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3 years ago

Find the product of -5x²y⁴ and 3xy³

Mathematics

1 answer:

ycow [4]3 years ago

8 0

Answer: -15x^3y^7

Step-by-step explanation:

-5x^2y^4(3xy^3)

Multiplty the coefficients

Multiply the x terms

and fianally multiply the y terms

-5(3) = -15

x^2 * x = x^3

y^4* y^3 = y^7

= -15x^3y^7

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Step-by-step explanation:

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3 years ago

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 7y = sin(x)

Elza [17]

The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
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Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
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3 years ago

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3 years ago

The school librarian, Mr. Marker, knows the library has 1,400 books but wants to reorganize how the books are displayed on the s

kipiarov [429]

Answer:

200 resource books

800 fiction books

400 nonfiction books

Step-by-step explanation:

Let's define x as the amount of resource books that are in the library. As he has four times as many fiction books as resource books, that means he has 4*x fiction books.

We also know he has half as many nonfiction books as fiction books, that is 1/2*4*x = 2*x nonfiction books.

We just need to find out the value of x.

We know there are 1,400 books in total and there are just 3 types of books. Therefore, if we sum all of them, we get the 1,400.

Written in math language, that is

x + 4x + 2x = 1,400

7x = 1,400

We divide by 7 on both sides and we get

7/7x = 1,400/7

x = 200

Now we replace the x with 200 to know how many books he has of each type:

Resource books = x = 200

Fiction books = 4*x = 4*200 = 800

Nonfiction books = 2*x = 2*200 = 400

Therefore, there are 200 resource books, 800 fiction books and 400 nonfiction books in the library.

The tape diagram is attached as an image.

8 0

3 years ago

Find the product of -5x²y⁴ and 3xy³​

Find the product of -5x²y⁴ and 3xy³