a. c = 3/2 b. c = 1/2 c. c = 0 d. c = - 2 e. none of the above

Given that g(t) is continuous, find the value of c: g(t) = {ct + 2 if

3/2 is ans

3/2 is answer because it is

the hell oobleck

oobleck tripping

Well, this problem seems to be a bit tricky, but don't worry, I'm here to help! Let's break it down step by step.

We are given that g(t) is continuous, which means that the function should be defined and have no abrupt jumps or holes in its graph.

Now, let's consider the two cases separately:

Case 1: t < -2
For this case, g(t) is defined as ct + 2.

Case 2: t >= -2
For this case, g(t) is defined as cos(pi*t/2).

Now, in order for g(t) to be continuous, the two cases must agree at the point where t = -2.

So, let's find the value of c by plugging in -2 into both expressions:

For the first case (t < -2):
g(-2) = c*(-2) + 2 = -2c + 2

For the second case (t >= -2):
g(-2) = cos(pi*(-2)/2) = cos(-pi) = -1

Since both cases must agree at t = -2, we can set the two expressions equal to each other:

-2c + 2 = -1

Simplifying this equation, we subtract 2 from both sides:

-2c = -3

Finally, we divide both sides by -2 to solve for c:

c = -3/-2 = 3/2

So, the value of c that makes g(t) continuous is c = 3/2.

Looks like the answer choice (a) c = 3/2 matches our solution! Isn't math just full of surprises?

I hope this answer brings a smile to your face!

To find the value of c, we need to evaluate g(t) at t = -2.

Let's start by evaluating g(t) at t = -2 using the given definition:

g(-2) = cos(pi(-2)/2) = cos(-pi) = cos(pi) = -1

Next, we compare this with the other part of the definition:

g(-2) = c(-2) + 2

Since we have already found that g(-2) = -1, we can substitute this into the equation:

-1 = c(-2) + 2

Now, we can solve for c:

c(-2) = -1 - 2
c(-2) = -3

Finally, dividing both sides of the equation by -2:

c = -3/-2
c = 3/2

Therefore, the value of c is 3/2.

Therefore, the correct answer is (a) c = 3/2.

you need the two pieces to agree at t = -2. That is,

-2c + 2 = cos(pi * -2/2)
Just solve for c.