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Given f(x,y) = sin (2x+3y), P(-6, 4), u = √(3)/2i-1/2j. Find:
1. The gradient of f.
2. Evaluate the gradient of f at point P.
3. Find the directional derivative of f passing through P in the direction of the vectur u.
What is the current weekly profit? How much profit would be lost if production and sales dropped to 9 laptops weekly? What is the marginal profit when x = 10?
The surface area of this pyramid is 189cm squared The area of the square base is 49cm squared. What is the area of one triangular face of the lateral surface?
Assume that the nonzero complex numbers from group G with respect to multiplication. If a and b are real numbers and i=sqrt -1, the conjugate of the complex number a+bi is defined to be a-bi.
The deception, however, is that the bond is not redeemable for 45 years. Find the real value of the "guarantee" that is, find the present value of $1800 in 45 years.
Find the continuous growth rate per hour. Write your answer as a percentage. Round your answer to one decimal place.
Celcius is 343 m/s. However the air temperature is 35 degrees Celcius, so the speed of sound is not 343 m/s. Assume that air behaves like an ideal gas, and find the wavelength of the sound.
1 three-person problem of points pascal fermat and their old friend the chevalier de mere each put ge10.00 into a pot
For the squeeze theorem to be applicable in this case, the constant A must be equal to a specific number. Find this number and assuming that A is that number for which the squeeze theorem is applicable, find lim x->48 f(x)
A company executive concludes that an accountant must have made a mistake because she prepared a report stating that 90% of the company's employees earn less than the mean salary.
If you have 284 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Give your answer correct to the nearest square foot.
A client has an order for a foot soak prepared with 25% povidine iodine and the total volume of preparation is to be 1 liter. How many mls of povidine/iodine should be used?
Find the volume of the ellipsoid generated by rotating around the x axis the region bounded by the ellipse with the equation (x/a)^2 + (y/b)^2 = 1
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