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3 years ago

The weight of 10 identical samples of a substance is 0.01 pound. what is the weight of 10000 samples?

1 answer:

3 0

The answer is 10 pounds.

I set up a proportion of 10 / 0.01 = 10000 / x.

Cross-multiply to get 10x = 10000(0.01). Simplify to get 10x = 100. Divide by 10 to isolate the variable.

x = 10. 10000 samples would weigh 10 pounds.

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Find values a and b that satisfy a∙〈5,-4,0〉+b∙〈2,2,-3〉=〈11,-16,-6〉.

WARRIOR [948]

The right hand side of the equation is 〈11 , -16 , 6〉

The values of a and b are a = 3 , b = -2

Step-by-step explanation:

If n . <a , b> + m . <c , d> = < x , y>, then

na + mc = x
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∵ a ∙〈5 , -4 , 0〉 + b ∙ 〈2 , 2 , -3〉 = 〈11 , -16 , 6〉

- By using the rule above

∴ a(5) + b(2) = 11 ⇒ (1)

∴ a(-4) + b(2) = -16 ⇒ (2)

∴ a(0) + b(-3) = 6 ⇒ (3)

Use equation (3) to find the value of b

∵ a(0) + b(-3) = 6

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∵ a(5) + b(-2) = 11

∴ 5a - 2b = 11

∵ b = 2

∴ 5a - 2(2) = 11

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- Add 4 to both sides

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- Divide both sides by 5

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To check your answer substitute a and b in equation (2)

∵ a(-4) + b(2) = -16

∴ -4a + 2b = -16

∵ a = 3 , b = -2

∵ The left hand side is -4a + 2b = -4(3) + 2(-2) = -12 - 4 = -16

∵ The right hand side is -16

∴ L.H.S = R.H.S

∴ The values of a and b are 3 , -2

The values of a and b are a = 3 , b = -2

Learn more:

You can learn more about the equations in brainly.com/question/11306893

#LearnwithBrainly

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