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4 years ago

Thesumoftwopositivenumbersis16.whatisthesmallest possible value of the sum of their squares?

1 answer:

5 0

X+y=16
the sum of the squares is
x^2+y^2=sum

solve for y in first equation
x+y=16
y=16-x
subsitiute that for y in other equation

x^2+(16-x)^2=sum
x^2+x^2-32x+256=sum
2x^2-32x+256=sum
take derivitive to find the minimum value (or just find the vertex because the parabola opens up)
derivitive is
4x-32=derivitve of sum
the max/min is where the derivitive equals 0
4x-32=0
4x=32
x=8

at x=8
so then y=16-8=8

the smallest value then is 8^2+8^2=64+64=128

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3 years ago

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3 years ago

Chord AB subtends two arcs with measures in the ratio of 1:5. Line l is tangent to a circle at point A. Find the measure of the

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30°

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4 years ago

Mais teacher gives 4 quizzes each worth 5 points after three quizzes she has the score 4, 3, and 4. What does she need to get on

skad [1K]

Answer:

Therefore, she must get 5 points from the last quiz to have a mean score of 4

Step-by-step explanation:

Mean is the average of a set of data, it is the sum of the data divided by the number of data.

To have a mean of 4 from 4 quizzes;

Let x represent the total;

mean = x/4

4 = x/4

x = 4 × 4 = 16

To have a mean of 4 he must have a total score of 16.

Let y represent her score in the last quiz;

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y = 16-11 = 5

Therefore, she must get 5 points from the last quiz to have a mean score of 4

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3 years ago