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storchak [24]
3 years ago
6

In calculus, we went over the subject of implicit differentiation. I feel pretty solid on how to do it, except when they give th

e problem with \frac{dx}{dt} or \frac{dx}{dy} instead of your standard \frac{dy}{dx}
How do you do these kinds of problems?
Mathematics
1 answer:
babymother [125]3 years ago
7 0
The same way.

\dfrac{dy}{dx} means it's derivative of function y with respect to x

\dfrac{dx}{dt} means it's derivative of function x with respect to t

\dfrac{dx}{dy} means it's derivative of function x with respect to y


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PLEASE HELP! A positive number is 1/3 of another number. The sum of the numbers is five less than the square of the larger numbe
antoniya [11.8K]

Answer: The numbers are 1 and 3.

Step-by-step explanation:

Let x = smaller number , y= larger number.

As per given,

x=\dfrac{y}{3}   ...(i)

x+y=y^2-5       ...(ii)

Put value of x from (i) in (ii)

\dfrac{y}{3}+y=y^2-5\\\\\Rightarrow\ \dfrac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=\dfrac{-5}{3}

Since numbers are positive , so y=3 is correct.

And x will be 1  [from (i)]

Hence, the numbers are 1 and 3.

7 0
3 years ago
John has 10 pounds of peanuts. He wants to put the peanuts into bags so that each bag
musickatia [10]

Answer:

The answer is 50 bags

8 0
3 years ago
I hope you could get this answer
larisa [96]

Answer:  -12

Step-by-step explanation:    x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.

3 0
2 years ago
A silversmith combined pure silver that cost $33.48 per ounce with 51 oz of a silver alloy that cost $24.35 per ounce. How many
Pavlova-9 [17]

Answer:

$38.31

Step-by-step explanation:

Given:

Pure silver that cost $33.48 per ounce used to form $24.35 alloy/ounce.

Question asked:

How many ounces of pure silver were used to make an alloy of silver costing $27.87 per ounce?

Solution:

At cost $24.35/ounce, pure silver is mixed = $33.48

At cost $1/ounce, pure silver is mixed = \frac{33.48}{24.35}

At cost $27.87/ounce, pure silver is mixed = \frac{33.48}{24.35}\times 27.87 = \frac{933.08}{24.35}  = 38.31

Thus, $38.31 ounces of pure silver were used to make an alloy of silver costing $27.87 per ounce.

5 0
3 years ago
The table gives estimates of the world population, in millions, from 1750 to 2000. year population year population 1750 790 1900
Tems11 [23]
The poopulation exponential model is given by

P(t)=P_0e^{kt}

Where, P(t) is the population after year t; Po is the initial population, t is the number of years from the starting year; k is the groth constant.

Given that the population in 1750 is 790 and the population in 1800 is 970, we obtain the population exponential equation as follows:

970=790e^{50k} \\  \\ \Rightarrow e^{50k}=1.228 \\  \\ \Rightarrow 50k=\ln{1.228}=0.2053 \\  \\ \Rightarrow k=0.0041

Thus, the exponential equation using the 1750 and the 1800 population values is P(t)=790e^{0.0041t}

The population of 1900 using the 1750 and the 1800 population values is given by

P(t)=790e^{0.041\times150} \\  \\ =790e^{0.6158}=790(1.8511) \\  \\ =1,462

The population of 1950 using the 1750 and the 1800 population values is given by

P(t)=790e^{0.041\times200} \\  \\ =790e^{0.821}=790(2.2729) \\  \\ =1,796

From the table, it can be seen that the actual figure is greater than the exponential model values.
7 0
3 years ago
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