Answer: option D
Step-by-step explanation:
Remember the cosine identity:
Given the right triangle DFE shown in the image, you can identify that the adjacent side and the hypotenuse for the angle F of this triangle are:
Now you can substitute values into and then reduce the fraction.
THerefore you get:
1) 155.91 grams would be left after 10 years
2) The population would be 376,478 in 2040
Step-by-step explanation:
The form of the exponential function is , where
1)
Scientists are studying a 500 grams sample of a radioactive element, which has an annual decay rate of 11%
∵ The initial amount is 500 grams
∴ a = 500
∵ The annual decay rate is 11%
∴ r = 11% = 11 ÷ 100 = 0.11
∵ b = 1 - r ⇒ decay
∴ b = 1 - 0.11 = 0.89
- We need to find how many grams of the sample would be left
after 10 years
∴ x = 10
- Substitute all of these values in the form of the exponential function
∵
∴ y = 155.9085996
- Round it to 2 decimal places
∴ y = 155.91
155.91 grams would be left after 10 years
2)
In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year
∵ The population of an Ohio town was 140,212
∴ a = 140.212
∵ The population is expected to grow at a rate of 2.5% each year
∴ r = 2.5% = 2.5 ÷ 100 = 0.025
∵ b = 1 + r ⇒ growth
∴ b = 1 + 0.025 = 1.025
- We need to find the population in 2040
∵ The number of years is 2040 - 2000 = 40 years
∴ x = 40
- Substitute all of these values in the form of the exponential function
∵
∴ y = 376478.1709
- Round it to the nearest whole number
∴ y = 376,478
The population would be 376,478 in 2040
Learn more:
You can learn more about the functions in brainly.com/question/11921476
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Answer:
Step-by-step explanation:
Hello, please consider the following.
When the parabola equation is like
The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))
As the vertex is (3,-2) we can say that h = 3 and k = -2.
We need to find a.
The focus is (3,2) so we can say.
So an equation for the parabola is.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A sphere with radius has surface area
. Divide the radius by 6 and you get a surface area of
, so that the final surface area is divided by 36.