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3 years ago

Which of the following expressions are equivalent? Justify your reasoning,

Mathematics

1 answer:

marshall27 [118]3 years ago

7 0

Answer:

B and D

Step-by-step explanation:

Anything to a negative power means that it is 1/that to the positive power.

E.g. x^-1 = 1/x^1

In other words, anything to the power of a negative switches sides of a fraction (i.e. if in numerator moves to denominator and vice versa.)

1/x^-1 = 1/1/x^1 which is just equal to x, because there are x number of 1/xs in one (1/x * x =1) Therefore Option B is equal to just x.

D: (assuming the first given term is x^1/3 and not X1/3 (?) Correct me if I'm wrong).

x^1/3 * x^1/3 * x^1/3 is also equal to just x.

This is because when multiplying together terms with the same base (x in this case) the exponents just add together, so:

x^1/3 * x^1/3 * x^1/3 = x^(1/3 +1/3 +1/3) = x^1 = x.

Therefore B and D are equivalent because they both equal x.

Hope this helped!

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Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodiu

Lesechka [4]

Answer:

Approximately $4.75$ .

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ are equal.

${\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}$

Since $\rm CH_3COONa$ is a salt soluble in water. Once in water, it would readily ionize to give $\rm CH_3COO^{-}$ and $\rm Na^{+}$ ions.

Assume that the $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ ions in this solution did not disintegrate at all. The solution would contain:

$0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COOH$ , and

$0.06\; \rm mol$ of $\rm CH_3COO^{-}$ from $0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COONa$ .

Accordingly, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ would be:

$\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

$\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

In other words, in this buffer solution, the initial concentration of the weak acid $\rm CH_3COOH$ is the same as that of its conjugate base, $\rm CH_3COO^{-}$ .

Hence, once in equilibrium, the $\rm pH$ of this buffer solution would be the same as the ${\rm pK}_{a}$ of $\rm CH_3COOH$ .

Calculate the ${\rm pK}_{a}$ of $\rm CH_3COOH$ from its ${\rm K}_{a}$ :

$\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}$ .

7 0

3 years ago

The otherSites Squared10.A cylinder has a diameter of 12 meters and a height of 9 meters. What is thetotal surface area of the c

Gelneren [198K]

The total surface area of a cylinder is given by the formula

$\begin{gathered} A_{cylinder}=2circular\text{ area+curved surface area} \\ =2\pi r^2+2\pi rh \end{gathered}$

Given diameter, d=12meters, we will solve for radius

$\begin{gathered} \text{diameter,d}=2\times radius,r \\ d=2r \\ r=\frac{d}{2} \\ r=\frac{12m}{2} \\ r=6m \end{gathered}$

The height is given as 9meters

Substituting for r and h in the formula will give

$\begin{gathered} A_{cylinder}=2\pi r^2+2\pi rh \\ r=6m;h=9m;\pi=3.14 \\ A_{cylinder}=2\times3.14\times6^2+2\times3.14\times6\times9_{} \end{gathered}$ $\begin{gathered} A_{cylinder}=6.28\times36+6.28\times54 \\ =226.08+339.12 \\ =565.2m^2 \end{gathered}$

Hence the surface area of the cylinder is 565.2m²

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1 year ago

How many minutes are there in 4 hours,30 minutes please help I will give you 12 points

Inessa [10]

There are 60 minutes in one hour. If we are trying to find how many minutes are in 4 hours and 30 minutes, we first need to find out how many minutes are in 4 hours.
To do that, we just need to multiply the amount of minutes in an hour by the amount of hours we have.

60 * 4 = 240

Then, we just add the remaining 30 minutes.

240 + 30 = 270

There are 270 minutes in 4 hours and 30 minutes.
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3 years ago

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MatroZZZ [7]

Answer:

Step-by-step explanation:

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FVn = PV x e^rn

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n = 12 years

plugin values into the formula:

FV₁₂ = $20,000 x e ⁰°⁰³⁸⁵ ⁽¹²⁾

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3 years ago

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marusya05 [52]

Answer:

Step-by-step explanation:

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