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Artemon [7]
2 years ago
15

A small forest fire is cited due north of a fire lookout tower on Pikes Peak. From a second tower located 12.6 miles due west of

the first tower a Ranger observed that the fires is 49.5° east of duo North. How far is the fire from the tower Pikes Peak

Mathematics
1 answer:
Brums [2.3K]2 years ago
5 0

Answer:

10.76 miles

Step-by-step explanation:

<em>The following figure can be drawn from the information given.</em>

<em>We have to find the adjacent side which is between the given angle and 90 degrees.</em>

<em>Tan formula will be applied</em>

Tan (anlge) = opposite/adjacent

Opposite = 12.6

Angle = 49.5°

Adjacent = x

Tan (49.5°) = 12.6/x

x = 10.76 miles

Therefore, the fire is 10.76 miles away from the tower Pikes Peak.

!!

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Determine the equation of the circle with centre (-3;5) and passing through a point (2;-9)
UNO [17]

Therefore, the equation of circle is: (x+3)^{2}+(y+5)^{2} = 100

<h3><u>What is a circle?</u></h3>
  • All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
  • The radius of a circle is the separation between any point on the circle and its center.
  • The radius must typically be a positive integer. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
  • A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.

Here we know that(h,k) = (-3,5)but we are not given the radius.

However, we can find the radius by using the distance formula.

\sqrt{x^{2} +y^{2} }, where x=x_{1} -x_{2} and y=y_{1} -y_{2}

Putting the values, we get:

\sqrt{8^{2} +6^{2} }

The radius comes out to be:

r=10

An equation of the circle with center (h,k) and radius r is

(x-h)^{2} +(y-k)^{2} = r^{2}

Now, substituting the values, we get:

(x--3)^{2} +(y-5)^{2} = 10^{2}

Therefore, the equation of circle is:

(x+3)^{2}+(y+5)^{2} = 100

Know more about circles with the help of the given link:

brainly.com/question/10618691

#SPJ4

7 0
1 year ago
The wingspan of different species of birds is as follows:
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A. albatross - blue jay = 3 1/2 - 39/100
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======================= (2*4)+1/4 - 11/5
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3 0
2 years ago
Help mee!! I will give a branlist answer!!
Nutka1998 [239]
Ok so here u go
<span>Simplifying 6(2x + -11) + 15 = 21        Reorder the terms: 6(-11 + 2x) + 15 = 21 (-11 * 6 + 2x * 6) + 15 = 21 (-66 + 12x) + 15 = 21         Reorder the terms: -66 + 15 + 12x = 21       Combine like terms: -66 + 15 = -51 -51 + 12x = 21     Solving -51 + 12x = 21 Solving for variable 'x'.          Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + 12x = 21 + 51 Combine like terms: -51 + 51 = 0 0 + 12x = 21 + 51 12x = 21 + 51       Combine like terms: 21 + 51 = 72 12x = 72 Divide each side by '12'. x = 6 Simplifying x = 6</span>
4 0
3 years ago
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wlad13 [49]
524
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6 0
2 years ago
Christine runs 10 miles in 75 minutes. At the same rate, how many miles would she ru<br> I miles
Len [333]

Answer:

\frac{46}{5}  miles  [or, 9.2 miles]

Step-by-step explanation:

<u>Complete Question:</u>

Christine runs 10 miles in 75 minutes. At the same rate, how many miles would she ru n in 69 minutes?

<u>Solution:</u>

We need to find the unit rate first and then find our answer. To get unit rate, we need to know the number of miles she runs in "1 minute". So, we will divide number of miles by number of minutes, that is given. Hence:

\frac{10}{75}=\frac{2}{15}

That means in 1 minute, Christine runs 2/15th of a mile.

Now, we want to know how many miles she will run in 69 minutes. We simply multiply unit rate (2/15) by the number of minutes (which is 69). Thus we have:

\frac{2}{15}*69=\frac{2*23}{5}=\frac{46}{5}

In decimal, doing division, that is 9.2 miles

7 0
2 years ago
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