MATHEMATICS
MIDDLE SCHOOL

Answer:

Answer:

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Step-by-step explanation:

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Answer:

COLLEGE

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answer is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =

Answer:

Therefore, the solution is:

Step-by-step explanation:

We calculate the given integral. We use the substitution t = 7x.

Therefore, the solution is:

HIGH SCHOOL

a kayaker travels x miles per hour downstream for 3 hours. on the 4-hour return trip, the kayaker travels 1 mile per hour slower. how far did the kayaker travel in total?

3x is the miles from downstream

4 (x - 1) is the return trip

Solution:

3x = 4 (x - 1)

3x =4x - 4

-x = -4

x = 4

The outward journey 3x = 12 miles

Return journey is same length

Therefore the distance travel is 24 miles

4 (x - 1) is the return trip

Solution:

3x = 4 (x - 1)

3x =4x - 4

-x = -4

x = 4

The outward journey 3x = 12 miles

Return journey is same length

Therefore the distance travel is 24 miles

Answer:

The answer is 24 miles.

Step-by-step explanation:

We know that distance = rate * time

Length of the journey = from downstream

Length of the journey = from return trip

As the distance is same, we will equate both the journey lengths.

Solving for x;

x = 4

Thus the forward journey, = 12 miles.

Return journey will be of same length that is 12 miles.

The total distance traveled is miles.

Therefore, the answer is 24 miles.

HIGH SCHOOL

Lim h--> 0

(sin (pi/6+h) - sin pi/6)/ h ...?

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Note that expression implies the derivative of sin(x) where x = π/6. We know that the derivative of sin(x) is cos(x). Therefore, cos(π/6) = √(3)/2.

Note that expression implies the derivative of sin(x) where x = π/6. We know that the derivative of sin(x) is cos(x). Therefore, cos(π/6) = √(3)/2.

HIGH SCHOOL

The _____ of a cone is the curved surface that connects the base of a cone to the apex of the cone.

Lateral surface or side is the name of the curved surface.