A projectile is shot into the air following the path, h(t) = -3t2 + 12t - 5. At what time, value of t, will it reach a maximum h
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You just have to factor the given expression. You do this by factoring the first term and the last term.
3
can only be factored with 3x • x, so let's put that into our parentheses.
(3x ?)(x ?)
Now the last term. -14 can be factored more ways than one. Here are some examples:
-14 <span>• 1
</span>14 <span>• -1
7 </span><span>• -2
-7 </span><span>• 2
We know we can't use the first two since they're not options in this question. We also know the middle term is something quite large, so that number is what should be multiplied by three.
(3x - 2)(x + 7)
Let's test it out. By multiplying the insides, the outsides, and adding them together.
-2 </span><span>• x = -2x
</span>
7 <span>• 3x = 21x
</span>
21x - 2x = 19x
Aha! That is correct! Now that we've gotten that figured out, we can eliminate B and D. But what about the others? Well, I usually just graph out the factors with a calculator and see the zeroes from there, but since I don't have that luxury in this case. I'll have to find out some other way. I would say to multiply the factors by each other and switch the signs (without the x).
7 = -7
-2 x 3 = -
- =
That should be your answer. If you have any questions, let me know.
3
(3x ?)(x ?)
Now the last term. -14 can be factored more ways than one. Here are some examples:
-14 <span>• 1
</span>14 <span>• -1
7 </span><span>• -2
-7 </span><span>• 2
We know we can't use the first two since they're not options in this question. We also know the middle term is something quite large, so that number is what should be multiplied by three.
(3x - 2)(x + 7)
Let's test it out. By multiplying the insides, the outsides, and adding them together.
-2 </span><span>• x = -2x
</span>
7 <span>• 3x = 21x
</span>
21x - 2x = 19x
Aha! That is correct! Now that we've gotten that figured out, we can eliminate B and D. But what about the others? Well, I usually just graph out the factors with a calculator and see the zeroes from there, but since I don't have that luxury in this case. I'll have to find out some other way. I would say to multiply the factors by each other and switch the signs (without the x).
7 = -7
-2 x 3 = -
-
That should be your answer. If you have any questions, let me know.
The mass of cesium left afer 120 years if the original mass of cesium is 8640 with an half-life of 30 years, is 540 grams.
<h3>What is half-life?</h3>This can be defined as the time taken for half the amount of a radioactive substance to decay.
To calculate the amount of cesium left after 120 years, we use the formua below.
Formula:
- R' = R/(
)............. Equation 1
Where:
- R = Original amount of Cesium
- R' = New amount of cesium
- T = Total time
- t = Half-life
From the question,
Given:
- R = 8640
- T = 120 years
- t = 30 years
Substitute these values into equation 1
- R' = 8640/(
)
- R' = 8640/
- R' = 8640/16
- R' = 540 grams.
Hence, The mass of cesium left afer 120 years is 540 grams.
Learn more about half-life here: brainly.com/question/25750315