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valkas [14]
3 years ago
9

Which of the following equations shows direct variations a) y= x/3 + 1 B) y= 3x c) Y=3/x

Mathematics
1 answer:
Korolek [52]3 years ago
7 0
A) Not a direct variation since it is not in the form y = k*x
B) is a direct variation since it is in the form y = k*x where k = 3
C) Not a direct variation. This is an inverse variation since it is in the form y = k/x

Answer: Choice B only
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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.
Tasya [4]

Answer:

\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]

Step-by-step explanation:

Given function:

y =\ln(\frac{(6 - x)^{\frac{3}{2}}}{x^{\frac{2}{3}}})

we know

\ln(\frac{A}{B}) = ln(A) - ln(B)

thus,

y = \ln((6 - x)^{\frac{3}{2}}) - \ln(x^{\frac{2}{3}})

or

also,

ln(Aⁿ) = n × ln(A)

thus,

y = (\frac{3}{2})\times\ln(6 - x) - (\frac{2}{3})\times\ln(x)

therefore,

\frac{dy}{dx}=[(\frac{3}{2})\times\frac{1}{(6-x)}\times(0 - 1)] - [ (\frac{2}{3})\times\frac{1}{x}\times1]

or

\frac{dy}{dx}=-(\frac{3}{2(6-x)}) - (\frac{2}{3x})

or

\frac{dy}{dx}=-[(\frac{3(3x)+2\times2(6-x)}{2(6-x)\times(3x)})]

or

\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]

5 0
3 years ago
What is the problem to h-16<24=
ELEN [110]
First, you have to add 16 to both sides because it's the opposite of subtracting.
h-16<24
  +16  +16
-16+16 will cancel each other out.
24+16=40
So, h<40
Or in other words, h is smaller than 40.

Hope it helps ^_^
5 0
3 years ago
Joshua earned $60 for working h hours. Which expression represents how much he earned in 1 hour?
Shkiper50 [21]
D. 60 divided by h.

Hope this helped.
5 0
3 years ago
Read 2 more answers
You row a canoe x miles per hour down a river for 20 minutes. On the return trip, you travel 1 mile per hour slower. The return
ozzi

Answer:

Total Distance = 2 miles

Step-by-step explanation:

We know D = RT where

D is distance

R is rate (speed)

T is time

First Leg:

Rate = x mph

Time = 20/60 = 1/3 hour

Hence, D = RT, Distance = x * 1/3 = x/3 miles

Second Leg:

Rate = x - 1

Time = 30/60 = 1/2 hour

Distance = (x - 1) * 1/2 = (x-1)/2

Total distance is the sum of both the legs, hence,

Total distance = \frac{x}{3}+\frac{x-1}{2}=\frac{2x+3(x-1)}{6}=\frac{2x+3x-3}{6}=\frac{5x-3}{6} miles

Since both the distance are equal we can equate and solve:

\frac{x}{3}=\frac{x-1}{2}\\2x=3x-3\\x=3

Plugging this x = 3 into the total distance expression, we get:

\frac{5x-3}{6}\\\frac{5(3)-3}{6}\\=2

Total distance, 2 miles

5 0
3 years ago
4. Solve using elimination.<br> 4x -3y = 9<br> 3x +2y = 11
UNO [17]
Answer: (3,1)

Explanation:
8 0
3 years ago
Read 2 more answers
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