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3 years ago

A circle with circumference 10 has an arc with a 162 degree central angle. What is the length of the arc

1 answer:

6 0

Answer: The length of the is 4.5 cm when the measure of the central angle is 162 degrees.

If the measure of the central angle is 162 degrees, that means that is comprises 45% of the circle. 162 / 360 = 45%

Therefore, the arc is also 45% of the circumference. If we multiply 10 by 45% we get an arc length of 4.5 cm.

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Work out the formula of the nth term in the following quadratic sequence:<br> 19, 15, 9, 1...

Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference. Let's verify that.

n 1 2 3 4

f(n) 19 15 9 1

1st diff -4 -6 -8

2nd diff 2 2

We see that we got a constant second difference. We could just extend that and work back up to get more values.

n 1 2 3 4 5 6 7

f(n) 19 15 9 1 -9 -21 -35

1st diff -4 -6 -8 -10 -12 -14

2nd diff 2 2 2 2 2

That's just an aside; we're after the general formula. We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an² + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c = 9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly. Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0

3 years ago

According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while

KonstantinChe [14]

Answer:

0.0656

Step-by-step explanation:

For each message, we have these following probabilities:

90% probability it is spam.

10% probability it is legitimate.

Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:

The first four all spam, each with a 90% probability.

The fifth legitimate, with a 10% probability.

$P = (0.9)^{4} \times 0.1 = 0.0656$

3 0

3 years ago

Please help me!! Due today

klasskru [66]

Answer:

Step-by-step explanation:

y = (-1/4)x - 4 has a y-intercept of (0, -4). Place a dark dot at (0, -4).

Now we use the info from the slope, -1/4:

Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down. You will now be at (4, -5). Place a dark dot there.

Then draw a straight, solid line through (0, -4) and (4, -5).

6 0

3 years ago

Which is the graph of<br><img src="https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7Bx%20%2B%201%7D%20-%202" id="TexFormula1" t

Anna11 [10]

ANSWER

See attachment.

EXPLANATION

The given function is

$y = \sqrt[3]{x + 1} - 2$