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3 years ago

If the arc length shown in blue is 15.5 inches, then theta to the nearest hundredth of a radian is?

1 answer:

3 0

If you need to refer to the figure you can open the pdf file that I attached.

If you do not know the relationship between arc lengths and angles in radians, you can derive it from the circumference of a circle. This is how:

[2π rad / 2π R] = [x / arc] , where R is the radius of the circle, arc is the length of the arc, and x is the angle in radians.

You can solve for the angle x.

x = arc / R

In the figure arc = 15.5 inches, R = 12 inches, and theta is the unknown angle. Then:

theta = arc / R = 15.5 / 12 = 1.29167 radians.

Which rounded to the nearest hundreth is 1.29

Answer: 1.29 radians

Download pdf

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The point (6, 7) is reflected across the y axis. what are the coordinates of the reflection

aev [14]

Answer:

Hello!!

the point (6, 7) is reflected across the y axis. what are the coordinates of the reflection?

(-6, 7)

Step by Step Explanation:

When reflecting (x, y) over the x axis is (x, -y)

When reflecting (x, y) over the y axis is (-x, y)

Hope this helps!

7 0

2 years ago

Read 2 more answers

On a beach trip, Lucy rents a bike from “Wheels by the Waves”, where they rent bikes for $12 plus $3 per hour. If Lucy spent $30

Paul [167]

Answer: 6 hours

Step-by-step explanation: If you write an equation for this scenario it would be y = 12+3x. 12 is the starting value and x represents how many hours the bike is rented, therefore 3 dollars would be added to the initial 12 each hour. So if Lucy spent $30 then it would change to 30= 12+3x. Now you essentially just need to work backwards. Rearrange the equation and move 12 to the left of the equal sign to make 30-12=3x. Combine vairable to make 18=3x. Divide 3x by 3 to isolate x and divide 18 by 3 as well to make it even. This looks like 18/3=3x/3. Meaning it would end up as 6=x.

6 0

3 years ago

The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions

Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

$\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}$

The quadratic equation can now be solve using factorization method:

$\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}$

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

$\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\ \\ Width=x=5\text{ }ft \end{gathered}$

7 0

11 months ago

Solve for h h - 3h - 8 = 14 H=?

sweet [91]

The initial step that must be taken before solving almost any problem is to understand what the problem is asking for us to do and what is provided to us to complete that goal. Looking at the problem statement, we can see that we are being requested to solve for h and we are provided an expression to do so. Let's begin solving the expression by combining like terms.

Combine like terms

$h - 3h - 8 = 14$

$(h - 3h) - 8 = 14$

$(- 2h) - 8 = 14$

Just a quick explanation on what combine like terms means, it basically just means to combine the coefficients of the numbers associated with the same variables. Like in this example we can combine h and -3h because they have have the variable h associated with them.

Add 8 to both sides