What is the equation for the translation of x2 + y2 = 9 four units to the right and three units down?
1 answer:
Assuming the equation reads:
To move the equation to the left or right, you will either add or subtract a value from x. Adding a value to x will move it to the left, and subtracting a value will move it to the right.
To move the equation up or down, you will either subtract or add a value to y. Subtracting a value from y will move it up, and adding a value will move it down.
The translation is 4 units right, and 3 units down. Movement to the right means that we'll subtract from x, and movement down means that we'll add to y. The following equation will represent the translation, and is your answer:
To move the equation to the left or right, you will either add or subtract a value from x. Adding a value to x will move it to the left, and subtracting a value will move it to the right.
To move the equation up or down, you will either subtract or add a value to y. Subtracting a value from y will move it up, and adding a value will move it down.
The translation is 4 units right, and 3 units down. Movement to the right means that we'll subtract from x, and movement down means that we'll add to y. The following equation will represent the translation, and is your answer:
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Answer:
Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.
Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:
A - A*0.1 = A*(0.9)
After another millennium, we will have a mass equal to:
A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2
And so on, this is an exponential decay.
We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:
M(x) = A*(0.9)^x
Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:
y = M(x) = 600g*(0.9)^x
And the graph of this equation is shown below.
