Find the gradient of the function at the given point. Function Point f(x, y) = x + 8y (7,3) y + 1 Vf(7, 3) = 15 2 X Find the maximum value of the directional derivative at the given point.

Q: 1. Let f(t) represent the amount of sea level rise, in mm, above mean sea level, where t represents…

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Q: Use the rational zeros theorem to list all possible rational zeros of the following.…

A: We need to find possible zeroes.

Q: Below a student uses the Substitution Rule for a definite integral incorrectly. -4½/2 √x√1-x²dx 71-7…

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Q: A particular dam contains approximately 1,200,000,000,000 cubic feet of water. For a week-long spike…

A: Topic- Algebraic operations We are given, Amount of water in the dam= 1,200,000,000,000 cubic feet…

Q: y² Consider the paraboloid f(x,y)=4- and the point P(6,0) on the level curve f(x,y) = 0. Compute the…

A: I am attaching image so that you understand each and every step.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. √6x² + 2x +7 dx 3 X…

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Q: Graph f(x)=3* and g(x) = log 3x in the same rectangular coordinate system.

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Q: x²y² Find the point on the paraboloid z = + that is closest to the point (3,0,0). 4 25 Hint: Let (x,…

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Q: Question Estimate (4x² + 3) dx using the midpoint rule and 4 subintervals. Enter an exact value.…

A: To evaluate: ∫024x2+3dx Let fx=4x2+3 Now, interval is from 0 to 2 We have 4 subinterval, therefore…

Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

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Q: f we want to integrate a rational function using partial fraction decomposition, what is the first…

A: if we want to integrate a rational function using partial fraction decomposition,   Step 1: Factor…

Q: 3. Let f(x, y) = cos(ex) + 4xy + 4y + 5 and P = (-1,3). a. b. C. Find the rate of change of f at P…

A: Concept: A vector field represents a function's gradient. It is produced by taking the scalar…

Q: 17. The science club members are to work in pairs on an experiment. a) If there are eight members…

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Q: Sketch the region that lies between the curves y = 2 sin(x) and y = 2 cos(x) from z=0 to z=0.7.…

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Q: Fill in the blank. The symbol C, represents a constant. Write this result as a linear first-order…

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Q: 6.8 23 & 24

A: We know that,

Q: ii. The curve with equation y = 2-x intersects the curve with equation y = 3 * 2x at the point P,…

A: B(ii) and B(iii) has been solved as per the requirement of the student.

Q: For the function f(x) = -3 sin (x- two periods. 3π x - ³7) determine its amplitude and period, and…

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with  so here we…

Q: A car was valued at $44,000 in the year 1992. The value depreciated to $14,000 by the year 2004. Use…

A: Given data, Principal P=$44000 Amount A=$14000 Time t=2004-1992=12 years

Q: 6. S x³ √9+ x² dx x = 3 tan 0

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Q: Graph the solution, to the following system of inequalities. 4x+3y212 -4x+7y<21 Then give the…

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Q: Let f(x) be a function. The average rate of change between = a and * = b is equivalent to: O The…

A: From the given statements, we have to find the equivalent meaning.

Q: if cost and revenue are given by C(x) = 187 +0.8x and R(x) = 8x-0.02x

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Q: Find the general solution for the problem in the form y=yc+yp y'' - 3y' - 4y = 2 + 6t + cost

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Q: Differentiate the following function. 3 y=xaex dy CX

A: We know, d/dx(xn)=nx(n-1), for any real number n  And d/dx(ex)=ex

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t)= 0.041³…

A: Given S(t)=0.04t3+0.8t2+4t+3We need to find(A)S'(t)(B)S(7) and S'(7)(C)Interpret S(13)=278.08 and…

Q: 11. Refer to the figure and find the volume generated by rotating the given region abou specified…

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Q: Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan B = B 11 Figure 1 A…

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Q: Find a particular solution Y(t) of y"" — 2y" — y' + 2y = t

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, write the…

Q: Find the first and second derivatives of the following function: h (x) h'(x) h" (x) = - 330 = tan-1

A: Given h(x)=tan-1(x2)We need to findh'(x) and h''(x)

Q: #8) Find the derivative of the function. y = sech(6x²)

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Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

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Q: A firm's revenue function from the sale of S21 is R(x) = 2x² - 9x - 221 and the firm's total cost…

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Q: In 1940, there were about 10 brown tree snakes per square mile on the island of Guam, and in 1993,…

A: Given data, No. of snakes in 1940 N0 =10 per sq. mile No. of snakes in 1993 N=10000 per sq. mile…

Q: help, other anser is unreadable

A: The volume for solid of revolution between curves is the volume of object between a curve fx and a…

Q: Use any method to evaluate the integral. S 243 dw w²√√81-w² 243 dw w²√√81-w² W (Type an exact…

A: Given data:- ∫243w281-w2 dw

Q: An unknown radioactive element decays into non-radioactive substances. In 480 days the radioactivity…

A: The decay formula: Nt=N0e-λtwhere Nt=Amount of substance left after 't' days            N0=Intial…

Q: Consider the ODE (a) The general solution y(t) of the corresponding homogenous ODE is Yh(t) Osin(at)…

A: NOTE: Refresh your page if you can't see any equations. . the given DE is

Q: Find the time it takes for $5,600 to double when invested at an annual interest rate of 8.6%,…

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Q: Evaluate the integral. +∞ S 3 x 2xe dx

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Q: h response xk and input u = 8k is modelled by the difference e

A: Solution of the problem as follows

Q: When food is left out at room temperature for a long period of time, mold begins to grow on it. For…

A: When food is left out at room temperature for a long period,mold begins to grow on it.For…

Q: a. Find f'(x) for: f(x) = (5x + 2)/(x^2 + 2x - 2) b. Find the derivative of the tangent line at x =…

A: Quotient Rule of Differentiation : ddx(uv) = v.dudx-u.dvdxv2.

Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for (a) lim X (b) lim X + +³7 - 32x…

A: Use limit concept

Q: Example 2 Sketch the feasible region for the following set of constraints: 3y - 2x ≥ 0 y + 8x ≤ 52 y…

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Q: Sunset Lake is stocked with 2000 rainbow trout and after 1 year the population has grown to 5200.…

A: I am attaching image so that you understand each and every step.

Q: Given the equation below, find 38x5 +10x⁹5y + yº 95 9 dy dx = y = = 49 dy da Now, find the equation…

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Q: 1 F(x) e(u) Set up an integral to find the area A of the region enclosed between f(x) = 0.9x² + 2…

A: Given Data: f(x)=0.9x2+2 g(x)=2

Q: Find the indefinite integral. (Use C for the constant of integration.) sinh(1 − 6x) dx

A: The given integral: ∫sinh1-6x dxWe need to evaluate the indefinite integral.

Q: Make a sign diagram for the derivative of the rational function. 4x x² + 1 f(x) = ---Select--- v…

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