Physics Electrostatics Level: Misc Level

In Figure a, small 80 g insulating sphere is suspended from point p by a silk thread that in 50 cm long.The sphere bears an unknown electric charge Q.A positive point charge q=+2.0uC is brought to a position directly below p,and the sphere is repelled to a new position,30 cm to the right of q,asshown.The charge Qin uC, is closest to;

A)+1.5

B)+2.0

C)+2.5

D)+3.0

E)+3.5

Mathematics Functions Level: Misc Level

sketch the graph of f (x)

Mathematics Functions Level: Misc Level

find the coordinates of any reflection points

Mathematics Calculus Level: Misc Level

find the coordinates of any relative extrema, and classify as maxima or minima.

Mathematics Calculus Level: Misc Level

the annual world rate of water use t years after 1960 was approximately 860e to the.04t power cubic kilometers per year.how much water was used between 1970 and 1980?

Mathematics Calculus Level: Misc Level

find all relative extrema for f(x,y)=7x2(squared)-5xy+y2(squared)+x-y, and classify each as a maximum or minimum.

Mathematics Calculus Level: Misc Level

find the volume of the solid bounded by f(x,y)=9-x29squared)-y2(squared) over the region for which 0 is less than or equal to x less than or equal to 2 and 0 is less than or equal to y and is lessthan or equal to 1.

Mathematics Calculus Level: Misc Level

the marginal cost of producing x units of a certain product is C, (x)=6x2 (squared)-4. Find the cost function C(x) if the cost of producing 3 units is $8.

Mathematics Calculus Level: Misc Level

A cylindrical can of radius 5cm and height 12 cm is leaking water at a rate of 4 cm 3 (cubed) per minute. How fast is the height of the water changing when the water level is 3 cm from the bottom of the can.(this is a,,related rates,, problem. Volume of a cylinder is given by V=pie r2(squared)h.)

Mathematics Calculus Level: Misc Level

Consider the function y=f (x)=6x-x2. What is the average value of the portion above the x-axis?First sketch the graph and clearly show the x and y intercepts.

Mathematics Calculus Level: Misc Level

A conical container open to the top is being filled at the rate of 10 ft3/min.The container is 20 feet high with a radius of 6 feet at the top.How rapidly is height of the fluid increasing when the height is 10 feet?

Hint;1; Express the cone,s liquid volume in terms of r and h. Then express r in terms of h using the given dimensions of the cone.That allows you to express the liquid volume in cone as a function of just h, the height of the liquid.

Hint;2;Keep n,in your expressions until the very end-tider.

Mathematics Calculus Level: Misc Level

We have a right triangle with one leg growing and one shrinking.By how much is the hypotenuse growing(or shrinking0 if x is increasing at 6 ft/sec and y is decreasing at 3 ft/sec when x= 60 ft and y=80 ft?Be sure to indicate if the hypotenuse is growing or shrinking.Be careful with the signs of the derivatives.Yes,you must first find the hypotenuse.

Mathematics Calculus Level: Misc Level

The velocity of a particle is given by v(t)=t/(t2+4)^0.5. Find the distance traveled during the first four seconds.Give the exact result using radicals; then a three-decimal place approximation.

Mathematics Integration Level: Misc Level

For f (x)=x^2 (5-7x^3)^4 find integral of f(x)

Mathematics Probability Level: Misc Level

On further reflection,the professor remembered that Tariq, Sean,Steven and Victoria each asked at least 3 questions, while Emily,Mila,Thomas and Eric didn,t ask any In light of this,in how many different ways could the 35 questions have been distributed among the students