If #y=166# when #x=83#, what is #y# when #x=23#?
Use proportions:
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To find the value of y when x is 23, we can use the given information to determine the relationship between x and y. Since we're given a specific point (x=83, y=166), we can use it to find the slope of the line. Then, we can use the slope to find the value of y when x=23.
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Calculate the slope using the given points: ( \text{slope} = \frac{{\text{change in y}}}{{\text{change in x}}} = \frac{{y_2 - y_1}}{{x_2 - x_1}} ).
Plug in the values: ( \text{slope} = \frac{{166 - y_1}}{{83 - x_1}} ).
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Now, use the slope to find y when x=23: ( y - 166 = \text{slope} \times (x - 83) ). Plug in the values and solve for y: ( y - 166 = \text{slope} \times (23 - 83) ).
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Simplify and solve for y: ( y - 166 = \text{slope} \times (-60) ). ( y - 166 = \text{slope} \times -60 ). ( y - 166 = \text{slope} \times -60 ).
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Add 166 to both sides: ( y = \text{slope} \times -60 + 166 ).
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Calculate the value of y: ( y = \text{slope} \times -60 + 166 ).
Therefore, ( y ) when ( x = 23 ) is the value obtained from the calculation in step 5.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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