a woman standing 14m away from a cliff observes that the angles of elevation of the top and bottom of a vertical pole mounted on top of the cliff are 65 degree and 58 degree respectively. find the height of the pole​

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

The ratio of the area of circle X to the area of circle Y is  0. 11

The formula for area of a circle is expressed as;

Area = πr²

Where; 'r' is the radius

For circle X, radius = 1/ 3 meter

Let's find the area

Area = 3. 142 × (1/3)²

Area = 3. 142 × 1/ 9

Area = 0. 35 square meters

For circle Y, radius = 1

Area = 3. 142 × 1²

Area = 3. 142 × 1

Area = 3. 142 square meters

Ratio of circle X to circle Y

= 0.35/ 3. 142

= 0. 11

Thus, the ratio of the area of circle X to the area of circle Y is  0. 11

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To determine the angle of rotation, we need to find the measure of the angle formed by the points P, A, and A'. the angle of rotation is 360 - arccos(1 - cos(x)).

To determine the angle of rotation, we need to find the measure of the angle formed by the points P, A, and A'. Similarly, we need to find the measure of the angle formed by the points P, B, and B', and so on for C, C', and D, D'. These angles will all be congruent since the rotation is about a single point. Let's call this angle x.

Using the distance formula, we can find the lengths of the line segments between each pair of points. For example,

PA' = sqrt((xA'-xP)^2 + (yA'-yP)^2)
PA = sqrt((xA-xP)^2 + (yA-yP)^2)

where (xA',yA') and (xA,yA) are the coordinates of A' and A, respectively.

Since the quadrilateral ABCD is the preimage of A'B'C'D', the corresponding sides are congruent. For example, AB = A'B', BC = B'C', etc.

Now, we can use the Law of Cosines to find x:

AB^2 = PA^2 + PB^2 - 2(PA)(PB)cos(x)
A'B'^2 = PA'^2 + PB'^2 - 2(PA')(PB')cos(x)

Substituting AB = A'B' and BC = B'C', we get:

PA^2 + PB^2 - 2(PA)(PB)cos(x) = PA'^2 + PB'^2 - 2(PA')(PB')cos(x)
PC^2 + PD^2 - 2(PC)(PD)cos(x) = PC'^2 + PD'^2 - 2(PC')(PD')cos(x)

Adding the two equations, we get:

PA^2 + PB^2 + PC^2 + PD^2 - 2(PA)(PB)cos(x) - 2(PC)(PD)cos(x) = PA'^2 + PB'^2 + PC'^2 + PD'^2 - 2(PA')(PB')cos(x) - 2(PC')(PD')cos(x)

Using the fact that AB = A'B' and BC = B'C', we can simplify further:

2AB^2 + 2BC^2 - 2(AB)(BC)cos(x) = 2A'B'^2 + 2B'C'^2 - 2(A'B')(B'C')cos(x)

Substituting AB = A'B' and BC = B'C' again, we get:

4AB^2 - 4(AB)^2cos(x) = 4A'B'^2 - 4(A'B')^2cos(x)

Dividing both sides by 4(AB)^2, we get:

1 - cos(x) = 1 - cos(x')

where x' is the angle of rotation in degrees.

Solving for x', we get:

x' = 360 - x = 360 - arccos(1 - cos(x))

Therefore, the angle of rotation is 360 - arccos(1 - cos(x)).

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The only number that is 10 times as much as 72 is 720.

To find the numbers that are 10 times as much as 72 or 1/10 of 72, we can perform the following calculations:

10 times 72 = 720

1/10 of 72 = 7.2

So, the numbers that are 10 times as much as 72 are 720.

The number 67 is not 10 times as much as 72 or 1/10 of 72. Therefore, it is not one of the numbers we are looking for.

On the other hand, 1/10 of 72 is 7.2, which is not one of the numbers we are looking for either.

Therefore, the only number that is 10 times as much as 72 is 720.

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complete question

Select all the numbers that are 10 times as much as 72, 67, or 1/10 of 72.

- 67

-46

-720

-480

The value of the sine of angle D to the nearest hundredth will be 0.25.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔCDE is given as,

CD / sin E = DE / sin C = EC / sin D

In triangle ΔCED, the measure of angle ∠E = 90°, ED = 63, DC = 65, and CE = 16. Then we have

65 / sin 90° = 63 / sin C = 16 / sinD

Compare the first and the last term, then we have

65 / sin 90° = 16 / sin D

65 = 16 / sin D

sin D = 16 / 65

D = 14.25°

The worth of the sine of point D to the closest 100th will be 0.25.

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The overall average of the 9 numbers is 13 and the average of the last 4 numbers is 20.

To find the overall average of the 9 numbers, we can use the formula for the weighted average:

overall average = (sum of all numbers) / (number of numbers)

We know that the average of the first 5 numbers is 10, so their sum is 5 * 10 = 50. We also know that the average of the next 4 numbers is 15, so their sum is 4 * 15 = 60. The sum of all 9 numbers is then 50 + 60 = 110. Therefore, the overall average is:

overall average = 110 / 9 ≈ 13

To find the average of the last 4 numbers, we can subtract the sum of the first 5 numbers from the sum of all 9 numbers, and then divide by 4:

average of last 4 numbers = (sum of all 9 numbers - sum of first 5 numbers) / 4

= (110 - 50) / 4

= 60 / 4

= 15

Therefore, the average of the last 4 numbers is 15, which is option C.

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Answer:

Value = 44,0000(0.75)^t

Where t = number of years

Value after 4 years = 44,000 (0.75)^4

1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

2. B. Type Ia supernovae

3. D. Downwards; towards the center of the Sun

The interpretation of the equations and the correct options for the given questions are as follows:

Question 1:

The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:

C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

Question 2:

To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:

B. Type Ia supernovae

Question 3:

Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:

D. Downwards; towards the center of the Sun

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Answer:

See below.

Step-by-step explanation:

a) y = 2x + 3 and y = -2x + 11

 One solution.  They are straight lines with different slopes, so they will intersect at some point.  

b) y = x + 2 and -2x + 2y = 4

  -2x + 2y = 4 can be rearranged to 2y = 2x +4 and then y = x + 4

    Both lines have the same slope, 1.  They are parallel and will never meet.  No solutions.

c) y = x - 3 and y = x + 6

 This has the same answer as c.  Parallel lines (both have slopes of 1.).  They will never meet:  no solutions.

d) y = 7 and y =3x-5

One solution.  Straight lines with different slopes (3 and 0) so they will cross at one point.  [At (4,7)]

e) y = -4x and y = -4x - 1

Same slopes.  There are no solutions.

The greatest length of the cube as calculated is 1 / 12.

A right rectangular prism contains six rectangle-shaped faces, twelve edges, and eight vertices in three dimensions. The prism's faces are all rectangles. Each of the vertices produces a right angle, or 90 degrees.

Given that it is a solid geometric form, a right rectangular prism would be divided into cubes of each dimension.

Putting the prism's measurements in  1 / 4 inches,

3 / 2 = 7 / 2

2 / 4 = 9 / 4

4 / 3 = 13 / 3

All of the dimensions' denominators must be the same.

So,

3 / 2 = 7 / 2 = 42 / 12

2 / 4 = 9 / 4 = 21 / 12

4 / 3 = 13 / 3 = 52 / 12

Since 2, 4, and 3 have a common multiple of 12,

Therefore, the cube's edge length is  1 / 12

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Answer:

They are parallel so also -4/3

Answer:

Step-by-step explanation:

Answer:

324 in^2

Step-by-step explanation:

If you transfer the 9 ft to inches you get 108 in

108x3=324

Answer:

21

Step-by-step explanation: 9 + 9 = 18 , 3 + 3 = 6 , 18 + 6 = 21.

Answer:

40 is

But it is not an

We have that f(x) exists described for all real values of x, except for \($x=x _0$\). \($\lim _{x \rightarrow x 0} f(x)$\)

The graph shows a rising trend when the derivative's sign is positive. In all cases where x > 0, the derivative's sign is positive.

A function is increasing, decreasing, or constant on an interval if the derivative is positive, negative, or zero on that interval.

It is possible to determine the slope of a tangent line to a curve at any time using a function's first derivative. The first derivative of a function provides us with a wealth of information about the function as a result of this definition. Obviously increasing if is positive. is decreasing if it is negative.

Remember that when we are taking the limit we are not evaluating the function in \($x_0$\), instead, we are evaluating the function in values really close to \($x_0$\) (values defined as \($\mathrm{xO}^{+}$\)and \($\mathrm{xO}^{-}$\), where the sign defines if we approach from above or bellow).

And because f(x) is defined in the values of x near \($x_0$\), we can conclude that the limit does exist if:

\($\lim _{x \rightarrow 0+} f(x)=\lim _{x \rightarrow 0-} f(x)$\)

if that does not happen, like in f(x) = 1 / x where \($x_0=0$\)

where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.

The complete question is:

Suppose that a function f(x) is defined for all real values of x, except x = xo. Can anything be said about LaTeX: \displaystyle\lim\limits_{x\to x_0} f(x)lim x → x 0 f ( x )? Give reasons for your answer.

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Answer:

m=7

Step-by-step explanation:

subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.

Answer: m=7

Step-by-step explanation:

\(5m+35=70\)

subtract 35 on both sides

\(5m+35-35=70-35\)

\(5m=35\)

divide 5 on both sides

\(35/5=7\)

\(m=7\)

The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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In an exhibition, the cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.  

What is   equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Equation relates the cost, y, of adult ticket in terms of the cost, x, of child ticket.

Cost of Adult ticket = y

cost of child ticket  = x

cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.  

=> cost of tickets for an adult = 5 + 3 (cost o f ticket for a child.)

=> y  = 5 + 3x

=> y = 3x + 5

Equation is   y = 3x + 5

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As Malia walks her dog 140% of the distance walked by Tiara’s, so Tiara walks her dog less as compared to Malia’s. And the distance Tiara walks her dog is 5 miles.

Let us consider the distance covered by Tiara and Malia in walking their dogs be ‘x’ and ‘y’ respectively.

we have been provided with the value of ‘y’,  i.e.

                                               y = 7 miles

Now,

            Distance walked by Malia’s dog = 140% of the distance walked by Tiara’s dog

                                                               Or

                                                            y  = 140/100 × x

                                                            7   =  140/100 × x

Therefore,                                           x   =  100/140 × 7

                                                            x   = 5 miles

Hence, the distance Tiara walked her dog was 5 miles.

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He drove 828 miles on the first day.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = distance Pete traveled on the second day

If on the first day, he traveled 1.5 times as far as he did the second day, then

distance Pete traveled on the first day = 1.5x

If Pete traveled 1,380 miles in two days, the the sum of the distance he traveled in two days is equal to 1380.

x + 1.5x = 1380

Simplify the equation and solve for the value of x.

x + 1.5x = 1380

2.5x = 1380

x = 552

distance Pete traveled on the second day = 552 miles

distance Pete traveled on the first day = 1.5(552) = 828miles

Therefore, he drove 828 miles on the first day.

The problem seems incomplete. The question must be

"Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on the first day?"

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Answer:

17 mpg

Step-by-step explanation:

divide 242.4 by 14 to get the answer

Answer:

Step-by-step explanation:

Option D is the correct option.

What is Mean Absolute Deviation?

'The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set.'

According to the given problem,

The mean height Variety A = 19 [ from the table ]

The mean height of variety B = 13 [ from the table ]

The spread is given by the mean absolute deviation, which 1.2 for Variety A and 2.4 for Variety B. So we can see that, the spread in Variety A is lesser than the spread in Variety B, which shows that the average height of Variety A varies less than the average height of Variety B.

We can see from the table that the average height of a variety A is indeed greater than that of Variety B. Also we can see that the Mean Absolute deviation of Variety A is 1.2 which is lesser than the Mean Absolute deviation of Variety B.

Hence, option D is correct since the average height of Variety A is greater than Variety B, and also the mean varies lesser in Variety A than in Variety B.

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Answer:

D

Step-by-step explanation:

hope this helps

Answer:

118

Step-by-step explanation:

E = 41

Colin is 10 years older than Emily.     C = E + 10 = 41 + 10 = 51, C = 51

Dan is 15 years younger than Emily.   D = E - 15 = 41 - 15 = 26, D = 26

E + C + D = 41 + 51 + 26 =  118

Answer:35/2=17.5*26= ?

Step-by-step explanation:

Answer:

omg im doing alg 2 next year. that looks so complicated im gunna scream

Step-by-step explanation:

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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Answer:

the value of x is twenty nine

Answer:

2

Step-by-step explanation:

8 / 4 = 2

8 = 8 slices

4 = 4 people