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umka21 [38]
3 years ago
5

A. If B is a basis for a subspace H, then each vector in H can be written in only one way as a linear combination of the vectors

in B.
b. If B= {V1,..... Vp} is a basis fora subspace H of Rn, then the Correspondence X →[X]B makes H look and act the same as IRE.
c. The dimension of Nul As the number of variables in the equation Ax=0.
d. The dimension of the column space of A is rank A.
e. If H is a p-dimensional subspace of Rn, then a linearly independent set of p vectors in H is a basis for H.
Mathematics
1 answer:
liraira [26]3 years ago
3 0

Answer:

68

Step-by-step explanation:

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To make an equation of a line, you must put it in Y=mx +b form.

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Find the dimensions of a cylinder of volume 17 m3 of minimal cost if the top and bottom are made of material that costs twice as
Viefleur [7K]

Answer:

The answer is below

Step-by-step explanation:

The volume of the cylinder with radius (r) and height (h) is given as:

Volume = πr²h

17 = πr²h

h = 17 / πr²

Let k represent the cost of the side and 2k the cost of the bottom.

The area of the side = 2πrh, hence the cost of the side = k(2πrh)

The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)

The total cost (T) = cost of side + cost of the top and bottom

T = k(2πrh) + 2k(2πr²)

T = 2kπ(rh + 2r²)

Put h = 17/πr²

T = 2kπ (r×17/πr² + 2r²)

T = 2kπ(17/πr + 2r²)

The minimal cost is at dT/dr = 0

\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2}  =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m

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3 years ago
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Given, Earth's diameter is approximately 12,760,000 meters.

This number in scientific notation will be 1.276 × 10⁷

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Answer:

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