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2 years ago

Question 7(Multiple Choice)

Mathematics

2 answers:

aalyn [17]2 years ago

6 0

Answer:

C.) $log_2(\frac{x^3z^2}{y^4})$

Step-by-step explanation:

To find the answer, you need to simplify the expression. To do so, you must combine the logs. You can combine the logs because they all have the same subscript (2).

$3 log_2x - 4log_2y + 2log_2z$ <----- Given expression

$log_2x^3-log_2y^4+log_2z^2$ <----- Raise coefficients to variables

$log_2x^3+log_2z^2-log_2y^4$ <----- Rearrange

$log_2(x^3z^2)-log_2y^4$ <----- Multiply added logs

$log_2(\frac{x^3z^2}{y^4})$ <------ Divide subtracted log

hram777 [196]2 years ago

4 0

Express the multiplication of a logarithm number of an expression as the logarithm of the power of the expression.

Take the product of the arguments

$\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}$

Therefore, the correct option is alternative "C".

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Find the slope of the line that passes through each pair of points

lyudmila [28]

Answer:

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Step-by-step explanation:

The slope of the line can be found by

m = (y2-y1)/(x2-x1)

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3 years ago

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3 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that <em>y</em> is a function of <em>x</em> :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ <em>x</em> ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

7 0

3 years ago

Jessa bought 15 pieces of ribbon. Each piece of ribbon was 2.25 yards long. What is the total amount of ribbon Jessa bought? ent

algol [13]

Hello,

15 pieces of ribbon, each is 2.25 yards long.
15 x 2.25 = 33.75 yards of ribbon.

Hope this helped!

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3 years ago

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there are 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. if you pick 2 cubes at random with replacement. what is p

Nimfa-mama [501]

There are 4 reds out of 10 so the probability for a red would be 4/10 and for a yellow it would be 1/10. multiply them together to get 4/100 so your probability would be 1/25 or 0.04 or 4%

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3 years ago

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