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klasskru [66]
3 years ago
8

Bryan drives up to a traffic circle from Elm Street. He drives 15 meters around the circle is a perfect circle with a radius of

10 meters, at what angle is Maple Street to Elm Street?

Mathematics
2 answers:
Tom [10]3 years ago
8 0

Answer:

<h2><em> 85.9° </em></h2>

Step-by-step explanation:

Using the formula for calculating the length of an arc to get the angle of Maple Street to Elm Street;

Length of an arc = θ/360 * 2Πr  where r is the radius of the circle.

Given r = 10m and length of the arc = 15m

On substituting;

15 =  θ/360 * 2π(10)

15 = θ/360 * 20π

θ/360 = 15/20π

θ/360  = 0.2387

θ = 360* 0.2387

θ = 85.9°

<em>Hence Maple street is at 85.9° to Elm street.</em>

<em></em>

elixir [45]3 years ago
4 0

Answer:

\approx \bold{85.98^\circ}

Step-by-step explanation:

Given that

Radius of circle = 10 metres

Bryan drives 15 metres around the circle.

To find:

The angle of Maple street to Elm street = ?

Solution:

Kindly refer to the image attached.

The Elm street meets the circle at A.

Maple street at B.

Given that arc length AB = 15m

Radius of circle = 10 m

We have to find the angle of arc.

Let us use the formula:

\theta = \dfrac{l}{r}\\\Rightarrow \theta = \dfrac{15}{10} \\\Rightarrow \bold{\theta = 1.5\ radians}

Converting to degrees:

\pi\ rad = 180^\circ\\1.5\ rad = \dfrac{180}{\pi} \times 1.5^\circ\\\theta \approx \bold{85.98^\circ}

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Find all solutions to x³+3x² − 9x − 27 = 0 by factoring the equation.
SCORPION-xisa [38]

Answer:

The solutions are x=-3,\:x=3

Step-by-step explanation:

To factor this cubic polynomial x^3+3x^2-9x-27 you must:

  • Group the polynomial into two sections

x^3+3x^2-9x-27=\left(x^3+3x^2\right)+\left(-9x-27\right)

  • Factor out -9 from (-9x-27)

(-9x-27)=-9\left(x+3\right)

  • Factor out x^2 from (x^3+3x^2)

(x^3+3x^2)=x^2\left(x+3\right)

x^3+3x^2-9x-27=-9\left(x+3\right)+x^2\left(x+3\right)

  • Factor out common term x+3

-9\left(x+3\right)+x^2\left(x+3\right)=\left(x+3\right)\left(x^2-9\right)

x^3+3x^2-9x-27=\left(x+3\right)\left(x^2-9\right)

  • Factor x^2-9

x^2-9=\left(x+3\right)\left(x-3\right)

x^3+3x^2-9x-27= \left(x+3\right)\left(x+3\right)\left(x-3\right)

x^3+3x^2-9x-27=\left(x+3\right)^2\left(x-3\right)=0

  • Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0

x+3=0, \quad{x=-3}\\x-3=0, \quad{x=3}

The solutions are

x=-3,\:x=3

3 0
2 years ago
Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).
Amanda [17]
Since you subtract 16 from the y value, P is (-2, 6), and the y value comes second (meaning that it's 6), we get 6-16=-10
4 0
3 years ago
Read 2 more answers
The Taylor family went on vacation. They traveled 412 miles on Monday. At the end of the day Tuesday, the average speed of the c
mixer [17]

Answer:

d = 56x + 412

Step-by-step explanation:

To find the total number of miles traveled on Monday and Tuesday, use a linear equation to write the function.

y = mx+b where m is the speed or rate of change and b is the starting point.

The starting point on Tuesday is 412 miles. This is b.

The number of miles traveled on Tuesday is found by calculating 56 miles times the number of hours traveled.  This is the slope or m.

So the equation is d = 56h + 412.

7 0
3 years ago
What is the answer to 11/12×6=​
Mademuasel [1]

Answer:

\frac{11}{2}

Step-by-step explanation:

\frac{11}{12} x 6 = \frac{11}{2}

5 0
3 years ago
DESPERATELY NEED HELP
In-s [12.5K]

Remark

You must use the sin law to find this.


\dfrac{Sin(75)}{22} = \dfrac{Sin(x)}{12}

Multiply through by 12

12 * \dfrac{Sin(75)}{22} = \dfrac{Sin(x)}{12} *12


\dfrac{12*sin(75)}{22} = \text{sin(x)}

0.5269 = sin(x)


Now you have to use the inverse of the sine function.

Use your calculator for that

2nd F

sin-1

(0.5269)

= 31.79 degrees. <<<<<< Answer.


There sometimes is a second answer. I don't think there is in this case.


3 0
3 years ago
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