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gulaghasi [49]
2 years ago
6

Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the

form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Mathematics
1 answer:
AveGali [126]2 years ago
7 0

Answer:

Not a subspace

Step-by-step explanation:

(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.

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$5 box of cereal; 40% discount. any kind of ceral.
vovangra [49]

Answer:

3

Step-by-step explanation:

4 0
2 years ago
The object on the right is made from a square-based pyramid joined to a cuboid.
spayn [35]

Answer:

Density of steel = 80.73 gm/cm^3

Step-by-step explanation:

The figure is made up of cuboid and square pyramid.

Height of cuboid, h = 9 cm

Length of cuboid, l = 6 cm

Width of cuboid, w = 6 cm

Volume of cuboid is given by the formula:

V_{Cuboid} = l \times w \times h

V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3

Density of Wood , D_{Cuboid}= 0.68g/cm^3

We know that formula of Density is:

Density = \dfrac{Weight}{Volume}

D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}

Putting the values:

W_{Cuboid} = 324 \times 0.68 = 220.32\ gm

Total weight = W_{Cuboid} + W_{Pyramid}

970 = 220.32 + W_{Pyramid}

W_{Pyramid} = 749.68 gm

Volume of pyramid is given as:

V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}

Base is a square with side 6 cm

V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3

Density of Steel/Pyramid:

D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3

5 0
3 years ago
Filbert makes $14 per hour. If he makes time and a half for overtime, how much will he make for working 63 hours?
Marina CMI [18]

Answer:

$1323.00

Step-by-step explanation:

A simple equation that can be used to figure this out is:

p*1.5*o=t

The variables mean:

p- hourly pay

o- hours worked overtime

t- total amount of money earned.

(Also, the 1.5 is always used to calculate overtime, no matter what job, unless otherwise specified, and as referred in the problem as "time and a half").

So, to finally work out this problem:

($14*1.5)*63=?

first, (14*1.5)= $21

($21*63)= $1323.

4 0
3 years ago
ILL GIVE BRAINLIEST A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equa
IceJOKER [234]
The answer is C
hope this helps :)
7 0
2 years ago
Read 2 more answers
To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x
Fiesta28 [93]

Given function is

f(x)=\left\{\begin{matrix}3x+k & x\leq -4 \\ kx^2-5 & x> -4\end{matrix}\right.

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

kx^2-5

so RHD= k(-4)^2-5

Now set both equal

k(-4)^2-5=3(-4)+k

16k-5=-12+k

16k-k=-12+5

15k=-7

k=-\frac{7}{15}

k=-0.47

<u>Hence final answer is -0.47.</u>




7 0
3 years ago
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