1. Show that the lines having the equations 4x- 3y + 12 = 0 and 8x 6y + 15 = 0 are parallel.

Q: sin t (c) y = 1- cost

A: The given function,         y=sin t1-cos t

Q: dx 2x x2

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Q: - Find the following derivatives. d. In(x2 + 1) dx

A: Given query is to find the derivative of the expression.

Q: 3. Differentiate the following x2-1 a) y = x2+1

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Q: Evaluate: A 3 2(,s–3) (c +C 15 4lnr None

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Q: Oil is leaking out of a tanker damaged at sea. The damage to the tanker is worsening as evidenced by...

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Q: 6. Use implicit differentiation to find dy dx x³ + xy-y3 = 7 %3D |

A: Answer: The solution is as given below :  

Q: Consider the surface defined by f (, y) = ln(5y – 7x). Find the equation of the tangent plane to f(x...

A: (x0 , y0 ) = (2,3) tangent plane formula  f(x,y) = (x-x0 )f'x(x0 , y0 ) + (y-y0 )f'y(x0 , y0 )  here...

Q: T "cos(x²)dxdy? What is the reversed order of integration of 'y a. I T cos(x²)dydx ST"cos(x²)dydx O"...

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Q: Honey is pouring out of a funnel at a rate of 3cm3/s. The funnel is in the shape of an inverted cone...

A: Given query is to find the rate of change of height when honey is at the level of 5 cm.

Q: For the given cost function C(x) = 57600 + 800x + x² find: a) The cost at the production level 1250 ...

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Q: QUESTION 3 dydx ? VX What is the reversed order of integration of a. e dxdy Ob. e dxdy Oc. e dxdy d....

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Q: At what point(s) does the curve y=; 3x – 4 have a derivative of -1? O 1) (2.0) 2) (-1,-7) 3) (-1,-7)...

A: Given query is to find the value of x where seri is -1.

Q: Evaluate the integral. dx 9 2 4 16x- 81

A: This question can be solved by the concept of special integrals.

Q: Determine if the following series converge or diverge. Make sure you state which test you use to mak...

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Q: Find y' and simplify: y = cot-(eSin ) - esincos t y' = 1+ e2sin t 2 sin t y' = 1+e2: e sin t 2 sin t...

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Q: Question 3 (1 point) Suppose a, 3, and 7 are vectors such that = (3, 1, -5) and 7xa= (7, -7, 1). , b...

A: Find your answer below 

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 65°C, it...

A: Given:    T (surroundings temp)= 20    T0 (initial temp)  = 95   Now      T = 65  dT/dt = 1

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If...

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Q: QUESTION 16 In(cos(2x)) Evaluate: lim (п - х)2 O a. 0 O b.2 O C. 1 O d.-2

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Q: Use the cross product to find the area of the triangle with the vertices P = (2, 2, 6), Q = (3,4, 3)...

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Q: Find the derivative of the vector function below r(x) = sin²(secx?)i +csc°(Vx² +1] 2 dd fil

A: Given: - The vector function is, r(x)=sin2(secx2) i+csc3x2+1j+8tan(x2) k To find: -The derivative of...

Q: What is the center and radius of the sphere that has (1, -2, 2) and (3, 4, -12) as endpoints of a di...

A: Given query is to find the the center and the radius of the sphere.

Q: QUESTION 5 Using double integral, find the volume of the solid that lies below the surface given by ...

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Q: Find the velocity and position vectors of a particle, given its acceleration and initial conditions ...

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Q: 2. Differentiate the follow a) y = e 2x -ex %3D ex

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Q: 4x-3, 15. What is the derivative of f(x) ? Зх+2 17 a. (3x+2)2 4x2-3x b. 3x2+2x С. 16 d. (3x+2) 16. W...

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Q: The birth rate of a population is b(t) = 2400e0.022t people per year and the death rate is d(t)= 149...

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Q: Find differential of the function ? = (x^2+2)^3 dy = ____ dx. When x = 4 and dx = 0.05, compute th...

A: We will differentiate the function Y=(x^2+2)^3 as follows 

Q: Write the equation for the linear function. A = {(x, y): (-4, 2)(-1. .) Oyr y= - 2 Oy= - + 1 y= 2 Oy...

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Q: QUESTION 17 How fast is the surface area of a sphere changing when the radius is 25 cm if the radius...

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Q: Let x, Y be positive real numbers. If x2 – y² =1, then x or y (or both) is not an integer.

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Q: If a and B, are two angles in standard position in Quadrant II, find sin(a - B) for the given fun 5 ...

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Q: Differentiate the function. t(t? + 1)4 V2t – 1 g(t) = In 5

A: Given  g(t) = lntt2+142t-15g'(t) = dlntt2+142t-15dtg'(t) = 1tt2+142t-15×dtt2+142t-15dt              ...

Q: "Зх — 1 (c) f(x) = x2 + 3

A:  

Q: Given the below differential equation, solve for the value of y(t) att = 3.8 s. 2.5y" + 11.2y' + 5.4...

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Q: Using double integration, find the volume of the solid bounded below by the plane z = 0and above by ...

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Q: How can the equation -2x2 + 3x + 4 = -7 be solved and why? Only by using the quadratic formula beca...

A: We have to solve the equation by quadratic formula

Q: Select the correct equation for the following graph: 10- 5- -10 5- 10 5- -10- 2x-6 O f(x) 22 +x-2 f ...

A: find the equation for given graph

Q: Find the absolute extrema of f(x, y) = x² – xy +y 4x + 4y within the domain a + y? < 16 Please show ...

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Q: The cylindrical equation z = r2 represents which of the following? O a paraboloid O a semisphere O a...

A: The cylindrical equation z=r2

Q: Section 3.4 p. 308/310 # 192 Express the rational function as a sum or difference of two simpler rat...

A:

Q: 28. Find the critical points of f(x) = x3 - 3x2 - 3. а. (0, —3)and (2, —7) b. (0,3)and(2,7) c. (0,2 ...

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Q: Find the slope of the line through (-1, -1) and (-1, 3). undefined -1/2 0 -4

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Q: determine o evaluate: The value of lim- 2+sin e if exist, otherwise states that limit does not exist...

A: Given query is to eveluate the limit.

Q: 1. Find the general solution of (y? – 1) = 4xy2

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Q: Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, tsin ...

A: To sketch: The curve r(t)→=&lt;tcost,t,tsint&gt; Solution: Given x=tcost,y=t,z=tsint x2+z2=tcost2+ts...

Q: Find the derivative of the vector function below r(x) = sin°(secx ?)i +csc'(Vx² +1)j +8tan(x ²) k

A: Given: - The vector function is, r(x)=sin2secx2 i+csc3x2+1j+8tan(x2)k To find: -The derivative of th...

Q: How fast is the volume of a sphere changing when the radius is 20 cm if the radius is changing at th...

A: We will find the rate of change of volume of sphere at a given radius.