Tan(-4pi/3) = 0.0731897502
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
The ordered pair is (-2, -3)
Step-by-step explanation:
- Step 1: To find whether an ordered pair is a solution, substitute values of x and y and see whether it satisfies the equation.
(-3, -2) ⇒ 7 × -3 - 5 × -2 = -21 + 10 = -11 ≠ 1
(-2, -3) ⇒ 7 × -2 - 5 × -3 = -14 + 15 = 1
(0, 4) ⇒ 0 - 5 × 4 = 20 ≠ 1
(4, 0) ⇒ 7 × 4 - 0 = 28 ≠ 1
So the ordered pair is (-2, -3)

Distribute

Combine like terms

Add 1 and subtract 6x from each side
0 = 12
The equation has no real solution
Answer:
Price = 20, Amount = 14
Step-by-step explanation:
A = Amount of Mangoes
P = Price for 1 Mango
P = A + 6
280 = P * A
insert A+6 for P
280 = (A+6) * A
280 = 6A + A²
280=1*a^2+6*a | Vertausche beide Seiten der Gleichung.
1*a^2+6*a=280 | quadratische Ergänzung: ergänze auf beiden Seiten (3)^2
1*a^2+6*a+(3)^2=3^2+280 | Rechne 3 hoch 2 aus.
1*a^2+6*a+(3)^2=9+280 | addiere 9 und 280
1*a^2+6*a+(3)^2=9+280 | Fasse die rechte Seite mit Hilfe der binomischen Formel zusammen.
1*(1*a+(3))^2=289 | Auf beiden Seiten Quadratwurzel ziehen.
1*a+(3)=+-*289^0.5
1*a_1+(3)=289^0.5
1*a_1+3=289^0.5 | Ziehe die Wurzel aus 289
1*a_1+3=17 | -3
1*a_1=14