Answer:
Step-by-step explanation:
[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]
Recall that we can express the squared trig functions in terms of cos(2x). That is,
And so inverting these,
.
Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).
Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).
So then,
This is now integrable (phew),
"Samira ran 3 miles more that twice the number of miles Ada ran." This means that to get the number of miles that Samira ran, we will multiply the number of miles that Ada ran and then add 3 to the product.
Assume that Ada ran m miles, the following the steps mentioned above, we can calculate the number of miles that Samira ran as follows:
Samira ran: 2m + 3 miles
Comparing this to the choices, we will find that the correct choice is the second one:
<span> If Ada ran m miles, then Samira ran 2m + 3 miles.</span>
Answer:
The answer is 198.
Step-by-step explanation:
First you need to know how much is a batch of cookies which is 60. Since she made 3 batches that means you will need to multiply 3 by 60, which will give you 180 cookies. Next you will need to add 2 to 10 because thats how much were took. That equals 12. Subtract 12 from 180 and that will give you 168. Last but not least you will need to add 30 because that is half the batch of cookies her neighbor gave to her. So 168 plus 30 equals 198.