Step-by-step explanation:
1.


Therefore,

2.


Use the identity

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

Solving for tan x:

a. By the fundamental theorem of calculus, the velocity function is

The particle starts at rest, so
, and we have

Then the position function is

with
, so

b. The particle is at rest whenever
; this happens for

where
is any integer.
The LCM is of 128 and 32 is 128
(C)
fraction of the marbles now in the bag is blue.
<h3>
What is a fraction?</h3>
- A fraction is a portion of a whole or, more broadly, any number of equal parts.
- In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
- A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line.
- Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
To find what fraction of the marbles now in the bag is blue:
- Important information is that immediately before the last step blue marbles formed
from the marble in the bag. - That means that there were
blue and
other marbles, for some
. - When we double the number of blue marbles, there will be
blue and
other marbles. - Hence, blue marbles now form
all marbles in the bag.
Therefore, (C)
fraction of the marbles now in the bag is blue.
Know more about fractions here:
brainly.com/question/17220365
SPJ4
Complete question:
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 1/2
Answer:
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Step-by-step explanation: