I’m here to help.
For this question here you need to use the sine formula for the area of a triangle and figure out the area of the sector

I’ll take you through it step-by-step

Area of the arc:

We only have 68.9 degrees out of 360 and we need to use the formula for the area of a circle.
Formula of a circle = pi x radius squared

68.9/360 x pi x 86.1184= 51.78 (2dp)

Area of triangle:
As you can see we have no height so we must use the sine formula for the area of a triangle.
Formula= 1/2abSinC

You should end up with
0.5 x 9.28x 9.28 x Sin(68.9)= 40.17 (2dp)

Now since you want the area of the segment shaded, just find the difference between these two values.

51.78-40.17 = 11.61
Answer= 11.6cm squared

Hope this helped!

3 0

3 years ago

Let f (x) = 3x − 1 and ε > 0. Find a δ > 0 such that 0 < ∣x − 5∣ < δ implies ∣f (x) − 14∣ < ε. (Find the largest

s344n2d4d5 [400]

Answer:

This proves that f is continous at x=5.

Step-by-step explanation:

Taking f(x) = 3x-1 and $\varepsilon>0$ , we want to find a $\delta$ such that $|f(x)-14|$

At first, we will assume that this delta exists and we will try to figure out its value.

Suppose that $|x-5|$ . Then

$|f(x)-14| = |3x-1-14| = |3x-15|=|3(x-5)| = 3|x-5|< 3\delta$ .

Then, if $|x-5|$ , then $|f(x)-14|$ . So, in this case, if $3\delta \leq \varepsilon$ we get that $|f(x)-14|$ . The maximum value of delta is $\frac{\varepsilon}{3}$ .