Angle in two ways Find the angle between ⟨2, 0, -2⟩ and ⟨2, 2, 0⟩ using (a) the dot product and (b) the cross product.

Q: In Exercises 1–8, let u = 83, -29 and v = 8-2, 59. Find the (a) component form and (b) magnitude (le...

A: Given that, u = 83i - 29j Then we get, The component vector: 3u = 3(83i - 29j) = 249i - 87j magnitud...

Q: Find the average rate of change of the function from x1 to x2.f(x) = x2 - 2x from x1 = 3 to x2 = 6

A: The function f(x)=x2-2x. We have to find the average rate of change of the function from x1=3 to x2=...

Q: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and...

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Q: x+1 Q3. For the following function y = find (a) its domain, (b) asymptotes, (c) х-2 critical points ...

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Q: Fill in the blanks with appropriate numbers to calculate the determinant. Where there is "t", choose...

A: a) Given determinant: 21-34 Expand the determinant 21-34=2×4--3×121-34=8+321-34=11

Q: Given that f(x) = 3x and g(x) = ln(x), evaluate both (g ◦f)(2) and (f ◦g)(2). If necessary, round yo...

A: Given that f(x) = 3x and g(x) = ln(x), evaluate both (g ◦f)(2) and (f ◦g)(2). We have to round our f...

Q: An equation of the line tangent to the graph of f at the point (2, 7) is y=4x−1. Find f(2) and f′(2)...

A: Given that y = 4x-1 is the tangent to f(x) at  point (2,7) (i)    it is clear that (2,7) is a point ...

Q: Evaluate the limit 7tỉ + 7t3 + 7 k t2 – 9 t-0 Enter your answer in i, j, k form.

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Q: Find the local extreme values of the function y = x + x- & + 5

A: Given function f(x) = x3+x2 - 8x + 5 f'(x) = 3x2+2x-8 f"(x) = 6x + 2 By Second derivative Test, f'(...

Q: The A-frame cabin shown below is 35 feet wide. The roof of the cabin makes a 55° angle with the cabi...

A: We have, the A-frame cabin is 35 feet wide. The roof of the cabin makes a 55° angle with the cabin’s...

Q: The graph below shows f '(x). Use left rectangles and n = 3 to estimate the accumulated change in f ...

A: Consider the given: Estimate the accumulated change: Δx=2.5−−23Δx=2.5+23Δx=4.53Δx=1.5Intervals are −...

Q: Use the shown table to find the indicated shown limit.

A: limx→22x2

Q: Solve. x- - Sx - 7> 0 O (, -7) U (-1, o) O (1. ) O (, -7) O +7, -1)

A: It is given that,x2+8x+7>0 We have to solve it.  

Q: Express the distance between the given numbers using absolute value. Then find the distance by evalu...

A: Express the distance between the given numbers using absolute value. Then find the distance by evalu...

Q: A metal rain gutter is made from sheets of aluminum that are 12 inches wide by using a machine that ...

A: Given that  sheets of aluminum that are 12 inches wide by using a machine that turns up the edges to...

Q: Integrate the following x2(x-4)ex(x-2)

A: find out the integral of x2(x-4)exx-2      

Q: Find X:

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Q: Pls help

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Q: Integrate (x2+2)(9x3+6)

A: Given that: ∫(x2+2)(9x3+6)dx

Q: An equation of a quadratic function is given f(x) = 3x2 - 12x - 1. a. Determine, without graphing, w...

A: Comparing given equation  f(x) = 3x2 - 12x - 1. with f(x) = ax2 + bx + c and Determining the values ...

Q: Let f(x)=csc x, Find f'(pi/2)

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Q: Simplify : see attached

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Q: Use the Binomial Theorem to expand the binomial (x2 - 1)4 and express the result in simplified form.

A: we have to Use the Binomial Theorem to expand the binomial x2-14 and express the result in simplifie...

Q: Limits with trigonometric functions Find the limits in Exercises 43–50.

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Q: Use a graph to estimate the value of the limit. Thenuse l’Hospital’s Rule to find the exact value.

A: Given

Q: Find the distance between (-1, 4) and (3, -2). Express the answer in simplified radical form and the...

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Q: I am not sure how to do this question.

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Q: evaluate f(x) =x2   -(2x/1000) for x= 0.04,0.02,0.01,0.005,0.003, and  0.001. guess again.

A:   we have function f(x)=x2-2x1000 We have to evaluate for   x=0.04,0.02,0.01,0.005,0.003 and 0.001  

Q: find the Jacobian ?(x, y)?(u, v) for the indicated change of variables.   x = u2 + v2, y = u2 − v2

A: We know that, the Jacobian of the transformation given by x = x(u, v) and y = y(u, v) is J=∂x∂u∂x∂v∂...

Q: For the following exercises, find the average rate of change of each function on the interval specif...

A: The average rate of change of a function is defined as the ratio of the difference in the value of t...

Q: Objective: Find derivatives and values of derivatives. 1.4.50 Find H'(x) for the given function. 5 H...

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Q: Find the area of the region enclosed by the curves y =x-4x and y = -x+2x. The area of the region enc...

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Q: The position of the sandbag is s(t) = 60 − 4.9t2. Find the rate, in meters per second, at which th...

A: Given that, the position of the sandbag is, s(t)=60-4.9t2. Obtain the value of t when the sandbag is...

Q: Evaluate the integral: =°/1+ 64z*dz

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Q: If a ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height in feet a...

A: Given that: A ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height ...

Q: Use the substitution u= 7x +x to evaluate the indefinite integral below. dx Write the integrand in t...

A: ∫(14x+1)7x2+xdx

Q: Express the function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) = ...

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) = ...

Q: Suppose the price charged per widget is related to the number of widgets that consumers will purchas...

A: Given, P=1000-2x

Q: Use a half-angle formula to find the exact value of the expression sin 15°

A: Our Aim is to find the exact value of the expression sin (15°).

Q: Evaluate the integral.

A: We have to find the integral: ∫x2+2x+2 dx Rewriting the integral, ∫x2+2x+2 dx=∫x2+2+2x-2xx+2 dx  ( a...

Q: Complete the table to find the balance A for P dollars invested at rate r for t years, compounded n ...

A: Consider the given values and the formula for compound interest. P=$ 1000r=10%=10100=0.1t=35 yearsA=...

Q: Calculus Question

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Q: A water sprinkler sprays water over a distance of 30 feet while rotating through an angle of 155 deg...

A: Given that Assume the lawn is circle of radiusr=30 feet. Subtended angle is θ=155° It is known that ...

Q: Find the vector equation that represents the curve of intersection of the cylinder a? + y = 25 and t...

A: Given equation of cylinder is, x2+y2=25

Q: Find a positive angle less than 360° or 2π that is coterminal with the given angle 19π/6.

A: Given angle= 19π6To evaluate  positive coterminal angle less than 360° 

Q: Graph: 4x2 - 24x - 25y2 + 250y - 489 = 0. Where are the foci located? Whatare the equations of the a...

A: Given equation, 4x2 - 24x - 25y2 + 250y - 489 = 0 we have to tell where are the foci located and  wh...

Q: Solve the equation 2x3 - 3x2 - 11x + 6 = 0 given that -2 is a zero of f(x) = 2x3 - 3x2 - 11x + 6.

A: Given that the equation 2x3 - 3x2 - 11x + 6 = 0 and  - 2 is a zero of  f(x) To solve the equation 2x...

Q: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x...

A: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x...

Q: In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

A: We know that, the mid point x,y of a line segment having end points x1,y1 and x2,y2 is calculated as...

Q: 14

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.