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3 years ago

-4x< 8 help please solving one step inequalities

Mathematics

2 answers:

Aloiza [94]3 years ago

8 0

Answer:

x>-2

Step-by-step explanation:

when dividing by a negative number, the inequality sign flips.

KonstantinChe [14]3 years ago

6 0

Answer:

x > -2

Step-by-step explanation:

-4x< 8 (divide both sides by -4)

-x < 8/4

-x < 2 (divide or multiply both sides by -1, remember to flip the inequality when multiplying or dividing by -1)

x > 2 (-1)

x > -2

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Calculate the quotient below and give your answer in scientific notation.<br> 2.64*10^-3\8.0*10^0

Zolol [24]

Answer:

The quotient of: $\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}$ is: $\mathbf{3.3\times 10^{-4}}$

Step-by-step explanation:

We need to find quotient of: $\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}$

We know that $10^0=1$

Now solving:

$\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}\\=\frac{2.64\cdot 10^{-3}}{8.0}\\=\frac{0.00264}{8}\\=0.00033$

Writing it in scientific notation

$0.00033\\=3.3\times10^{-4}$

So, the quotient of: $\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}$ is: $\mathbf{3.3\times 10^{-4}}$

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After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decrease

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Answer:

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3 years ago

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A rental car agency charges $220.00 per week plus 50.15 per mile to rent a car. How many miles can you travel in one week for $3

babymother [125]

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

Calculus 2

FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

$\displaystyle \int_1^47\sqrt{\ln(x)}\, dx$

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

The trapezoidal rule is given by:

$\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)$

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

$\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}$

Therefore, the trapezoidal approximation is:

$\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)$

Evaluate:

$\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337$

The midpoint rule is given by:

$\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x$

Thus:

$\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)$

Simplify:

$\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319$

Simpson's Rule is given by:

$\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)$

So:

$\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)$

Simplify:

$\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834$

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3 years ago