A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?

Answers

Answer 1

Answer:

Answer:

$103.78\:\mathrm{ft}$

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

$\tan 34^(\circ)=(70)/(x)$ , where $x$ is the distance between the base of the tower and the fire.

Solving, we get:

$x=(70)/(\tan 34^(\circ))=103.779267796\approx \boxed{103.78\:\mathrm{ft}}$

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Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

Answers

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

The intersection of the sphere with the yz- plane gave the equation $(y-2)^(2) + (z-5)^(2) = 7$ which is a 2D- circle with center (0,2,5) and radius $√(7)$ .

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

where, $x,$ $y,$ and $z$ are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

$(x-(-3))^(2) +(y-(2))^(2) + (z-(5))^(2) = 4^(2)$

Then,

$(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The $yz -$ plane is where $x = 0$ , then we set $x = 0$

Them the equation $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$ becomes

$(0+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

$(3)^(2) +(y-2)^(2) + (z-5)^(2) = 16\n9 +(y-2)^(2) + (z-5)^(2) = 16\n(y-2)^(2) + (z-5)^(2) = 16 - 9\n(y-2)^(2) + (z-5)^(2) = 7$

This equation is the equation of a 2D- circle with center (0,2,5) and radius $√(7)$

This is the part of the sphere that intersects with the yz-plane.

PLEASE HELP The probability distribution for a
random variable x is given in the table.

Answers

Step-by-step explanation:

p(x≤20)=p(x=-10) +p(x=-5)+p(X=0) +p(x=5) +p(x=10)+ p(X=15)+p(X=20)

This, p(X≤20)=0.20+0.15+0.05+0.1+0.25+0.1+0.15

What is 6,720 divided by 14??

Answers

480 because 6,720 divided by 14 is 480

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

Answers

The answer is 38 peas per pod

228÷6 = 38

Glad to help you :)

Final answer:

By dividing the total number of peas (228) by the number of peas per pod (6), we find that Gregor Mendel has 38 pods of peas.

Explanation:

This question is asking how many pods of peas Gregor Mendel has if he has a total of 228 peas and each pod contains 6 peas. To find out this, you can divide the total number of peas by the number of peas per pod.

So, 228 peas ÷ 6 peas/pod = 38 pods.

Therefore, Gregor Mendel has 38 pods of peas that he is examining for his research.

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Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?

Answers

Answer:

y = -2x + 5

slope = -2

y intercept = 5

Step-by-step explanation:

Slope intercept form of equation of line is given by y = mx + c

where m is the slope of line

c is the y intercept i.e point where given line intersect y axis.

________________________________________________

given equation 4x + 2y = 10

we have to re-write this equation in form y = mx + c

4x + 2y = 10

subtraction 4x from LHS and RHS

4x + 2y - 4x= 10 - 4x

2y = 10- 4x

we have to eliminate 2 from y for that we

divide LHS and RHS by 2 we

2y /2 = 10/2- 4x/2

y = 5 - 2x

rearranging it in y = mx+c form

y = -2x + 5

thus, m = -2 , c = 5

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A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?​

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Final answer:

Explanation:

Learn more about Division here:

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A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?