If x represents the average rate of a plane in still air and y represents the average rate of the wind, the plane's rate with the wind is represented by and the plane's rate against the wind is represented by

Q: 1. The line A cuts the x-axis at the point (q, 0) and the y-axis at (0, p) 2. The line B cuts the…

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Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: If airplanes A and B are moving southwest with peed VA=550 mph, and northwest with speed VB= 459…

A: Given that the plane A and B are moving southwest and northwest with speed 550 mph and 549 mph…

Q: If z varies directly with x and y, find y when x = 1.2 and z =5.4 if x = 3.2, y =2.3, and z= 4.6.

A: z varies directly with x and y that means z α xz α y

Q: If y2 is positive, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: Consider a function y=sinx+1. Here y1=sinx and y2=1>0positive.

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: parallel

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Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

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Q: At 9:00AM, ship B is 65 km due east of another ship A. Ship B is then sailing due west at 10 km/h…

A: Given- Ship B is 65 km due east of another ship A., ship b is sailing due west at 10 km/h and A is…

Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: W= x"+y+Z",

A: This is a problem of partial differentiation. Based on the general formula of PDE we will solve the…

Q: The area bounded by the curve y=4x y=4x  and the lines x=6x=6 ,x=10x=10 and x−axisx−axis is: Choose…

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Q: Which of the following represents two lines that are coplanar and do not intersect?

A: We want to find the lines which are coplanar and don't intersect.

Q: If x2 + y2 = 4 which has domain Dr=[-2,2] range Rf=[0,2]. Shrink and stretch it vertically by 3…

A: We are given:  x2+y2=4⇒y=4-x2=f(x) For shrinking vertically by 3 units , we have: f(x)→13f(x) Hence,…

Q: 2 The Range (Ry) of y = v9 – x² -

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Q: If ∆MNP is reflected across the line y = 2, then translated using the rule (x + y) → (x – 8, y – 1),…

A: We have been given the coordinates of the point P(7, 4) using the rule  (x + y) → (x – 8, y – 1).

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: An airplane is flying at an airspeed of 600 km/hr in a cross-wind at 50 km/hr that is blowing from…

A: Given: A  = The Airspeed     = the speed of airplane in wind. = 600 km/h  (Black vector) w = The…

Q: Lara and Sheila both starts from point A and drive along perpendicular roads. AB and AC…

A: Speed of lara is 45 km/hr ⇒dxdt=45 speed of shelia is 40 km /hr ⇒dydt=40 Shelia starts one hour…

Q: Consider the following diagram of a transverse line to a pair of parallel lines, l1 and l2. (2x…

A: Given : l1 and l2 are parallel lines.

Q: The equation of the line that goes through the point (1,1) and is perpendicular to the line 4x+4y=4…

A: Given,           The equation of the line that goes through the point (1,1) and is perpendicular to…

Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: Let A(x,y) be the point on the line y = x + 1 that is closest to the point B(2,0). Then the square…

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Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: Suppose z – 2z +x=5, What is the value of y ?

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Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)>0    3t2…

Q: If y = x*+2 then y' at x = 1 is equal to

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Q: If point A is reflected over the y-axis and its original location was (2,3), where is its new…

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Q: Write down a solution to y' = 4(y − 5) that tends to −∞ as t →∞.

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Q: Differentiate with respect to t 100 = x2 + y2

A: give equation ;- 100=X2+Y2 when we differentiate above equation with respect to t , we get

Q: If x represents the average velocity of a plane in still air and y represents the average velocity…

A: If x represents the average velocity of a plane in still air and y represents the average velocity…

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

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Q: 1. The line A cuts the x-axis at the point (q, 0) and the y-axis at (0, p) 2. The line B cuts the…

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Q: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the…

A: The solution for the above solution is as shown below.

Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: If the direction vector of a line is 3˜i + 2˜j and the gradient of another line is −5/2, find the…

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