A balloon leaves the ground 30 m from an observer. If it rises at the rate of 2 m/s, how fast is it receding from the point of observation when it is 40 m above the ground?

Q: In Problems 67-72, use the demand equation to find the revenue function. Sketch the graph of the rev...

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Q: (2 + 5æ) ei dr 9, 2.

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + 3.4 1 1 + + 5.6 2.3 4.5 (Use symbolic notation and ...

A: Given:-     To find:- S2  S4  S6

Q: Determine the behavior of the functions defined below. Note that it is common to write g(x) → 0" to ...

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Q: 5dx If Verz+1= 2, what is the value of b? %3D A.) 2 B.) 4 C.) 8 D.) 9 A D B A

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Q: 9. An object is shot upwards from ground level with an initial velocity of 3 meters per second; it i...

A: When a object is shot upward (vertically) , its obtained height is given by                   H = (u...

Q: x²-16 Find k so that f(x)={ x-4 is continuous for all x. k = k ;x=4

A: Given,f(x)=x2-16x-4;      x≠4k          ;       x=4 Here f(4)=4limx→4f(x)=limx→4x2-16x-4limx→4f(x)=l...

Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero betw...

A: Given function,f(x)=9x3+10x+6 between -1 and 0Therefore ,f(-1)=9(-1)3+10(-1)+6f(-1)=9(-1)-10+6f(-1)=...

Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve y = ...

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Q: Let f(x, y) = (4x – y)". Then a²f даду dxðydx dx²dy

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Q: 1. 4x cos(2 – 3x) dx

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Q: v(v² –1)dv v² +1

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Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx b...

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Q: The Laplace Transform of

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Q: An open-box with a square base is to have a volume of 500 cubic inches. The material for the top and...

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Q: (sin x 1) dx + (cos x+ 1) dx = C.)-1 D.) - (1+) A.) -89 В.) -91 A B в) А

A: Given:       ∫-π40sinx-1dx+∫0-π4cosx+1dx Apply sum rule:         ∫fx±gxdx=∫fxdx+∫gxdx      =∫-π40sin...

Q: 3x 3x 16 cos + isin 4. 4. Sa 5x 34 cos + isin 3 3

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Q: Linear differential equetion with constand coefficients -メ ダーンツ e

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Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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Q: J, 4. lim X-3 x2 - 9 x - 3 lim X3 x2 – 2x – 3 5. X - 3 lim X"i x2 – 2x – 3 6.

A: We need to find limit.

Q: For the Ordinary DE y '= f (x, y) to be guaranteed to have a unique solution containing the point (x...

A: Here we have to find when the ordinary differential equation y'=f(x,y) to be guaranteed to have a un...

Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = 6x from...

A: moment about the x axis is given by Mx=12∫abf(x)2-g(x)2dx

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increas...

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. S 1, 0sx s 1 x > 1 ...

A: Given that dydx+y=fx  , y0=1  fx=1  ,0≤x≤1-1    x>1Solution:When 0≤x≤1dydx+y=1 this is the linear...

Q: (sin x – 1) dx + (cos x + 1) dх %— 0. D.) - (1+) А.) —89 C.)- 1 В.) —91

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Q: 1 k + 2 k=4

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is x...

A: Given query is to rewrite the integrand in integrable manner.

Q: Evaluate f*27 dx. x+3 A.) + 9x + C B.) 3 3x2 + 9x + C 3x2 C.) 9x + C 2 3x2 D.) ++9x + C I + +

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Q: 1 Find the derivative of 24 – 3x² +5 글(21-3교2 + 5)글 (4z3 - 6z) 글 (21-3교2 + 5)굴 This function is not ...

A: We can take logarithmic to solve it easily.

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e- sin x and passes thr...

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Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

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Q: What is the position function?

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Q: a. Y= x* + 1 а. a²x b. Y = a²+x?

A: Follow the procedure given below.

Q: P(#) Question 4: When working with rational functions of the form f (x) = and the function does inde...

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Q: Given f (x) = {r²+ k_ if-1< x skx – 3 if x<-1 | . Find the value of k such that lim f(x) exists. X--...

A: Topic = Functions

Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x² + 10. ...

A: According to the question: It is given that dPdx=0.0006x2+10. we have to find P when x=100. Now  dPd...

Q: If f(x) = Vr, match each formula to its corresponding graph. the graph in red 1. g(x) = -f(2x) 2. h(...

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Q: Consider the graph of f. y 4 3 1 1 2 2 3 4 5 6 7 8 9

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Q: Question 8 ... (sin x – 1) dx + | (cos x + 1) dx = 4 C.) – 1 D.) - (1+) А.) —89 В.) —91 2 A A в) в D

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Q: A. Manually Sketch the curve with the given polar equation by first sketching the graph of as a func...

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Q: road length (in kilometers), T is the total county land area (in hundred-acres (Ha)), U is the urban...

A: We will find the number of accidents. 

Q: Q3 Given the following non-homogeneous system of first-order linear differential equation: yi' = 5y,...

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Q: 5,4 R(x,y) = 3x* - 3x°y" + 5x°yª Ryx Ryy = Rx y = Ryx = II

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Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, w...

A: We can find the centroid as below using the required formula.

Q: The slope of a curve is given as (2x + b and has a value of at 16 2x3 x = 2. What is the value of y ...

A: Given slope of curve dydx=2x+b+12x3

Q: 15 4 -4-3 -2 4 2- -3 3.

A: Accordimg to given graph a. As x→-2-  fx→∞b. As x→-2+  fx→-∞

Q: 4. -[lp A~ q) A r] = ¬p V q V ¬r 5. -[p → (¬q)] = p A q 6. (p → r) A (q → r) = (p V q) → r

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Q: Question 6 Evaluate the integral f w(2w + 3)² dw ... A.) w4+4w³+w² + C B.) w4+2w³+9w² + C C.) w?(w2+...

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Q: Show Intro/Instructions Suppose f is a quadratic function that has roots at 3 and x = 6, and f(0) = ...

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