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3 years ago

PLEASE HELP ME OK SO WHAT IS X/5 + 6 <2

Mathematics

1 answer:

4vir4ik [10]3 years ago

6 0

Answer:

x < -20

Step-by-step explanation:

$\frac{x}{5}$ + 6 < 2

subtract 6 from both sides of the equation

$\frac{x}{5}$ < 2 - 6

$\frac{x}{5}$ < -4

multiply both sides of the equation by 5

x < -4 * 5

x < -20

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You’re given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side

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3 years ago

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How do you solve this problem? 2|x-3|-5=7

Leona [35]

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3 years ago

Solve the initial value problems.

slavikrds [6]

Both equations are linear, so I'll use the integrating factor method.

The first ODE

$xy' + (x+1)y = 0 \implies y' + \dfrac{x+1}x y = 0$

has integrating factor

$\exp\left(\displaystyle \int\frac{x+1}x \, dx\right) =\exp\left(x+\ln(x)\right) = xe^x$

In the original equation, multiply both sides by eˣ :

$xe^x y' + (x+1) e^x y = 0$

Observe that

d/dx [xeˣ] = eˣ + xeˣ = (x + 1) eˣ

so that the left side is the derivative of a product, namely

$\left(xe^xy\right)' = 0$

Integrate both sides with respect to x :

$\displaystyle \int \left(xe^xy\right)' \, dx = \int 0 \, dx$

$xe^xy = C$

Solve for y :

$y = \dfrac{C}{xe^x}$

Use the given initial condition to solve for C. When x = 1, y = 2, so

$2 = \dfrac{C}{1\cdot e^1} \implies C = 2e$

Then the particular solution is

$\boxed{y = \dfrac{2e}{xe^x} = \dfrac{2e^{1-x}}x}$

The second ODE

$(1+x^2)y' - 2xy = 0 \implies y' - \dfrac{2x}{1+x^2} y = 0$

has integrating factor

$\exp\left(\displaystyle \int -\frac{2x}{1+x^2} \, dx\right) = \exp\left(-\ln(1+x^2)\right) = \dfrac1{1+x^2}$

Multiply both sides of the equation by 1/(1 + x²) :

$\dfrac1{1+x^2} y' - \dfrac{2x}{(1+x^2)^2} y = 0$

and observe that

d/dx[1/(1 + x²)] = -2x/(1 + x²)²

Then

$\left(\dfrac1{1+x^2}y\right)' = 0$

$\dfrac1{1+x^2}y = C$

$y = C(1 + x^2)$

When x = 0, y = 3, so

$3 = C(1+0^2) \implies C=3$

$\implies \boxed{y = 3(1 + x^2) = 3 + 3x^2}$

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2 years ago

I give you a tricky one Express 108 ×125as a product of prime factors in exponential form

lana [24]

Answer:

$108 \times 125=2^2 \times 3^3 \times 5^3$

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

$108=2^2 \times 3^3\\125=5^3$

Step 2: Write the product together, and combine any like terms if any

Therefore,

$108 \times 125=2^2 \times 3^3 \times 5^3$

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3 years ago

The standard form of the number 5, 976,000,000,000,000,000,000,000 is

nirvana33 [79]

Answer:

$5.976\times10^{24}$

Step-by-step explanation:

Standard form, also called scientific notation, is a more compact way of writing very big or very small numbers. All numbers in scientific notation have the form

$m\times10^b$

where m is a number between 1 and 10, and b is an integer that represents how we've shifted the decimal point from the original number. For example, the number 23,000 in standard form would be written as 2.3 × 10⁴, since we have to shift the decimal point 4 places to the right to get back our original number.

We can turn 5,976,000,000,000,000,000,000,000 into a number between 1 and 10 by shifting the decimal 24 places to the left, giving us 5.976. We'll save that 24 as the exponent for our 10, giving us the final form

$5.976\times10^{24}$

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3 years ago