trigonometry word problem

The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the Cartesian Plane to make an argument.The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .For example, the following is a coordinate proof of the Triangle Midsegment Theorem , which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half the length.Without loss of generality, we can assume that one side of the triangle lies on the xx -axis with one vertex at (0,0)(0,0) and the other vertex at(a,0)(a,0).Let the third vertex have the coordinates (b,c)(b,c) . We can assume without loss of generality that this third vertex lies in the first quadrant. (If it doesn't, you can just reflect the triangle over the xx - and/or yy -axis until it does.)

Example:

To Prove: XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ and

XY=12PRXY=12PR

Proof:

Using the midpoint formula , the coordinates of the midpoints XX and YY are

X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)

First note that the slope is 00 , since

m=riserun     =(c2−c2)(b2−(a+b2))     =0(b2−(a+b2))     =0m=riserun     =(c2−c2)(b2−(a+b2))     =0(b2−(a+b2))     =0

So, XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ .

Now, compare the lengths of the two segments.

XY=a+b2−b2        =a2PR=a−0        =aXY=a+b2−b2        =a2PR=a−0        =a

So,

XY=12PRXY=12PR

Thanks to google for example

hope this helps

Answer:

n = 55

Step-by-step explanation:

55/5 = 11!

Greater than or equal to 11 and 55 is greater than, 11.

The answer 55 also works with /5!

Please make sure to take care and have a great day!

A) Let x = cost of t-shirt:

x= 22.95-12.25

B) x = 22.95 -12.25 = 10.70

C) the t-shirt cost $10.70

The ratio of male fish with egg cells to male fish without egg cells is 130:290, which simplifies to 13:29.

To determine the ratio of male fish with egg cells to those without, you must subtract the number of male fish with egg cells from the total number of surveyed male fish. According to Anna's survey, she found that 130 male fish out of 420 had egg cells. This implies that 420 - 130 = 290 male fish do not have egg cells.

Now, to find the ratio:

Male fish with egg cells: 130

Male fish without egg cells: 290

The ratio of male fish with egg cells to male fish without egg cells is 130:290. This ratio can also be simplified by dividing both parts by the greatest common divisor, which is 10 in this case. After simplification, the ratio becomes 13:29.

Hi There!

1. Not Linear (Because it has a exponent)

2. Linear (Stated in Point Slope Form)

3. Linear

4. Linear

Hope This Helps :)

The first term of the given arithmetic sequence is 2.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the fourth term of an arithmetic sequence is 8 and the common difference is 2.

Here, a₄=a+(4-1)×2

8=a+6

a=2

Therefore, the first term of the sequence is 2.

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the top number of a fraction is the numerator, the bottom number is the denominator

 to turn a fraction into a decimal divide the numerator by the denominator (Top number by the bottom number)

The pressure exerted on the ice by the skater, who weighs 500-N and has blade contact area of 0.001 m², is 500,000 Pa (Pascals).

The question is asking about the pressure exerted on the ice by a skater. To find the pressure, we use the formula P = F/A, where P is the pressure, F is the force, and A is the area in contact with the ice.

If the skater weighs 500-N and is gliding on one skate blade, which has an area of contact of 0.001 m2, the pressure is calculated by dividing the weight by the area. Using the provided data from the similar situation of a skater with a weight of 736 N and a blade area of 5.0 × 10-4 m2, we would calculate the pressure using these figures. However, we need to calculate the pressure using the data specific to this skater, with a weight of 500-N and a blade area of 0.001 m2.

The pressure exerted on the ice can be calculated as:

P = 500 N / 0.001 m2 = 500,000 Pa (Pascals)

The problem involves trigonometry to determine the width of the sandpile. The angles of depression equate to angles of elevation from ground up. Using the tangent function and the provided angles of depression, the distances to the rocks are calculated and added together to get approximately 52 feet as the pile's width.

This problem involves the application of trigonometry, specifically the tangent function (tan) in relation to angle of depression. To start with, we need to note that the angle of depression is equivalent to the angle of elevation as observed from the ground upwards. Hence, if the angles of depression are 28° and 19° respectively, it would mean that the angles of elevation at the rocks would be 28° and 19° respectively.

We can use the formula for tangent, which is tan(θ)=Opposite/Adjacent. In this context, 'Opposite' is the height of the pile (11 feet), and 'Adjacent' is the distance from the base of the pile to the rock. We get two equations:

We rearrange to find D1 and D2. Finally, the total distance (width of the pile) is simply D1 + D2. Using a calculator, D1 is approximately 21 feet and D2 is approximately 31 feet. Hence, the width of the sandpile is approximately 52 feet when rounded to the nearest foot.

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Using the formula of average distance = total distance traveled / total time taken, we find that Phaelon had the fastest average speed of 10.86 mi/hr.

To find out who had the fastest average speed, we'll need to calculate the average speed for each person. We can do this by dividing the total distance traveled by the total time taken.

Serra's average speed: 15 mi / 1.5 hr = 10 mi/hr

Phaelon's average speed: 38 mi / 3.5 hr = 10.86 mi/hr

Justice's average speed: 22 mi / 2.25 hr = 9.78 mi/hr

So, by comparing these speeds, we can conclude that Phaelon had the fastest average speed of 10.86 mi/hr.

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The inverse function of y = 3x + 2 is y = ( -x + 2 )/3 obtained by switchig the places of x and y.

A function can be thought of as an output for the given set of inputs.

To find the inverse of a function algebraically first we have determine whether the given function is one-to-one or not. A one-to-one function is a function in which each different value of the domain corresponds to a different value in the range of the function.

Suppose we have a function f(x) = 3x + 2 which can be written as y = 3x + 2.

Now to obtain the inverse of this function we have to switch x and y in their respective places and solve for y.

∴ y = 3x + 2

x = 3y + 2.

3y = - x + 2.

y = ( -x + 2 )/3.

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Answer:

  16.9 units

Step-by-step explanation:

Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...

  14.87 + 2 = 16.87 ≈ 16.9 . . . units

_____

The distance formula can be used to find the lengths of individual segments. It tells you ...

  d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

If the segments are labeled A, B, C, D, E in order, the distances are ...

  AB = √(5²+1²) = √26 ≈ 5.099

  BC = √(1²+3²) = √10 ≈ 3.162

  CD = Δx = 3

  DE = √(3²+2²) = √13 ≈ 3.606

  EA = Δy = 2

Then the perimeter is ...

  P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

  P ≈ 16.9

His friend's garden is 18.22 meters long.

R (Read):

Leeland's garden is 15 meters and 24 centimeters long.

His friend's garden is 2 meters and 98 centimeters longer than Leeland's.

We need to find the length of his friend's garden.

D (Define):

Let L be the length of Leeland's garden in meters.

Let F be the length of his friend's garden in meters.

W (Write):

We can write the given information as equations:

L = 15.24 meters (converting 24 cm to meters)

F = L + 2.98 meters

Solve:

Substitute equation 1 into equation 2:

F = (15.24 meters) + 2.98 meters

F = 18.22 meters