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puteri [66]
3 years ago
13

Use the laws of logarithms to rewrite the expression ln 4throot(xy) in terms of ln x and ln y. After rewriting ln 4throot(xy) =

A ln x + B ln y we find A= and B=
Mathematics
1 answer:
Ugo [173]3 years ago
4 0
\bf log_{{  a}}(xy)\implies log_{{  a}}(x)+log_{{  a}}(y)
\\ \quad \\\\
% Logarithm of exponentials
log_{{  a}}\left( x^{{  b}} \right)\implies {{  b}}\cdot  log_{{  a}}(x)\\\\
and\qquad a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\

\bf ln\left( \sqrt[4]{xy} \right)\implies ln\left[ (xy)^{\frac{1}{4}} \right]\implies ln\left[ x^{\frac{1}{4}} y^{\frac{1}{4}} \right] 
\\\\\\
ln\left( x^{\frac{1}{4}} \right)+ln\left( y^{\frac{1}{4}}  \right)\implies \frac{1}{4}ln(x)+\frac{1}{4}ln(y)
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tia_tia [17]

Answer:

Step-by-step explanation:

Each of the four sides of this triangular prism has height 8 m and base 12 m.  The area of each face this thus A = (1/2)(base)(height), or

A = (1/2)(12 m)(8 m) = 48 m^2.   The total side area is thus 192 m^2.

This is the surface area.  If we want to include the base area, that would be another (12 m)^2 , or 144 m^2.

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4 years ago
A 12-pint bucket of paint costs $51.60. What is the price per quart?
My name is Ann [436]

Answer: $8.60

Step-by-step explanation:

1 pint = 0.5 quart

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6 0
3 years ago
It’s asking for the area<br> Please help me! Thank you!
Sliva [168]
<h3>Answer:   x^2+9x+8</h3>

==============================================================

Explanation:

With many math problems, a good strategy is to break things down into smaller pieces. In this case, we need to find the area of each individual smaller rectangle

A = blue rectangle area = length*width = x*x = x^2

B = purple rectangle area = length*width = x*1 = x

C = green rectangle area = length*width = 8*x = 8x

D = orange rectangle area = length*width = 1*8 = 8

Add up A through D to get the overall area of the entire or largest rectangle possible

total area = A+B+C+D = x^2+x+8x+8 = x^2+9x+8

notice how x+8x turns into 9x. You can think of it as 1x+8x = (1+8)x = 9x

This is because x and 8x are like terms which can be combined. Everything else is left as is.

Because we don't know what number goes in place for x, we cannot simplify or evaluate x^2+9x+8 any further.

4 0
4 years ago
Teresa bought 8 packages of paper. Each package contained 10 pads of paper, and each pad of paper cost $2. How many pads of pape
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7 0
3 years ago
HELPPPPPPPP<br><br> In WXY, y=690 cm, w=440 cm and angle X=163°. Find angle W to the nearest degree
Ede4ka [16]

Answer:

The angle W is approximately 7°.

Step-by-step explanation:

Since angle X is adjacent to sides y and w and opposite to side x, we calculate the length of side x by Law of the Cosine:

x = \sqrt{y^2+w^2-2\cdot y\cdot w \cdot \cos X} (1)

Where:

y, z - Side lengths, in centimeters.

W - Angle, in sexagesimal degrees.

If we know that y = 690\,cm, w = 440\,cm and X = 163^{\circ}, then the length of the side x is:

x = \sqrt{y^2+w^2-2\cdot y\cdot w \cdot \cos X}

x\approx 1118.199\,cm

By Geometry we know that sum of internal angles in a triangle equals 180°. If X is an obtuse, then Y and W are both acute angles. By Law of the Sine we find angle W:

\frac{x}{\sin X}= \frac{w}{\sin W} (2)

\sin W = \left(\frac{w}{x} \right)\cdot \sin X

W = \sin^{-1}\left[\left(\frac{w}{x} \right)\cdot \sin X\right]

If we know that X = 163^{\circ}, w = 440\,cm and x\approx 1118.199\,cm, then the angle W is:

W = \sin^{-1}\left[\left(\frac{w}{x} \right)\cdot \sin X\right]

W \approx 6.606^{\circ}

Hence, the angle W is approximately 7°.

3 0
3 years ago
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