Grade 12 Calculus Help: Find Answers Now!

[JessiMen]

I have a test in a few hours and i have a few review questions that i don't understand its for Grade 12 calculus

 

[Greg]

What are the questions?

 

[JessiMen]

Sorry Uhm how do I send pictures on this because I can't make all the little symbols on here and there's like 7 questions

 

[Greg]

Use the "Insert Image" button: seventh in from the right on the middle row of buttons above the "Reply to Thread" text box.

Let's start with the first one - you can upload the others as we move along (possibly in other threads).

 

[JessiMen]

View attachment 5701

 

[Greg]

The dimensions of a conical tank is of radius 3 in. and height 6 in. Water is added at a rate of $\pi\,\text{in}^3/\text{min}$. Find the rate of change of the water level when the height is 3 in.

\(\displaystyle V=\dfrac13\pi r^2h\)

Get $r$ in terms of $h$:

$$r=\dfrac h2$$

$$V=\dfrac13\pi\dfrac{h^3}{4}$$

Differentiate implicitly with respect to time:

$$\dfrac{dV}{dt}=\dfrac{\pi h^2}{4}\cdot\dfrac{dh}{dt}$$

Substitute known values and solve for $\dfrac{dh}{dt}$:

$$\pi=\dfrac{\pi(3)^2}{4}\cdot\dfrac{dh}{dt}\implies\dfrac{dh}{dt}=\dfrac49$$

Hence the water level is rising at a rate of $\dfrac49\text{ in/min}$.

Ok?

 

[JessiMen]

OH MY GOSH THAT makes so much more sense thanks you so much. I only have two or three more questions left after this that i don't understand. My teacher gave us 65 questions o review and she's only putting 7 on the test
View attachment 5702

 

[Greg]

That image is too difficult to read even with zoom. Can you type it out?

 

[JessiMen]

View attachment 5703

 

[MarkFL]

Now the image is sideways.

 

[JessiMen]

A wind surfer sails from Kingston sailing club with the intention of land in due south of the club on Wolfe Island. The normal summer wind is blowing from the South 42 degrees WEST at 40 knots. If the wind surfer can maintain a velocity of 50 knots, what direction must she sail to guarantee arriving at her planned destination?

 

[Greg]

A wind surfer sails from Kingston sailing club with the intention of landing due south of the club, on Wolfe Island. The normal summer wind is blowing from the S42$^\circ$W at 40 knots. If the wind surfer can maintain a velocity of 50 knots, what direction must she sail to guarantee arriving at her planned destination?

I get S32$^\circ$W as the desired direction.

You want to construct a triangle with one side of length 40 units, one side 50 units and a third side of unknown length (the resultant). Can you see how to orient the triangle? Use the information given to determine the angles of this triangle and then solve for the angle between the sides of 40 and 50 units in length, using the law of sines and the fact that three angles in a triangle sum to 180$^\circ$. From there, you should be able to determine the desired direction.

I know this is somewhat vague but make an effort and if you get stuck post back, showing your work.