The correct options for the linear combinations of the vectors are given by:
A, B, C, D, E and F.
<h3>What is a span between two vectors?</h3>
The span between two vectors is the set that contains all linear combinations between these two vectors.
Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:
k1u1 + k2u2
In which k1 and k2 are real numbers.
With k1 = 4 and k2 = -7, we get that option A is correct.
For option B, the vector 0 will always be a part of the span, as it can be formed with constants 0, hence it is correct.
The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.
The underlying vectors will always also be part of the span, as they can be formed with their constant 1 and the others at 0, hence options D and F are correct.
The size of the span of any vectors is of infinity, hence option E is correct while option G is not.
More can be learned about linear combinations at brainly.com/question/15885826
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If a shape is translated (has it's vertex' coordinates moved/changed), then it retains its original values but just has different vertex coordinates.
Thus since DE is equal to UV, then,
DE = UV; substitution:
5=5
The value of that <span>(√5 + 1)/8 and We can prove it like this:
</span>cos 2A= 2cos^2 A-1=1-2sin^2 A
<span>so cos^2 48 – sin^2 12 </span>
<span>=(1/2)(1+cos 96) - (1/2)(1-cos24) </span>
<span>=(1/2)(cos 96 +cos 24) and using cos(A)+cosB)=2cos((A+B)/2)cos((A-B)/2) </span>
<span>=cos60cos36 </span>
<span>=(1/2)cos36 </span>
<span>and you have to find cos36. </span>
<span>Suppose 5x=180, then </span>
<span>cos(5x)=cos(180) then x=-180,-108, -36, 36, 108 </span>
<span>Also 3x=180-2x </span>
<span>so cos(3x)=cos(180-2x)=-cos2x </span>
<span>so 4cos^3(x) -3cos(x)=1 - 2cos^2(x) </span>
<span>giving 4c^3+2c^2 - 3c-1=0 where c=cosx </span>
<span>c=-1 is a root and factorizing gives </span>
<span>(c+1)(4c^2-2c-1)=0 </span>
<span>so 4c^-2c-1=0 giving </span>
<span>c=(2±√20)/8=(1±√5)/4 and these have values cos(36) and cos(108) </span>
<span>the positive root is therefore cos(36)=(1+√5)/4 </span>
<span>and the required value (1/2)cos(36)=(1+√5)/8
</span>I think this can be very useful
Hello.
The answer is: 3×10³
3.05 = (3 x 1) + (0/10) + (5/100)
Have a nice day
Answer:
Time taken to fill the pool = 7.81 hours
Step-by-step explanation:
We are given that it takes 19 seconds to fill 2 gallons. Therefore, we can use cross multiplication to know how long will it take to fill one gallon as follows :
Time taken to fill 2 gallons of tank = 19 seconds
Therefore, it takes 9.5 seconds to fill one gallon of water.
One gallon is equivalent to 0.133681 cubic feet
Therefore, it takes 9.5 seconds to fill 0.133681 cubic feet
Now, to find Volume of the pool :
radius of pool = 6 ft
volume of pool = pi × (radius)² × height
volume of pool = 3.14 × 6² × 3.5
volume of pool = 395.64 cubic feet
Time taken to fill 0.133681 cubic feet of water = 9.5 sec
Hence, Time taken to fill the pool = 7.81 hours
