The equation t^3=a^2 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?

Answers

Answer 1

Answer:

     2√2

Step-by-step explanation:

We can find the relationship of interest by solving the given equation for A, the mean distance.

Solve for A

  [tex]T^3=A^2\\\\A=\sqrt{T^3}=T\sqrt{T}\qquad\text{take the square root}[/tex]

Substitute values

The mean distance of planet X is found in terms of its period to be ...

  [tex]D_x=T_x\sqrt{T_x}[/tex]

The mean distance of planet Y can be found using the given relation ...

  [tex]T_y=2T_x\\\\D_y=T_y\sqrt{T_y}=2T_x\sqrt{2T_x}=(2\sqrt{2})T_x\sqrt{T_x}\\\\D_y=2\sqrt{2}\cdot D_x[/tex]

The mean distance of planet Y is increased from that of planet X by the factor ...

  2√2


Related Questions

Can you please find x?

Answers

Answer:

x=7

Step-by-step explanation:

The angle of a straight line is 180 degrees, so let's just say the other angle to the right of 15x+34 is "a" that means that 15x + 34 + A = 180, and since the sum of interior angles of a triangle is 180 degrees, that means that 29 + A + 12x + 26 = 180, and we can define A using this equation in terms of x.

Original equation (sum of interior angles)

A + 29 + 12x + 26 = 180

Combine like terms

A + 12x + 55 = 180

Subtract 12x and 55 from both sides

A = -12x + 125

Original equation (since a line is 180 degrees)

15x + 34 + A = 180

Substitute -12x + 125 as A

15x + 34 + (-12x + 125) = 180

Combine like terms

3x + 159 = 180

Subtract 159 from both sides

3x = 21

Divide both sides by 3

x = 7

how do u multiply 1x100000000000000000000000000000??

Answers

By using mind ig -,-

Hope Helpful ~

Answer:

by using 1 to multiply the first digit that is, ‘1’ and repeating the rest of the zeros, so it will be 1 x 1 = 1. So, since the answer we got from multiplying the first digit is ‘1’ , then you’ll repeat the zeros after the answer we got from the multiplication.

So, therefore the answer will be; 100,000,000,000,000,000,000,000,000,000 .

Simplify this expression.
2√5 (13+√2)
O 2√65+2√10
O 2√5 +2√7
O26√65 +2√10
O 26√5 +2√10

Answers

Answer:

The solution for the expression is choice D 265 +210

Step-by-step explanation:

Hello!

First, apply distributive law: a(b+c)= ab+ac

2√5(13+√2) ....given expression 2√5.13 +2√5.√2...multiply the numbers2.13=26√5.√2=√1026√5 +2√10

Charlize accidentally omitted two consecutive integers when adding the elements of the arithmetic sequence, $\{1, 2, 3, \ldots, n\}$. If the sum she obtained is $241$, what is the smallest possible value of $n$

Answers

The smallest possible value of N is 23.

According to the statement

we have given that the sequence {1,2,3.....n}

and the sum is 241. we have to find the smallest value of n.

So, for this purpose we use summation formula of an arithmetic sequence

Sn = n /2 ( a1 +an )

Put the values in it then.

Note that the sum of the first 21 integers  is   21 * 22 /2  =  231...this isn't large enough as compare to given value.

And the sum of the first  22 integers  =   22 * 23 / 2  =   253

So    253 - 241  =  12 = omitted sum.....  

but  the sum of two consecutive integers must be odd

And......the sum of the first 23 integers is  23 * 24 / 2  = 276

So.......276 - 241   =  35    = omitted sum

So....the   consecutive integers omitted must be  17  and 18

So....... the smallest value of n  is   23

So, The smallest possible value of N is 23.

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A 393939-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at 101010 meters per minute. At a certain instant, the bottom of the ladder is 363636 meters from the wall. What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)

Answers

The rate at which the distance between the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

Given length of ladder 39 m and the rate at which the wall is increasing is 101, the bottom of the ladder is 36 m from the wall.

Let bottom is x and the length of wall be y.

We have to find the rate at which the distance between the top of the ladder and the ground at that instant.

we have to find dy/dt.

We have to apply pythagoras theorem first.

[tex]x^{2} +y^{2} =39^{2}[/tex]---------------1

[tex]x^{2} +y^{2} =1521[/tex]

put the value of x=36 in the above equation

[tex]36^{2} +y^{2} =1521[/tex]

[tex]y^{2} =225[/tex]

y=15 m

We have to find the derivative of equation 1 with respect to t.

2x*dx/dt+2y*dy/dt=0

Because it is given that bottom is increasing at 101 meters per minute so dx/dt=101

2x*101+2y*dy/dt=0

put the value of y=15

2x*101+2*15*dy/dt=0

2x*101+2*15*dy/dt=0

dy/dt=-3030/2*36

dy/dt=-42.08

Hence the rate at which the rate at which the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

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Question is wrong so it includes ladder length be 39 meters and the rate of increasing of bottom of ladder from bottom of wall is 101 meters per minute and the bottomis 36 m from the wall.

There are 752 cal in 8 ounces of a certain ice cream how many calories are there in 2 pounds

Answers

So, 8 ounces is equivalent to .5 pounds. Therefore, 32 ounces is equivalent to 2 pounds. Or, there are 4 8ounce measurements to get to 2 pounds.

752 calories * 4 = 3008 calories in 2 pounds of ice cream.

Determine if the set (x1,x2)+(y1,y2)=(x1-x2, y1+y2) is a vector space

Answers

The set  (x1,x2)+(y1,y2)=(x1-x2, y1+y2) is not a vector space.

A set is a vector space if it satisfy all the addition operation axiom and scalar multiplication axiom.

Addition operation:

Commutativity -

(x1, x2) + (y1, y2) equals  (x1 - x2,  y1 + y2) equals  (y1, y2) + (x1, x2)

Associativity -

(x1, x2) plus ((y1, y2) plus (z1, z2)) = (x1, x2) + (z1 + y1, z2 + y2) = (x1+ y1 + z1, x2 + y2 + z2) =

((x1, x2)   + (y1, y2)) + (z1, z2)

Zero element -

(0, 0)  → (x1, x2) + (0, 0) = (x1, x2)

Inverse element -

(x1, x2)  adding (-x1, -x2) = (0, 0)

Scalar multiplication:

Compatibility -

a(b (x, y)) = a(bx, 0) = (abx, 0) = b(ax, 0) = b(a(x, y))

Identity element -

1(x, y) = (x, 0) ≠ (x, y)     [Identity element doesn’t exist for this operation.)

Distributivity law -

a((x1, x2) + (y1, y2)) = a(x1 + y1, x2 + y2) = (a(x1 + y1), 0) = a(x1, x2) + a(y1, y2)

Distributivity law -

(a + b)(x, y) = ((a + b)x, 0) = (ax, 0) + (bx, 0) = a(x, y) + b(x, y)

The scalar multiplication postulate is not fulfilled in this space (this operation does not have the identity element). It is therefore not a vector space.

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Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. 2x^3+4x-6 3x^3-8x+7

Answers

The addition of the polynomials [tex]2x^3+4x-6[/tex] and [tex]3x^3-8x+7[/tex] in the proper location on the grid is [tex]5x^3-4x+1[/tex]

How to find the addition of two polynomials is proper location on the grid ?

Polynomials addition in proper location means add the coefficient of same power of variable

So the addition of polynomials like this

[tex]2x^3+4x-6+3x^3-8x+7[/tex]

[tex]2x^3+3x^3=5x^3\\4x-8x=-4x\\-6+7=1[/tex]

The addition of the polynomials is [tex]2x^3+4x-6+ 3x^3-8x+7=5x^3-4x+1[/tex]

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5.5(x+6 1/2)-(x+9 1/3)-(19-x)

Answers

The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12

What is the simplified form of the expression

Given the expression;

5.5(x+6 1/2) - (x+9 1/3) - (19-x)

First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction

6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2

So, we have

(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )

Next, we remove the parentheses

11x/2 + 143/4 - x - 28/3 - 19 + x

11x/2 + 143/4 - 28/3 - 19

11x/2 + 317/12 - 19

11x/2 + 89/12

Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.

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What is the multiplicative inverse of -13/14

Answers

The multiplicative inverse of -13/14 as in the task content is; -14/13.

What is the multiplicative inverse of -13/14?

The multiplicative inverse of a number x is given as; 1/x.

On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.

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For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f (x) = startfraction 2 x superscript m baseline over x a endfraction

Answers

Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

[tex]f(x) = \frac{2x^m}{x + a}[/tex]

It has a vertical asymptote at x = 1, hence:

x + a = 0

1 + a = 0

a = -1

It has a horizontal asymptote at y = 2, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]

[tex]2^{m-1} = 2[/tex]

Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.

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Help with this word problem!

Answers

Answer:

  2.0 km

Step-by-step explanation:

The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.

Setup

The law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Using the given values, we have ...

  c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)

Solution

Simplifying the equation, we get ...

  c² = 37.89 -37.8cos(26°) ≈ 3.91559

  c ≈ 1.979 . . . . km

The width of the strait is about 2.0 km.

Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.

Number of Hours vs. Amount Left in Tank
Number of Hours Spent Driving (h)

3

5

7

9
Amount of Gas Left in Tank, in gallons (g)

12

8

4

0

Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?
g = 18 – 2h; 18 gallons
g = 18 – 2h; 16 gallons
g = 3h + 3; 30 gallons
g = 3h + 3; 12 gallon

Answers

The equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank is g = 3h + 3; 12 gallon

Equation

Number of hours = 3 hoursAmount of gas left = 12 gallons

Check all equation

g = 18 – 2h; 18 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 18 – 2h; 16 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 3h + 3; 30 gallons

= 3(3) + 3

= 9 + 3

= 12

g = 3h + 3; 12 gallon

= 3(3) + 3

= 9 + 3

= 12

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James sleeps for 8 hours in a day. what percentage of the day is james a. asleep b. awake

Answers

Step-by-step explanation:

asleep percentage :- ( 8h /24h ) 100 % = 33.33%

awake percentage :- ( 16h / 24h ) 100 % = 66.67%

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours

Answers

The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.

The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.

Equation of cosine function:

The following is a presentation of the cosine function's generic form;

y =  a + cos(bx - c) + d

amplitude = a

b = cycle speed

Calculation for the model height;

The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Obtain amplitude 'a' as

[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]

The time 'T' is calculated as-

[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]

Now, calculate 'd'

[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]

Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:

h=0.5cos([tex]\pi[/tex]/6t)+9.5

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The complete question is-

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A. h=0.5cos([tex]\pi[/tex]/12t)+9.5

B. h=0.5cos([tex]\pi[/tex]/6t)+9.5

C. h=cos([tex]\pi[/tex]/12t)+9

D. h=cos([tex]\pi[/tex]/6t)+9

Six pyramids are shown inside of a cube. The height of the cube is h units. Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid

Answers

The height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

What is the volume of a cube?

A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

Volume of cube [tex]= (side)^3 \ unit^3[/tex]

Given the height of cube is [tex]h[/tex] unit.

Volume of cube is [tex]h^3 \ unit^3[/tex]

Let the height of squared pyramid is [tex]x[/tex] unit

Volume of squared pyramid is [tex]\frac{1}{3} h^{2} \times x \ unit^3[/tex]

According to the question, we have

Volume of cube = [tex]6 \times[/tex] volume of squared pyramid

[tex]\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h[/tex]

Therefore, the height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

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The nth term of a sequence is 3nsquared/2 1 find the second term of this sequence

Answers

Answer:

6

Step-by-step explanation:

Substituting in n = 2,

[tex]\frac{3(2)^{2}}{2}=6[/tex]

Help me please, I'm stuck

Answers

Answer:

Gradient: 5

y-intercept: (0, 15)

Step-by-step explanation:

The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.

The relationship between distance travelled, d, and time, t, can be represented by a linear relation. In 56 minutes, a person
runs 6 miles. In 104 minutes, the same person runs 10 miles. An equation that represents this linear relation is?

Answers

Answer:

[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]

Step-by-step explanation:

The average rate of change is (10-6)/(104-56) = 1/12.

So, the equation is of the form d = t/12 + c for some constant c.

Substituting in d=6 and t=56 gives that c=4/3.

So, the equation is

[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]

The lifespan of a car battery averages 5 years. Suppose the battery lifespan follows an exponential distribution. What is the probability that the battery lasts more than 3 years

Answers

The probability that battery lasts more than 3 years is [tex]e^{-0.6 }[/tex].

Parameter of Exponential Distribution

It is given that the average lifespan of the car battery = 5 years

⇒ μ = 5

And, we have to find the probability that the car battery lasts more than 3 years.

Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,

1/ λ = μ

⇒ λ = 1/5

Calculating the Probability

The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.

P(N>3) = 1 - P(N≤3)

P(N>3) = 1-F(4)

Here, F is the exponential distribution  for the lifespan of the car battery.

P(N>3) = 1-(1-e^(-λn))

P(N>3) = [tex]e^{-3/5}[/tex]

Thus, the required probability is,

P(N>3) = [tex]e^{-0.6 }[/tex]

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Computer geometric modeling is used regularly to help design solid figures we see and use every day. Software programs use techniques such as scaling and rotation to create solid figures that model objects. Research computer geometric modeling and then answer these questions. What basic shapes are used in modeling real-world objects? How are some of the concepts you learned in this unit related to computer geometric modeling? Why is creating a geometric model of something before producing it important?

Answers

The geometric modeling is analyzed below.

How to illustrate the information?

Basic shapes are generally created using points, lines, circles, and triangles. Some basic shapes are rectangles, ellipses, triangles, and curves.

In geometric modeling, we make a cad model of parts for virtual analysis. By geometric modeling, one can model, and perform CAE analysis to optimize the product.

The best part is the period of doing all this is very small compared to practical manufacturing and looking at the product. In CAD one can very quickly alter the design and come up with new concepts in a very small span of time.

Here chances of error can be shorted easily and there is no wastage of material hence cost saving is there compared to practically manufacturing the part and altering it.

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The power of the algebraic expression
7xy + 3xy² - x³y² + 4 is

Answers

The power of the algebraic expression 7xy + 3xy² - x³y² + 4 is  1.

How to estimate the power of algebraic expression?

An expression that denotes repeated multiplication of the exact factor exists named a power. The number 5 stands named the base, and the number 2 exists named the exponent. The exponent equals the number of times the base exists utilized as a factor.

Given: 7xy + 3xy² - x³y² + 4

An expression that represents repeated multiplication of the same factor is called a power.

So, the power of the given expression will be 1.

Therefore, the correct answer is 1.

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If AD BD, which of the following relationships can be proved and why?
B
OA. AACD ABCD, because of AS.
OB. AACD ABCD, because of ASA.
OC. There is not enough information to prove a relationship.
D. AACD ABCD, because of SAS.

Answers

IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.

Relationship that can be proved if AD=BD

The relationship that can be proved is ΔACD ΔBCD, because of SAS.

The reason is that m<CDA=M<CDB=90°

CD=CD

AD=BD

Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when  the angle between the two side is equal.

Therefore the correct option is D.

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Instructions:Given the coordinates the translation (x,y)>(x-4,y).

Answers

(-4,-3)
(-4,-2)
(-2,-2)
(0,-4)
subtract 4 from the x-value

A chemist has three different acid solutions. the first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . he wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. how many liters of each solution should be used? the chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.

Answers

Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.

The chemist wants to end up with a total volume of 54 liters, so

[tex]a + b + c = 54[/tex]

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]

He will also use twice as much of the 60% solution as the 30% solution, so

[tex]c = 2b[/tex]

Substitute this into the first two equations and solve for [tex]a,b[/tex].

[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]

Solve for [tex]b[/tex].

[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]

Solve for [tex]c[/tex].

[tex]c = 2(15) \implies \boxed{c=30}[/tex]

a = 9, b = 15 and c = 30 liters of each solution should be used.

What liter means?According to the metric system, a liter is a unit for measuring volume. A bottle of Coke that holds 33.76 ounces, or 1.0567 quarters, is an example of a liter. 2. The fundamental metric unit of liquid volume or capacity, which is equivalent to 1.06 quarts or 2.12 pints.

What is a liter of water?Let's examine this with the help of the following justification. Despite the fact that there is no established standard size for glasses, their capacity varies. In contrast, we estimate that a glass of water holds 8 ounces, and a liter holds 32 ounces.

According to the question:

Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.

a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

0.20a + 0.30b + 0.60c = 24.3

Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.

Substitute this into the first two equations and solve for a,b

a + 3b = 54

0.20a + 1.50b = 24.3

Eliminating b,  we have

[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]

a = 9.

Solve for b.

9+3b = 54

3b = 45

b = 15.

Solve for c.

c = 2(15)

c = 30.

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A bicycle race follows a triangular course. The 3 legs of the race are, in order, 2.3 km, 5.9 km, 6.2 km. Find the angle between the starting leg and the finishing leg, to the nearest degree.
How did you get the answer?

Answers

Answer:

About 71.77 degrees

Step-by-step explanation:

The starting leg is 2.3 km and the finishing leg is 6.2 km.

Using the law of cosines C^2 = A^2 + B^2 -2AB*cos(c) where A = 2.3 km, B = 6.2 km, C = 5.9 km, and angle c is the opposite angle to side C, we get:

5.9^2 = 2.3^2 + 6.2^2 -2(2.3)(6.2)*cos(c)

cos(c) = -(5.9^2 - 2.3^2 - 6.2^2)/(2*2.3*6.2)

c = 71.77 degrees

Answer:

72°

Step-by-step explanation:

when we have all the sides and need an angle, we use the law of cosine (the extended Pythagoras) :

c² = a² + b² - 2ab×cos(C)

where c is the side opposite of the angle C.

so, since the starting leg is 2.3 km, and the finishing leg is 6.2 km, we know that 5.9 km is the side opposite of the angle between the starting and finishing legs.

so, we have

5.9² = 2.3² + 6.2² - 2×2.3×6.2×cos(C)

34.81 = 5.29 + 38.44 - 28.52×cos(C)

-8.92 = -28.52×cos(C)

cos(C) = -8.92/-28.52 = 0.312762973...

C = 71.77418076...° ≈ 72°

Henry walked on a flat field 9 meters due north from a tree. He then turned due east and walked 24 feet. He then turned due south and walked 9 meters plus 32 feet. How many feet away from his original starting point is Henry

Answers

Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.

What is the Pythagorean theorem?

The theorem says that,

In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.

I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,

AC² = AB² + BC²

Calculation:

It is given that,

Henry walked on a flat field,

9 meters - towards the north

24 feet - towards the east

9 meters + 32 feet - towards the south

This can be shown in the diagram below.

In the diagram, the distance from the starting point is X, and the last point is  S.

To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.

So, according to the Pythagorean theorem,

XS² = (24)² + (32)²

(here 32 feet is the only distance from the assumed point to the endpoint)

⇒ XS² = 1600 = 40²

XS = 40 feet

So, Henry is 40 feet away from the original starting point.

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El triángulo ABC es equilátero y L, M y N son los puntos medios de BC, AB y CA respectivamente. Si MN = 3, ¿cuál es el valor de ML?

Answers

The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

MN || BC, and MN = (1/2)BC,ML || AC, and ML = (1/2)AC, andNL || AB, and NL = (1/2)AB.

Assuming AB = BC = AC = x units, we get:

MN = (1/2)BC = x/2,ML = (1/2)AC = x/2, andNL = (1/2)AB = x/2.


Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

Which expression is equivalent to (x^6y^8)^3/x^2y^2

Answers

Answer:

x^7y^9

Step-by-step explanation:

Remembering the laws of indices and applying BODMAS

(x^6y^8)^3/x^2y^2

(x^6 * y^8)^3/x^2 * y^2

opening bracket

we get;

x^6+3 * y^8+3/x^2 * y^2

x^9 * y^11/x^2 * y^2

Applying law of indices at which when the values are the same during division we pick one coefficient and minus the power

therefore;

x^9-2 * y^11-2

x^7 * y^9

=x^7y^9

Your professor selects three students from your Stats class to form a study team. How many study teams are possible from a class of 30 students

Answers

Total number of teams are 10

Linear Equation

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.

As given in the problem,

total number of students in class=30

now professor want to create study teams .

one team consist of 3 members,

lets suppose professor will form n teams

So,

3×n=30

solve this equation to get value of n

n=30÷3

n=10 teams

hence total number of teams are 10 .

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