All categories

2 years ago

What is the domain of the function y = l n (StartFraction negative x 3 Over 2 EndFraction).

Mathematics

1 answer:

Ymorist [56]2 years ago

3 0

The domain of the provide function where the function is defined is x less than the number three.

<h3>What is the domain of the function?</h3>

Domain of a function is the set of all the possible input values which are valid for that function.

The function given in the problem is,

$y=\ln\left(\dfrac{-x+3}{1}\right)$

The above function is the function of logarithm. For the logarithmic function, it is defined for all the real numbers except 0.

Thus, the function should be greater than zero as,

$\left(\dfrac{-x+3}{1}\right) > 0\\(-x+3) > 0\\-x > -3$

Change the sign of both side, by changing the inequality,

$x < 3$

Thus, the domain of the provide function where the function is defined is x less than the number three.

Learn more about the domain of the function here;

brainly.com/question/2264373

You might be interested in

Given P(A) = 0.36, P(B) = 0.2 and P(ANB) = 0.122, find the value of P(AUB), rounding to the nearest thousandth, if necessary.

aliya0001 [1]

Answer:

The value of P(AUB) = 0.438

Step-by-step explanation:

Given:

P(A) = 0.36

P(B) = 0.2

P(A∩B) = 0.122

Find:

The value of P(AUB)

Computation:

P(AUB) = P(A) + P(B) - P(A∩B)

The value of P(AUB) = 0.36 + 0.2 - 0.122

The value of P(AUB) = 0.56 - 0.122

The value of P(AUB) = 0.438

7 0

3 years ago

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

Which theorem shows how the triangles are similar:

yan [13]

Answer:

AA similarly is correct....

6 0

3 years ago

Helppppppppppppppppppppppppp

VashaNatasha [74]

First you need to find out how long she worked

7:32 to 3:43 is 8 hours and 11 minutes.

Multiply 6.75(her per hour salary) by 8 and you have $54. But you still have 11 minutes. 11 minutes is roughly 18.33% of an hour. So multiply 6.75 by 0.18 which is 1.25. Your answer is $55.24

7 0

3 years ago

89.87 is 215% of what number

andre [41]

4 0

3 years ago