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blsea [12.9K]
2 years ago
12

Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨2,−3,4⟩, b=⟨−4,5,−1⟩, and c=⟨−2,−1,5⟩.

Mathematics
1 answer:
NikAS [45]2 years ago
7 0

Answer:

derivative of the vector function given = ( -16-22t, 14-36t, -2-16t )

Step-by-step explanation:

given data:

vector function : r(t) = ta*(b+tc)

a = ( 2,-3.4) .   b = (-4,5,-1).  c = ( -2,-1,5)

to find the derivative of the vector function we will differentiate with respect to x attached below is the detailed solution

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Each gallon of paint covers $200$ square feet. I have to paint one side of a wall that is $12$ meters tall and $80$ meters long.
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Step-by-step explanation:

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2 years ago
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The front walkway from the street to Pam's house has an area of 250ft^2. Its length is two less than four times its width. Find
OleMash [197]

Answer: the length of the walkway is 30.64ft

The width of the walkway is 8.16ft

Step-by-step explanation:

Since the walkway has length and width, it is rectangular in shape. For a rectangle, the two lengths and two widths are equal. The area is expressed as length, L × Width,W.

The front walkway from the street to Pam's house has an area of 250ft^2. It means that

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W(4W - 2) = 250

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Using the general formula for quadratic equations,

W = [- b ± √b^2 - 4ac]/2a

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b = -2

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W= [- - 2 ±√-2^2 -4(4 × -250)]/2×4

= (2 ± √4 + 4000)/8

= (2 ±63.277)/8

W= (2 + 63.277)/8 or W = (2 - 63.277)/8

W = 8.16 or W = - 7.91

Since the width cannot be negative, width = 8.16 ft

LW = 250

8.16L = 250

L = 250/8.16 = 30.64 ft

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2 years ago
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The resultant of a certain system of forces has the X and Y components shown in Fig. 220. Determine the components of this resul
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First, you need to determine the resultant force and its angle. This one is real easy, since you only have one (x) and one (y) component. X = 300 and Y = 480 

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<span>Now, you should have a resultant force value and its angle, from zero, in the first quadrant and between the Y and N axes. Draw yourself a diagram showing all of the axes, the resultant and the angles. You're going to have to do some very easy math to determine the angles between the Y and N axes and the resultant. Call these new angles α and β. α is the angle between N and the resultant and β is the angle between T and the resultant. Hint: one of them is 28 deg. </span>

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A student claims that the expression “9 times the sum of a number and 13” is translated to the algebraic expression 9n + 13. Is
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Answer:

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Hence, the rate of change of an edge is -1/4 meter per minute.

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1 year ago
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