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nataly862011 [7]
3 years ago
9

The Olympic swimmer, Michael Phelps, required 10,000 calories during training. He needed 30% protein, 50% carbohydrates and 20%

fat. How many calories did he need for each nutrient?
1 gram of carbs= 4 calories, 1 gram of protein=4 calories, 1 gram of fat= 9 calories.
Mathematics
1 answer:
ehidna [41]3 years ago
8 0

Answer:

750 grams of protein, 222.22 of fat, and 1,250 of carbs.

Step-by-step explanation:

3,000 calories from protein, 2,000 from fat, and 5,000 from carbs.

3000 / 4 = 750 grams of protein.

2,000 / 9 = 222.22 grams of fat.

5,000 / 4 = 1,250 grams of carbs.

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(1) Let {v1,v2,v3} be a set of vectors in Rn . If u is Span {v1,v2,v3}, show that 3u is in Span {v1,v2,v3}.
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Answer:

(1)

Multiplying by 3 both sides of the equality you get that

3u = 3c_1v_1+3c_2v_2+3c_3v_3

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(2)

That's not true, consider the following counter example.

v_1 = (0,0,0,1)\\v_2 = (0,0,1,0)\\v_3 = (0,1,0,0)\\v_4 = (1,0,0,0)\\u = (0,1,1,1)

u is a linear combination of v_1,v_2,v_3 but is NOT a linear combination of v_1,v_2,v_3,v_4.

Step-by-step explanation:

(1)

As the hint indicates, you know that

u = c_1 v_1 + c_2v_2+c_3v_3

Then, if you multiply both sides of the equality by 3, you get that

3u = 3c_1v_1+3c_2v_2+3c_3v_3

And that's it. 3u  is in the Span of the vectors \{v_1,v_2,v_3\}

(2)

That's not true, consider the following counter example.

v_1 = (0,0,0,1)\\v_2 = (0,0,1,0)\\v_3 = (0,1,0,0)\\v_4 = (1,0,0,0)\\u = (0,1,1,1)

u is a linear combination of v_1,v_2,v_3 but is NOT a linear combination of v_1,v_2,v_3,v_4.

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3 years ago
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