unit

Q: Give an example of a 2 X 2 matrix that is its own inverse.

A: Given:2×2 matrix

Q: A man standing on a cliff 200 meters high drops a stone. How long does the stone remain in the air? ...

A: Initial velocity of the stone, u=0 Height, h=200   Use the second equation of motion, h=ut+12gt2200=...

Q: 4.5.19 Find the directions in which the function increases and decreases most rapidly at Po. Then fi...

A: given that f(x,y)=x2+xy+y2 ,P0(-4,-3) to find the direction in which the given function increases mo...

Q: Evaluate the double integral I|. (10z + y) dA where Ris the region between the curves a? + y? = 12 a...

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Q: Rewrite the Cartesian equation y = 5z² as a polar equation. r(@) - Enter theta for e if needed.

A: Given: y=5x2

Q: Integrate the following

A:

Q: Consider the region R that is between the graphs of y = x2-1, y = -x+1 on the interval x = 0 to x = ...

A: The area between the graphs of y=x2-1 and y=-x+1 on the interval x=0 to x=2 will be: A=∫02x2-1--x+1d...

Q: Determine whether the statement " If u ≠ 0, u ∙ v = u ∙ w, and u × v = u × w, then v = w " is true o...

A: If u ≠ 0, u ∙ v = u ∙ w, and u × v = u × w, then v = w. Consider 45° as the angle between u and v. A...

Q: Find f if f' (x) = 12a³ + 14x + 2 and f(1) = 2.

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Q: Let a = (– 3, – 4) and 5 = (1, 2). Find the projection of b onto a. proja b

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Q: Please who calcul steps and words explanation, thank you!

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Q: In the following exercises, evaluate the integral using area formulas. 83.  3 ∫ (3−|x|)dx - 2

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Q: Use calculus to find the intervals where ?(?)=6x-x^2 is increasing or decreasing

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Q: 5. Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are sho...

A: Given that: The dimensions are 42 feet and 25.5 feet Since it is rectangular wall, the area of trian...

Q: Calculus Question

A: Integration:  

Q: sec 10.2

A: Given a=13cmb=5cmc=12cm

Q: 1. Find two possible equations for a parabola with a vertex V(0,3) that passes through the point P(4...

A: Given: A parabola with a vertex V(0, 3) that passes through the point P(4, 6). The axis of symmetry ...

Q: Calculus Question

A: Given that, ∫01xdx=12 ∫01x2dx=13 ∫01x3dx=14 The integral to be evaluated is given as, I=∫011-2x3dx...

Q: Consider the following. Fx) = sin(2x) + 2, g(x) = 5 sin(2x) + 2; [-2m, 2m] by [-3.5, 7.5] (a) Graph ...

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Q: 1. Use Newton's Method to find the second approximate solution X2 of the equation x'-x-1= 0 if the f...

A: Given equation is, x3-x-1=0 First approximation is, x1=2 Differentiating the given equation, fx=x3-x...

Q: Show analytically (that is, without reference to a graph) that h(x) = v1 + x is always increasing, g...

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Q: Derivatives of power and constant functions Evaluate the followingderivatives.

A: Given : a. ddxx9b. ddxxc. ddx28

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the pa...

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Q: 4. Use differential to estimate v15. (3 points total)

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Q: Evaluate the derivative of the following function. ƒ1y2= tan-112y2 - 42

A: Consider the given derivative fy=tan-112y2-42

Q: Use calculus to compute the absolute maximum and minimum values of ?(?)= 6x-x^2 on [0, 5].

A:

Q: Solve the differential equation and initial condition and verify that your answer satisfies both the...

A: Given: y2y'=2xy(0)=4

Q: Evaluate the integral ∫x(x - 1)10 dx

A: the given integral is: ∫xx-110dx let the given integral be I. therefore, I=∫xx-110dx substitute x-1=...

Q: Solve each inequality for x   a )  1<e3x-1<2    b)1-2 In x<3

A: a) Given- 1<e3x-1<2 To find- The value of x of the above inequality. Concept Used- The above i...

Q: Suppose 1 3 4 5 a2 1 3 - 3 az a4 1 5 – a5 1 6-승' 2 a) Find an explicit formula for a,:

A:

Q: 5) Find limits (if one exits) for each of the following (suggest you use L'Hôpital's Rule). (a) 7eSx...

A: If for two functions are fx and gx, limx→0fxgx form indterminate form  like 00, ∞∞, 00, ∞∞ . Then th...

Q: Evaluate the integral (by interpreting it as the area between two curves)   Please show full work, T...

A: Consider the given integral: ∫04x+2-xdx Here, the objective is to evaluate the given integral.

Q: sec 10.2

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Q: 4th question

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Q: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 27). (Enter your answe...

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos and y = r sin , and note that (x, y) (...

A: To find limit: limx,y→0,0x2y2x2+y2 Solution: In polar coordinates we have, x=rcosθ and y=rsinθ  And ...

Q: When is an angle said to be in standard position?

A: An angle said to be in a standard position: If the position of an angle with its vertex at the origi...

Q: Find the critical points of f(x)=6x-x^2.

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Q: The table gives the values of a function obtained from an experiment. Use them to estimate F(x) dx u...

A: To find the value of three equal subintervals with right endpoints, left endpoints and mid points

Q: A person leaves home and walks 6 miles west, then 3 miles sout How far from home is she? miles In wh...

A:

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.