, the right answer is T = 8 hours

A principal of $3300 is invested at 8.5% interest, compounded anually. How much will the investment be worth after 11 years? Round your answer to the nearest dollar. Please help..

Answers

Answer:

[tex]\boxed{\$8378}[/tex]

Step-by-step explanation:

The formula for compound interest is:

A = P(1 + r)ⁿ

Data:

    P = 3300

APR = 8.5 %

     t = 11 yr

Calculations:

n = 11 × 12 = 132

r = 0.085/12 = 0.007 083

A = 3300(1 + 0.007 083)¹³²

  = 3300 × 1.007 083¹³²

  = 3300 × 2.5539

  = 8378

[tex]\text{The investment will be worth }\boxed{\mathbf{\$8378}}[/tex]

When Joe got out of bed, it was 58 in his room. He turned on the heater, and the temperature warmed up to 67 in five minutes. How many degrees per minute did the temperature rise?

Answers

Answer: 1.8

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

(67 degrees - 58 degrees) / 5 minutes

1.8 degrees per minute

solve for b. -1/3b = 9​

Answers

Answer:

B=-27

Step-by-step explanation:

Answer:

-27

-1/3b=9

Divide both sides by -1/3 to get b by itself

-1/3b=9

/-1/3 /-1/3

b=-27

what is x in 25-3x=40

Answers

Step 1: Subtract 25 to both sides. This will cancel 25 on the left side and bring it over to the right

(25 - 25) - 3x = 40 - 25

(0) - 3x = 15

-3x = 15

Step 2: Isolate x by dividing -3 to both sides (the opposite of multiplication is division).

-3x ÷ (-3) = 15 ÷ (-3)

x = -5

Check:

25 - 3(-5) = 40

25 + 15 = 40

40 = 40 ....................................Correct!

Hope this helped!

The value of x in this equation is -5.

What is an equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.

Equation given in the question:

25 - 3x = 40

25 - 40 = 3x

-15 = 3x

x = -5

The value of x in this equation is -5.

Learn more about equations on:

https://brainly.com/question/2972832

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Please help and thank you

Answers

Answer:

A

Step-by-step explanation:

Define each of the terms.

f(x) is the total level of radioactivity.

x is the total number of weeks.

[tex]\frac{1}{2}[/tex] is the weekly decay factor.

30 is the initial level of radioactivity.

Express 0.6239 as a fraction.

Answers

The answer is 6239/10000.

The value of 0.6239 as a fraction or proportion is

A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:

1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.

2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.

Multiply and divide 0.6239 by 10000,

0.6239 = [tex]\frac{0.6239}{10000} \times[/tex] 10000

            = [tex]\frac{6239}{10000}[/tex].

Learn more about fractions here:

https://brainly.com/question/10354322

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Really need help with this!!!

Answers

Answer:

Principal Amount= $500

Formula for compound interest:

[tex]A = p (1 + \frac{r}{n} )^{nt}[/tex]

Formula for simple interest:

A = p(1 + r(t) )

Apply the distributive property to factor out the greatest common factor.
30+42=

Answers

Answer:

[tex]30+42=6(5+7)[/tex]

Step-by-step explanation:

Let [tex]a,b,c\in \mathbb R[/tex], according to the distributive property:

[tex]a(b+c)=ab+ac[/tex]

The prime factorization of 30 is

[tex]30=2\cdot 3\cdot 5[/tex]

The prime factorization of 42 is

[tex]42=2\cdot 3\cdot 7[/tex]

The Greatest common factor is [tex]2\times 3=6[/tex]

[tex]\implies 30+42=6\times5+6\times7[/tex]

[tex]\implies 30+42=6(5+7)[/tex]

Answer:

Step-by-step explanation:

6(5+7

21/35 in simplest form.

Answers

The answer would be 0.6 if you divide 21/35.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To simplify divide the numerator/denominator by the highest common factor of 21 and 35, that is 7

[tex]\frac{21}{35}[/tex] = [tex]\frac{3}{5}[/tex] ← in simplest form

which equation can you use to solve for x​

Answers

As for a specific equation, I could not say. However, I can tell you how to find x!

The first thing to remember is that a straight line has a 180 degree angle.

You see on the bottom side that we have a 146 degree angle. Now look at the top side. Look closely, and you will see that the two sides are actually identical!

Don't see it? Look at the line on top between x and 56, and imagine it is not there. You see that we actually have the same 146 degree angle, just flipped right side up!

However, this angle does not say 146, but makes an extra line between them with x and 56. This means that x + 56 equals 146!

So we can find x by subtracting 56, from 146, which is... 90!

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