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2 years ago

Pls help !!!!!!!!! i need help fast !!!!

Mathematics

1 answer:

Zepler [3.9K]2 years ago

7 0

9514 1404 393

Answer:

the product is equal to 409
the product is less than 751
the product is less than 173

Step-by-step explanation:

A fraction has a numerator (above the fraction bar) and denominator (below the fraction bar). The denominator tells you the number of equal pieces one whole is divided into. The numerator tells you how many of those pieces you have.

If you have fewer than the total number of pieces, you have less than the whole amount.

If the numerator and denominator are equal, you have exactly the whole amount.

If the numerator is larger than the denominator, you have more than the whole amount.

The first fraction, 72/72 is equal to 1. Multiplying by that value gives the original number. The product is equal to 409.

The second and third fractions have numerators less than their denominator. They represent less than the whole amount, so multiplying by those values will give a product less than the original number:

less than 751

less than 173

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is a

Lyrx [107]

Answer:

A) 0

Step-by-step explanation:

When x is divided by 11, we have a quotient of y and a remainder of 3

x/11 = y + 3

x = 11y + 3 ........(1)

When x is divided by 19, we have a remainder of 3 also

x/19 = p + 3 (p = quotient)

x = 19p + 3 ..........(2)

Equate (1) and (2)

x = 11y + 3 = 19p + 3

11y + 3 = 19p + 3

11y = 19p + 3 -3

11y = 19p

Divide both sides by 11

11y/11 = 19p/11

y = 19p/11

y and p are integers. 19 is a prime number. P/11 is also an integer

y = 19(integer)

This implies that y is a multiple of 19. When divided by 19, there is no remainder. The remainder is 0

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3 years ago

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borishaifa [10]

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Number of blocks to fill prism = 4/27 / 1/216 = (216*4) / 27 = 32

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