MATHEMATICS COLLEGE

I need some help with this calculus 1 implicit diffrention problem?

Answers

Answer 1

Answer:

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

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Write the related series for the finite sequence 1.5, 2.7, 3.9, . . ., 8.7? Then find the sum.

How many strings of length 5 can be written using the letters {a,b,c,d,e,f} if no two consecutive letters can be the same? For example, we'd count adede but not acdde.

Answers

Answer:

3750 strings.

Step-by-step explanation:

First we have 6 different letters to choose from (a, b, c, d, e, f) and we will make a string of length 5.

First, we would have to choose one of the letters, to do this we would have 6 choices.

For our second choice, we can only choose from 5 letters since we cannot choose the one that we already chose (no two consecutive letters can be the same).

Then, for our third choice, we would have to choose from 5 different letters (any letter but the one before).

Similarly for our fourth and fifth choice, we can choose 5 different letters.

Then, the total amount of strings would be:

6 x 5 x 5 x 5 x 5 = 6 x 5⁴ = 3750 strings.

a store is having a 35 percent off sale, if the original price of the shirt is $18 what is the price of the shirt after the discount is applied (not including tax)

Answers

11.70 dollars would be your answer

$6.3. Turn the percentage into a decimal and multiply that and the amount of money.
Ex. 35—> .35 x 18 = 6.3

Solve the following expression: (9 x 10) - (30 + 30). Show all steps taken.

Answers

Answer:

First multiply each brackets

90-60

Step-by-step explanation:

Answer:

9 x 3= 27 and 30 + 30= 60.. so 60- 27= 33, but if you want to do 27- 30.. it would be -33.

Step-by-step explanation:

Hope that answers your question!

Which expression is equivalent to (m2p–2r7)(m–5p4r2)?

Answers

Answer:

=(m2p+−2r7)(m+−5p4r2)

=(m2p)(m)+(m2p)(−5p4r2)+(−2r7)(m)+(−2r7)(−5p4r2)

=m3p−5m2p5r2−2mr7+10p4r9

=10p4r9−5m2p5r2−2mr7+m3p

Step-by-step explanation:

The weather report says the temperature is 20°C and will drop 5°C per hour for the next 6 hours. Daryl plans to begone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above -10°C,
should Daryl move his plant to a warmer location before leaving?
An inequality to model the problem is
The solution is

Answers

Answer:

yes.

Step-by-step explanation:

if he's gone for EXACTLY 6 hours, the plant will be at -10°C when he returns. However, it's stated that he plans to be gone for AT LEAST 6 hours, which means he should probably put the plant indoors or somewhere warmer so he doesn't have to rush home.

The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. If the level of significance for this two-tailed test is 0.10, what is/are the critical value(s)

Answers

Answer:

At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Step-by-step explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

Let $\mu$ = mean gross annual incomes of certified welders

So, Null Hypothesis, $H_0$ : $\mu$ = $20,000

Alternate hypothesis, $H_A$ : $\mu \neq$ $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is One-sample z teststatistics as we know about the population standard deviation;

T.S. = $(\bar X-\mu)/((\sigma)/(√(n) ) )$ ~ N(0,1)

where, $\bar X$ = sample mean income

$\sigma$ = population standard deviation = $2,000

n = sample size

Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

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