Coast Guard Patrol Search Mission The pilot of a Coast Guard patrol aircraft on a search mission had just spotted a disabled fishing trawler and decided to go in for a dloser look. Flying in a straight line at a constant altitude of 1000 ft and at a steady speed of 260 ft/s, the aircraft passed directly over the trawler. How fast (in ft/s) was the aircraft receding from the trawler when it was 1600 ft from the trawler? (Round your answer to one decimal places.) 1000 ft ft/s

Q: Suppose that the demand for a product is given by  2p2q = 30,000 + 5000p2. (a) Find the elasticity w...

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Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: Simplify the expressions

A: We know  alogax=x alogx=logx2  

Q: The graph of a function f is shown. y4 800 400 20 40 60 (a) Find the average rate of change of f on ...

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Q: Determine whether or not F is a conservative vector field. If it is, find a functionf such that F = ...

A: Given Fx,y=2x-5yi +-5x+8y-6j

Q: domain of (g o f)(x)

A: Consider the following functions: fx=3x-17gx=2x-3 gfx=2fx-3=23x-17-3=23x-1-217=23x-227=143x-22

Q: Graph the family of polynomials in the same viewing rectangle, using the given values of c. P(x) = ...

A: Given, P(x) = x4 − cx;    c = 0, 1, 8, 27

Q: A ball dropped into a hole reaches a depth d = 4.9t² meters, where t is the time in seconds since it...

A: Given equation : d=4.9t2 where d is the depth of the hole and 't' is the time in seconds we need to ...

Q: Find the derivative of ry = -3+x*y° using implicit differentiation.

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Q: Verify that the general solution satisfies the differential equation. Then find the particular solut...

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Q: solve for x: ln(x-1)+ln(x+1)=ln(x2+9x+2)-(x-2)

A: Consider the given logarithmic function and the addition and quotient properties for logarithmic fun...

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x appraoa...

A: The given expression limx→∞cothx

Q: that S cot udu=In ace n Sin ul tC.

A: Explanation is given below..

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then ...

A: ∫2x3-5x+7dx=2∫x3 dx -5∫x dx +7∫dx          [    ∫xn  dx=xn+1n+1    ]=2x44-5x22+7x=x42-5x22+7x∫2x3-5x...

Q: A graphing calculator is recommended. A digital delay device echoes an input signal by repeating it ...

A: Given: The device receives the pure note: f1(t)=6sin(t)  The device echos the pure note: f2(t)=6cos(...

Q: Find the limit

A: Consider the given function, limx→∞sin2xx since is a continuous periodic function, as sin2x∈-1,1. as...

Q: In Exercises 41-44, verify by differentiation.

A: Evaluate, ∫x+136dx        ...(1)

Q: How?

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Q: Calculus hw

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Q: find domain of (f o g)(x)

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Q: Use technology to solve the system of equations. Express all solutions as decimals, rounded to one d...

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Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution, ent...

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Q: y" -2y'+5y=0

A: Given differential equation, y''-2y'+5y=0

Q: 17

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Q: The Power Rule for Rational Functions. Assume that p and q are non-zero integers.Then   d/dx(xp/q) =...

A: We know  ddx(xn)=nxn-1 Here n=p/q  

Q: Your car is traveling 50 miles per hour due south and is half a mile north of an inter-section. A po...

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Q: The solution of Sinx dx - x sinx+ y cosx= 0 is (y– 1) sinx =? A C-x sinx B C+ x cosx с-х cosx D C+ x...

A: sinxdydx-xsinx+ycosx=0sinxdydx+ycosx=xsinxddx(ysinx)=xsinx

Q: Please show step by step instructions

A: Given that: The function f(x) has a domain of all real number except x=6 and the derivatives of the ...

Q: Simplify and condense 2(ln(x)-ln(x+1)+3/2ln(x-1))

A: 2(ln(x)-ln(x+1)+32ln(x-1))=2lnxx+1+lnx-132

Q: The radius of a sphere as a function of a volume

A: The volume V of a sphere with radius r is given by the formula V=43πr3.

Q: Use a double integral in polar coordinates to find the area of the region bounded on the inside by t...

A: Shaded region above x-axis, R=r,θ:0≤θ≤π2,4≤r≤41+cosθ Therefore, the area of the shaded region above ...

Q: Use implicit differentiation to find dy/dx. (a) y=x+1/y+ 1 (b) tan y=x

A: Given,           (a) y =x + 1y + 1           (b) tan y = x 

Q: If H is the integrating factor of 6xy dx + 5(x² + y)dy= 0, then compute H(8). A 1 в) 2

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Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt(5-x)    3<...

A: Given curve is y=5-xdydx=-125-x Now, area of the surface obtained by revolving y=f(x) from x=a to x=...

Q: For the function -a- x3 - 2x?,

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Q: Find the average value of the function f(x) = (2lnx)/x , over the interval [1, e]

A: we have to find the average value of the  function f(x) = 2lnxx, over the interval [1, e]

Q: Given cost and revenue functions C(q)=q^3-11q^2+59q+5000 and R(q)=-3q^2+24000q, what cost is incurre...

A: Given, Cost function, C(q)=q3-11q2+59q+5000 and Revenue function R(q)=-3q2+24000q

Q: Solve the equation: tan 2x = √3, 0 ≤ x < 2π.

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Q: A population P is initially 550. Find an exponential growth model in terms of the number of time per...

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Q: 9

A: Given Data: Function: fx, y, z=zexy Point: x, y, z=0, 1, 2   The gradient of the function is, ∇fx, y...

Q: Use a linear approximation (or differentials) to estimate the given number. (8.06)2/3

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Q: Let f(x) = 3√(x + 1) − 4 = (x + 1)1/3 − 4. Use the limit definition of the derivative to show that f...

A: Consider the given function: fx=x+13-4=x+113-4 Vertical tangent at point indicates that at that poin...

Q: Let f(x, y) = 3x 2 − 5x 3y 2 + y 4 . Calculate all 1st and 2nd order partial derivatives of f.

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Q: A patient is administered 250 mg of a therapeutic drug. It is known that of 45% of the drug is expel...

A: Let the exponential model be At=A0ert At t = 1 hour A(t) = 55% of 250 mg = 137.50 mg A0 = 250 mg

Q: Determine whether the integral is convergent or divergent. 1 dx a (x - 7)32 O convergent O divergent...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.