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3 years ago

5. (9r 3 + 5r 2 + 11r) + (-2r 3 + 9r - 8r 2)

Mathematics

1 answer:

ad-work [718]3 years ago

3 0

Answer:

7r³ - 3r² + 20r

Step-by-step explanation:

(9r³ + 5r² + 11r) + (-2r³ + 9r - 8r²)

You can get rid of the parentheses since there is nothing to distribute.

9r³ + 5r² + 11r - 2r³ + 9r - 8r²

Combine like factors.

7r³ - 3r² + 20r

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Implicit differentiation of 1/x +1/y=5 y(4)= 4/19 y'(4)=?

Aneli [31]

$\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\$

Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

$-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}$

Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.

$\frac{dy}{dx}=-5(\frac{4}{19})^2-\frac{(\frac{4}{19})^2}{(4)^2}\\\\\frac{dy}{dx}=-5(\frac{16}{361})-\frac{(\frac{16}{361})}{16}\\\\\frac{dy}{dx}=\frac{-80}{361}-\frac{1}{361}\\\\\frac{dy}{dx}=\frac{-81}{361}$

5 0

3 years ago

A salesperson is paid a flat rate plus a fixed percentage of her sales. Last month, she sold $16,000 worth of goods and was paid

Feliz [49]

Answer:

She will be paid $1,350

Step-by-step explanation:

Linear Modeling

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

y=mx+b, where m and b are constants.

The payments for a salesperson will be linearly modeled. There are two known points: When the sales were $16,000, the payment was $1,600. This makes the point (16,000;1,600).

We also know when the sales were $12,000, the payment was $1,400. The point is (12,000;1,400)

Let's use the points to find the values of m and b.

Using (16,000;1,600):

1,600=m*16,000+b

Using (12,000;1,400):

1,400=m*12,000+b

Subtracting both equations:

200=16,000m-12,000m

200=4,000m

Solving:

m=200/4,000=0.05

Using the first equation and the value of m:

1,600=0.05*16,000+b

1,600=800+b

Solving:

b=800

The equation is now complete:

y=0.05x+800

She sold $11,000 this month, so the payment is:

$y=0.05\cdot 11,000+800$

Y=550+800=1,350

She will be paid $1,350

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3 years ago

Which of the following are square roots of the number below check all that apply 225

denpristay [2]

15*15=225. There's only one square root of 225... there's only one square root of any number ...

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3 years ago

Which property is illustrated, 1n = n

steposvetlana [31]

1n=n Answer:

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3 years ago

How to write half of a number is equal to -5?

Oxana [17]

1/2x=-5 is the answer

7 0

3 years ago

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