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2 years ago

How do you implicitly differentiate: sqrt(xy)=x^2y+1

1 answer:

3 0

Implicit expression refers to equation that are not strictly expressed in terms of y and x separately. In this case, the derivative of expression
sqrt(xy)=x^2y+1 is

sqrt x * 0.5 y ^-0.5 dy + sqrt y * 0.5 x ^-0.5 dx= x^2 dy + 2xy dx
dy (x^2 - 0.5 (x/y) ^0.5) = dx (2xy - 0.5 (y/x)^0.5)
dy/dx = (2xy - 0.5 (y/x)^0.5) / (x^2 - 0.5 (x/y) ^0.5)

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Craig has of collection of 220 marbles. He lets his friend have 14 of his collections and sells 15 of his collection to the nove

Illusion [34]

220-14= 206
206-15=191
191-15=176
Answer: 176

3 0

3 years ago

Please help explanation if possible

hram777 [196]

Answer:

y = 1/7x + 0

Step-by-step explanation:

3x + 21y = 21

21y = -3x + 21

y = -3/21x

y = 1/7x

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2 years ago

9. The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversel

Vsevolod [243]

Answer:

The situation that represents this situation is:

$t = \frac{60}{n}$

Step-by-step explanation:

The amount of time t needed to assemble the set is inversely proportional to the number people n working.

This means that:

$t = \frac{k}{n}$

In which k is the constant of proportionality.

Twelve people can assemble the set in 5 hours.

This means that for $n = 12, t = 5$ . We use this to find k.

$t = \frac{k}{n}$

$5 = \frac{k}{12}$

$k = 12*5 = 60$

Write an equation to represent the situation.

$t = \frac{60}{n}$

8 0

2 years ago

Trudy invested $3,200 into an account that will increase in value by 2.5% each year. Write an exponential function to model the

miskamm [114]

Answer:

Example: Suppose you give $100 to a bank which pays you 10% compound interest at the end of every year. After one year you will have $100 + 10% = $110, and after two years you will have $110 + 10% = $121.

compound interest image

Problem:

If you deposit $4500 into an account paying 7% annual interest compounded semi anualy , how much money will be in the account after 9 years?

Result:

The amount is $8358.7 and the interest is $3858.7.

Explanation:

STEP 1: To find amount we use formula:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

After plugging the given information we have

STEP 2: To find interest we use formula , since 8358.7 P = we have:

3858.7

Step-by-step explanation:

3 0

2 years ago

A data set lists earthquake depths. The summary statistics are nequals300, x overbarequals5.89 km, sequals4.44 km. Use a 0.01

kirza4 [7]

Answer:

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

Step-by-step explanation:

It is given that a data set lists earthquake depths. The summary statistics are

$n=300$

$\overline{x}=5.89km$

$s=4.44km$

Level of significance = 0.01

We need to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00.

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The formula for z-value is

$z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$

$z=\frac{5.89-5.00}{\frac{4.44}{\sqrt{300}}}$

$z=\frac{0.89}{0.25634351952}$

$z=3.4719$

The p-value for z=3.4719 is 0.000517.

Since the p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

6 0

2 years ago