A park ranger is in a tower that stands 258 feet tall. He sees a fire at an angle of depression of 38 °. How far
away from the base of the tower is the fire? Round your answer to the nearest tenths.
Pls help ASAP

The equation of the plane passing through the points Po(1, -5,3), Q,(-1, -5, -1), and Ro(3,5,-4), using a coefficient of 20 for x, is 20x - 11y - 10z = 45.

To find the equation of the plane passing through three non-collinear points, we can use the cross product of the vectors formed by subtracting one point from the other two points. Here are the steps:

Step 1: Find two vectors on the plane.

Let's take vector PQ from point P to point Q as PQ = Q - P = (-1, -5, -1) - (1, -5, 3) = (-2, 0, -4), and vector PR from point P to point R as PR = R - P = (3, 5, -4) - (1, -5, 3) = (2, 10, -7).

Step 2: Find the cross product of the two vectors.

The cross product of two vectors PQ and PR is given by the formula: N = PQ x PR = (PQy × PRz - PQz × PRy, PQz × PRx - PQx × PRz, PQx × PRy - PQy × PRx).

Substituting the values we found in Step 1, we get:

N = (-2 × -7 - -4 × 10, -4 × 2 - -2 × -7, -2 × 10 - 0 × 2) = (-14 - (-40), 8 - 14, -20) = (26, -6, -20).

Step 3: Write the equation of the plane using the normal vector.

The equation of a plane passing through a point (x0, y0, z0) with a normal vector N = (A, B, C) is given by the equation: Ax + By + Cz = D, where D = Ax0 + By0 + Cz0.

Substituting the values we found in Step 2, we get:

26x - 6y - 20z = D.

Step 4: Substitute one of the given points to find the value of D.

Let's substitute point P(1, -5, 3) into the equation:

26 × 1 - 6 × -5 - 20 × 3 = D

26 + 30 - 60 = D

D = -4.

Therefore, the equation of the plane passing through the points Po(1, -5,3), Q,(-1, -5, -1), and Ro(3,5,-4), using a coefficient of 20 for x, is 20x - 11y - 10z = 45.

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Answer:

122 degrees

Step-by-step explanation:

Take the warmer temperature and subtract the colder temperature

82 - (-40)

82+40

122

The difference is 122

The inverse functions are:

a) g(x) = (x - 2)/2

b) g(x)= {(3, 8), (1, 4), (-1, 0), (-3, -4)}

We know that two functions f(x) and g(x) are inverses if:

f( g(x)) = x

g(f(x)) = x

a) We want to find the inverse of:

f(x) = 2x + 2

If it is g(x), then we must have:

f(g(x)) = 2*g(x) + 2

And that must be equal to x, then:

2*g(x) + 2 = x

2*g(x) = x - 2

g(x) = (x - 2)/2

b) Now we want to find the inverse of:

f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

The inverse will be a function where the inputs are the outputs and the outputs are the inputs, so it is:

g(x)= {(3, 8), (1, 4), (-1, 0), (-3, -4)}

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Answer: We can't see the picture

Step-by-step explanation:

Answer:

F type connector

Step-by-step explanation:

Use an F-type connector for broadband cable connections that use coaxial cable.

The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,

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F type connector

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The volume of the given rectangular prism is approximately 578.9 cubic units.

The mathematical expression for the volume of a rectangular prism is given by the formula: Volume = length × width × height.

In this case, we are given a rectangle with a length of 6.5 units, a width of 8.3 units, and a height of 10.7 units. To find the volume, we substitute these values into the formula.

Volume = 6.5 × 8.3 × 10.7

Now, we can perform the multiplication to calculate the volume. However, since the multiplication involves decimal numbers, it is important to consider the significant figures and maintain accuracy throughout the calculation.

Multiplying 6.5 by 8.3 gives us 53.95, and multiplying this by 10.7 gives us 578.915. However, we must consider the significant figures of the given measurements to determine the final answer.

The length and width are given with two decimal places, indicating that the values are likely measured to the nearest hundredth. The height is given with one decimal place, indicating it is likely measured to the nearest tenth. Therefore, we should round the final answer to the same level of precision, which is one decimal place.

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Answer:  2 1/9 is the mixed number that  is equivalent to 2.1111 repeating

Step-by-step explanation:

Try dividing 1÷9 on a calculator to get the decimal value of 1/9.

Then just keep 2 as the whole number in front of the fraction.

Answer:

For me, it always helps to break down equations like this. Divide it up into two separate parts.

4^2*4^2=x

4^2=16

Replace both 4^2 with 16

16*16=256

For every hour that passes, the container loses 1.5 liters of oil.

To write a linear equation to estimate the remaining amount of oil based on the elapsed time, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the remaining amount of oil, x represents the elapsed time, m represents the slope of the line, and b represents the y-intercept.

Since the container is leaking at a constant rate, we can assume that the slope of the line is constant. We can find the slope by using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) represents the first data point (hours, liters of oil), and (x2, y2) represents the second data point.

Using the given data, we have:

m = (y2 - y1) / (x2 - x1)

m = (4.5 - 6) / (2 - 1)

m = -1.5

This means that for every hour that passes, the container loses 1.5 liters of oil.

To find the y-intercept, we can use one of the data points and solve for b:

y = mx + b

6 = (-1.5)(1) + b

b = 7.5

This means that at time zero (when no time has elapsed), there are 7.5 liters of oil remaining in the container.

Therefore, the linear equation to estimate the remaining amount of oil based on the elapsed time is:

y = -1.5x + 7.5

This equation tells us that as time passes, the amount of oil in the container decreases at a constant rate of 1.5 liters per hour. The y-intercept of 7.5 represents the initial amount of oil in the container before any time has elapsed.

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The distance that each boy ran is as follows:

Donnie = 24 miles

Karim = 12miles

Shawn = 9 mile.

Ratio is defined as an expression that is used to represent the part of a whole entity or structure.

The total distance covered by the three boys = 46miles.

Distance covered by Donnie = 200% of Karim (ratio 4)

That is;

200/100×4 = 8

Now the ratio of the three boys = 8:4:3

To calculate the distance of each boy is by finding the total ratio of the whole boys such as:

= 8+4+3 = 15

For Donnie = 8/15×45 = 24 miles

For Karim = 4/15×45 = 12 miles

For Shawn = 3/15 × 45 = 9 miles

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Step-by-step explanation:

Volume of Cone=

\( \frac{1}{3} \pi \: r {}^{2} h\)

Volume of Sphere=

\(\frac{4}{3} \pi \: r {}^{3} \)

Since VC = VS

\( \frac{1}{3} \times 3.14 \times 8 {}^{2} \times h = \frac{4}{3} \times 3.14 \times 216\)

66.99h = 904.32

h = 904.32 ÷66.99

h= 13.5 feet

Step-by-step explanation:

Hello!

        Part A            

Peter can use the fact that 10% of 87 is 8.70 to find the amount he would save because 40% is just 4 times bigger than 10% so he can take 8.70 from to total of the coat 4 times to find out how much it cost.

        Part B            

Using the same method we know that 10% of 64 is 6.40 so we subtract that from the price of the coat 4 times to find out how much it cost

64 - 6.40 = 57.6

57.6 - 6.40 = 51.2

51.2 - 6.40 = 44.8

44.8 - 6.40 - 38.4

The price of the coat is $38.4

Hope this helps!

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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60 students chose chocolate ice cream If 84 students chose vanilla ice cream.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.

Since,

The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5

Thus,

for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream

If 84 students chose vanilla ice cream

Thus, students choose chocolate ice cream = 5/7 * 84

students choose chocolate ice cream = 12* 5

students choose chocolate ice cream = 60

Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.

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The rate of change in this context refers to the change in the value of p, specifically between the peak and closing.This allows us to understand how much p changes on average between these two points in time.

It is a measure of how quickly or slowly the value of p is changing over time.

By calculating the average rate of change, we can understand the overall trend of the value of p and whether it is increasing or decreasing at a steady rate or if there are fluctuations.

This information can be useful for understanding the performance of a stock or investment, as well as predicting future trends.

Additionally, the rate of change can also help to identify any potential issues or opportunities within the market.

Overall, the rate of change provides a clear picture of the stock's performance over a certain period of time.

To calculate the average rate of change of p between peak and closing, we need to find the difference in p values (p(14) - p(8)) and divide that by the difference in time (14 - 8).

p(14) - p(8) = ? - ? = ?

(14 - 8) = ?

The average rate of change of p is ?/6.

The meaning of the rate of change in the context of this problem is the average change in the value of p per unit of time.

In this case, we are looking at the average change in p between the peak and closing, and expressing that change as a ratio of p(14) - p(8) to (14 - 8). This allows us to understand how much p changes on average between these two points in time.

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The cost of 4.5 tonnes of rock is $56.25

Given,

cost of 1 tonne of rock=$12.50

then

to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,

cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25

Thus ,the cost of 4.5 tonnes of rock is $56.25.

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The TQ is a chord, PR is a secant line and WU is a tangent line.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

A chord of a circle is the line segment joining two points on the circle.

Line segments TQ and QV are chords.

TV is also a chord, which is the diameter.

A secant line is a line which intersects the circle at two different points.

Line PR is a secant line which intersects the circle at T and Q.

A tangent line is a line which intersects the circle at exactly one point.

Line WU is a tangent line which intersects the circle at V.

Hence the chords in the given figure are TQ and QV, secant line is PR and tangent line is WU.

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Answer:

they form a 90 degree angle

Step-by-step explanation:

perpendicular (⊥) always implies 90 degree angles

parallel (║) always implies they never intersect

Answer:

Step-by-step explanation:

Answer:

30+40x=1310

Step-by-step explanation:

x = hours

so how many hours would be pluged in as x you would multiply then get your answer.

but in order to find x you must first subtract 30 from 1310

1310-30 then equal it to 40x then divide your answer by 40 and you would get 320 for x

When x = 6 and y = 2, the value of the expression 6x² / y³ is 27.

The given expression is

6x² / y³

The value of x is 6 and the value of y is 2.

Substituting the values of x and y in the given expression, we get:

6(6)² / (2)³

Simplifying the above expression, we get:

6(36) / 8

= 216 / 8

= 27

Therefore, when x = 6 and y = 2, the value of the expression

6x² / y³ is 27.

Evaluation of a given expression involves substituting the values of the variables with given values and then simplifying the expression.

In this case, the value of x is given as 6 and the value of y is given as 2.

Substituting these values in the given expression gives 6(6)² / (2)³ which can be simplified further as 6(36) / 8 which equals

216 / 8 = 27.

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Answer:

c=50

Step-by-step explanation:

Answer:

c = 50

Step-by-step explanation:

-0.2 multiplied by 50 would give you -10.

Answer:

<

Step-by-step explanation:

93%= 0.93

0.8 is less than 0.93%

so then the answer is <

Liverwort do not have special tissues to deliver food and water to its cells.

They are referred to as descendants of the first land plants and are flowerless and spore-producing.

They are however non-vascular which means they lack special tissues to deliver food and water to its cells thereby making option D the most appropriate choice.

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The vertex of the parabola is (6,-680).

To find the coordinates of the vertex of the parabola represented by the equation y= -5x^2-60x-200, we need to use the vertex formula. The vertex formula is given as (-b/2a, f(-b/2a)), where a and b are coefficients of x^2 and x respectively. In this case, a=-5 and b=-60.

So, substituting these values in the vertex formula, we get:

x = -(-60)/(2*(-5)) = 6

To find y, we need to substitute x=6 back into the equation:

y = -5(6)^2 - 60(6) - 200 = -680

Therefore, the vertex of the parabola is (6,-680).

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The distance between the two cities would be 10.67 inches. On the original map, two cities are 4 inches apart, with a scale of 20 miles per inch.

The desired scale for the new map is 2 inches = 15 miles. We need to determine the real-life distance between the cities and the distance between the cities on the new map using the new scale.

To determine the real-life distance between the cities, we can use the scale of the original map. If one inch on the map represents 20 miles in real life, then four inches on the map represent 80 miles in real life. Therefore, the real-life distance between the two cities is 80 miles.

To determine the distance between the cities on the new map, we need to use the new scale of 2 inches = 15 miles. We can start by finding out how many inches on the new map represent 80 miles in real life. To do this, we can set up a proportion:

2 inches / 15 miles = x inches / 80 miles

Solving for x, we get:

x = (2 inches * 80 miles) / 15 miles

x = 10.67 inches

Therefore, on the new map, the distance between the two cities would be 10.67 inches.

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Answer:

The answer is 20 gallons of yellow paint

Answer:

20 gallons of yellow paint.

Step-by-step explanation:

4/6 = x/30 is the equation.

4 represents yellow paint.

6 represents blue paint.

We know 30 gallon of blue paints was used.

But we dont know x , the amount of yellow paint.

Criss cross bottom to top

6× X = 4×30

6x= 120

x=20

The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

Given that,

A parabola can be drawn with a focus of (8,10) and a directrix of y=6.

We have to find the equation of the parabola in any form.

We know that,

The distance of any point P is (h,k) on a parabola form a focus is equal to its perpendicular distance from the directrix.

So,

√((h-8)²+(k-2)²) = | (k-6)/√0²+1² |

Squaring on both sides

(h-8)²+(k-2)² = (k-6)²

From th formula (a-b)² = a²-2ab+b²

We get,

h²-16h+64+k²-4k+4 = k²-12k+36

h²-16h+64+k²-4k+4 - k²+12k-36 =0

h²-16h+64-4k+4+12k-36=0

h²-16h+8k+32=0

Therefore, The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

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The general solution to the differential equation y''+4y=0 is y(x) = c₁ cos ₂x + c₂ sin ₂x and the value of β is 2.

To find the value of β, we substitute the general solution into the differential equation and solve for β. We start by finding the first and second derivatives of y(x):

y'(x) = -c₁β sin βx + c₂β cos βx

y''(x) = -c₁β² cos βx - c₂β² sin βx

Substituting these expressions into the differential equation, we get:

-c₁β² cos βx - c₂β² sin βx + 4(c₁ cos βx + c₂ sin βx) = 0

Simplifying this equation, we get:

(c₁β² + 4c₁) cos βx + (c₂β² + 4c₂) sin βx = 0

This equation must hold for all values of x, which means that the coefficients of cos βx and sin βx must both be zero. Therefore, we have the following system of equations:

c₁β² + 4c₁ = 0

c₂β² + 4c₂ = 0

We can solve for β by dividing the second equation by c₂ and substituting c₁ = -4β²/c₂ from the first equation:

β² = -4c₁/c₂ = 4

Since β>0, we take the positive square root of 4, which gives β=2.

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