Answer:
It will take 27.19 years
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
, where
- A = the future value of the investment, including interest
- P = the principal investment amount (the initial amount)
- r = the interest rate of interest in decimal
- t = the time the money is invested for
∵ Steve deposits $1250 in an account
∴ P = 1250
∵ The account paying 3.4% annual interest compounded continuously
∴ r = 3.4%
- Change it to decimal by dividing it by 100
∴ r = 3.4 ÷ 100 = 0.034
∵ The account balance will reach to $3150.5
∴ A = 3150.5
- Substitute The values of A, P and r in the formula above to find t
∵ 
- Divide both sides by 1250
∴ 
- Insert ㏑ to both sides
∴ ![ln(2.5204)=ln[e^{0.034t}]](https://tex.z-dn.net/?f=ln%282.5204%29%3Dln%5Be%5E%7B0.034t%7D%5D)
- Remember that 
∵ 
∴ ln(2.5204) = 0.034t
- Divide both sides by 0.034
∴ 27.18875 = t
∴ t ≅ 27.19
It will take 27.19 years
A scatter plot shows the relationship between two sets of data.
Answer:
- 60 percent of a number subtracted from 25
- 4 more than 2/3 of a number
Step-by-step explanation:
"60 percent of a number subtracted from 25" is a phrase that translates into 0.6 for 60% and "of a number" as 0.6x. Take this number and its subtracted from 25: 25-0.6x.
"4 more than two thirds of a number" is a phrase that translates into addition for "4 more" and multiplication with "two thirds of a number". This means 4 + 2/3y.
Answer:
4/3
Step-by-step explanation:
The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...
tan(θ) = y/x
__
For the given point on the terminal side, the tangent is ...
tan(θ) = (-4)/(-3) = 4/3
_____
<em>Additional comment</em>
There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:
(x, y) = (r·cos(θ), r·sin(θ))
Then the ratio y/x is ...
y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)
Answer:
50m is the length of the pool
Step-by-step explanation:
area= length * width
length= area/ width
1275/ 25.5 = 50
