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1 year ago

An angle of 1.5 rad intercepts an are on the unit circle. What is the length of the intercepted arc?

Mathematics

1 answer:

Maslowich1 year ago

4 0

The arc length is related to the angle and length of the radius of the circle via the equation

$S=r\theta$

This is a unit circle, hence, r = 1. The angle is given as 1.5 radians or can be written as 1.5π. Hence, the length of the intercepted arc is computed as

$\begin{gathered} S=(1)(1.5\pi) \\ S=1.5\pi \end{gathered}$

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NEED HELP ON THIS PLEASE! Oregon Trail: Percents.

harina [27]

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5 0

2 years ago

The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing w by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

1 year ago

Please help Thank you

Kaylis [27]

Answer:

I don't know sorry :)

Step-by-step explanation:

6 0

3 years ago

When plotted on a grid, the paths between four neighborhood houses form the shape of a kite as shown.

KatRina [158]

Answer:

The area of the figure is 1,000 square feet

Step-by-step explanation:

we know that

The area of the kite ABCD

is equal to

$A=\frac{1}{2}[AC*BD]$

where

AC and BD are the diagonals of the kite

we have

$BD=50\ ft\\AC=40\ ft$

substitute

$A=\frac{1}{2}[40*50]=1,000\ ft^2$

3 0

3 years ago

Evaluate the expression for x = 3.4, x = 7.6

Scrat [10]

u have to multiply both of the numbers

3 0

2 years ago