Multiplying a vector by a scalar means to multiply each coordinate of the vector by said scalar.
So, we must multiply both entries by 7:
A flagpole is 12 feet tall. Its shadow is 14 ft long. How far is it from the top of the
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D. 192in^2
This would be a simple area problem with a triangle. REMEMBER THIS EQUATION: a=bh*1/2 (b for base and h for height, these are multiplied together then that answer is halved out.)
So we just need to plug in our values into the equation, so the equation would look like a= (16)*(24)*1/2. 16 times 24 would then give you 384, you could either divide by 2 or multiply by 0.5 to get the next answer, as long as your HALVING the answer.
So we have our bh value so now we can multiply by 1/2 which will give us 384*1/2 which leaves us with 192.
I have also attached a photo of doing a longer(ish) way than this, that also proves that this equation works. Either one will provide you an answer.
This would be a simple area problem with a triangle. REMEMBER THIS EQUATION: a=bh*1/2 (b for base and h for height, these are multiplied together then that answer is halved out.)
So we just need to plug in our values into the equation, so the equation would look like a= (16)*(24)*1/2. 16 times 24 would then give you 384, you could either divide by 2 or multiply by 0.5 to get the next answer, as long as your HALVING the answer.
So we have our bh value so now we can multiply by 1/2 which will give us 384*1/2 which leaves us with 192.
I have also attached a photo of doing a longer(ish) way than this, that also proves that this equation works. Either one will provide you an answer.
The Lagrangian is
It has critical points where the first order derivatives vanish:
From the first two equations we get
Then
At these critical points, we have
(maximum)
(minimum)