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3 years ago

Find the coordinates of the point (x,y,z) on the planez=4x+3y+1 which is closest to the origin.

1 answer:

8 0

Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).

Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.

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Answer:

$f(x) =\sqrt{x} sin (x)$

And on this case we can use the product rule for a derivate given by:

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$

Step-by-step explanation:

We assume that the function of interest is:

$f(x) =\sqrt{x} sin (x)$

And on this case we can use the product rule for a derivate given by:

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$

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3 years ago

Please help me,ASAP

pav-90 [236]

Answer:

b. They can both be 90 degree angles

c. Acute angles are by definition 90 degrees, and acute is less than but not equal to 90 degrees

d. should be always

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Step-by-step explanation:

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4 years ago

Kermit's favorite iced tea is made with 151515 tea bags in every 222 liters of water. Peggy made a 121212-liter batch of iced te

muminat

Answer:

The answer is (Choice C) It is just right.

Step-by-step explanation:

The question is incomplete, so the complete question is below:

Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags. What will Kermit think of Peggy's iced tea? Choose 1 answer: (Choice A) It is too strong. (Choice B) It is too weak. (Choice C) It is just right.

Now, to find which of the choice is correct.

So, we find first the unit rate of Peggy's iced tea bags per liter:

If, Peggy made a 12-liter batch of iced tea with 90 tea bags.

Then, Peggy would made a 1-liter batch of iced tea with = $\frac{90}{12} =7.5\ tea\ bags.$

Now, to get the unit rate of Kermit's iced tea bags per liter:

If, Kermit made a 2 liter of iced tea with 15 tea bags.

Then, Kermit would made a 2 liter of iced tea with = $\frac{15}{2} =7.5\ tea\ bags.$

Thus, the quantity of tea bags per liter is same of both Kermit and Peggy.

Hence, Kermit will think of Peggy's iced tea that it is just right.

Therefore, the answer is (Choice C) It is just right.

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3 years ago

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3 years ago

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