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Anton [14]
2 years ago
5

Y=f(x) = (1/3)^x

Mathematics
1 answer:
Soloha48 [4]2 years ago
4 0

Answer:

0.333

Step-by-step explanation:

f(x)=1/3^x

x=1

f(1)=(1/3)^1

=1/3

1/3=.3333....

Round to 3 decimal place

f(1)=0.333

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Solve the following differential equations or initial value problems. In part (a), leave your answer in implicit form. For parts
shepuryov [24]

Answer:

(a) (y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) y = arctan(t(lnt - 1) + C)

(c) y = -1/ln|0.09(t + 1)²/t|

Step-by-step explanation:

(a) dy/dt = (t^2 + 7)/(y^4 - 4y^3)

Separate the variables

(y^4 - 4y^3)dy = (t^2 + 7)dt

Integrate both sides

(y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) dy/dt = (cos²y)lnt

Separate the variables

dy/cos²y = lnt dt

Integrate both sides

tany = t(lnt - 1) + C

y = arctan(t(lnt - 1) + C)

(c) (t² + t) dy/dt + y² = ty², y(1) = -1

(t² + t) dy/dt = ty² - y²

(t² + t) dy/dt = y²(t - 1)

(t² + t)/(t - 1)dy/dt = y²

Separating the variables

(t - 1)dt/(t² + t) = dy/y²

tdt/(t² + t) - dt/(t² + t) = dy/y²

dt/(t + 1) - dt/(t(t + 1)) = dy/y²

dt/(t + 1) - dt/t + dt/(t + 1) = dy/y²

Integrate both sides

ln(t + 1) - lnt + ln(t + 1) + lnC = -1/y

2ln(t + 1) - lnt + lnC = -1/y

ln|C(t + 1)²/t| = -1/y

y = -1/ln|C(t + 1)²/t|

Apply y(1) = -1

-1 = ln|C(1 + 1)²/1|

-1 = ln(4C)

4C = e^(-1)

C = (1/4)e^(-1) ≈ 0.09

y = -1/ln|0.09(t + 1)²/t|

8 0
3 years ago
60° 2x + 149 degrees​
MAXImum [283]

Answer:

x = 23

Step-by-step explanation:

60°=x+14

60+14=84=X

8 0
2 years ago
Marcus earned $54,000 last year when the Social Security tax was 6.2% of income up to $94,200. His Medicare tax was 1.45%. How m
AysviL [449]

Answer

Social security tax amount = $3348

Medicare tax amount = $743

Step by step explanation

The amount earned by Marcus = $54000

Social security tax = 6.2% = 6.2/100 = 0.062

Social security tax amount = 54000*0.062

Social security tax amount = $3348

Medicare tax = 1.45% = 1.45/100 = 0.0145

Medicare tax amount = 54000*0.0145

Medicare tax amount = $743

Hope this will help you.

6 0
2 years ago
Read 2 more answers
2. At the local park, there is an annual fair that
mafiozo [28]

Answer:

132 children and 88 adults

Step-by-step explanation:

let x represent the amount of kids and y represent the amount of adults.

since the problem says there was a total of 220 people at the fair an equation can be made

x+y=220

the problem tells that each childrens ticket was 1.5$ and each adult ticket was $4 and that a total of $550 was made that day, we can use the knowledge to make an equation:

1.5x + 4y = 550

using the equations we can make this systems of equations:

1.5x + 4y =550

x + y =220

solve the systems of equations by subracting y on both sides of th bottom equation:

x=220-y

since x is equivant to 220-y it can be substitued for x in the first equation to make this:

1.5(220-y)+4y =550

--solve for y--

y=88  - there were 88 adults

substute 88 for y in the second equation

x+88=220

--solve for x--

x=138 - there were 132 children

7 0
2 years ago
Simplify (6⁴)³<br><br>A. b<br>B. b³<br>C. b⁹<br>D. b¹²​
-Dominant- [34]
Answer is d
it would be b^12
5 0
3 years ago
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