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2 years ago

Simplify 1. √28 2. √72 3. √2 times √10 Please help

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

5 0

Answer:

Step-by-step explanation:

1. 2 square root 7

2. 6 square root 2

3. 2 square root 5

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write the logarithm as a sum or difference of logarithms. simplify each term as much as possible. log4(6ab)

Dominik [7]

The logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

<h3>Simplifying Logarithms</h3>

From the question, we are to write the given logarithm expression as a sum or difference of logarithms

The given logarithm is

$log_{4 }6ab$

This can be written as

$log_{4 }6 \times a \times b$

From one of the rules of logarithm, we have that

$log_{x }yz= log_{x }y + log_{x }z$

Thus,

$log_{4 }6 \times a \times b$ becomes

$log_{4 }6 + log_{4 }a + log_{4 }b$

This can be further simplified into

$log_{4 }3 \times 2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b$

If desired, this can be further simplified into

$log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b$

$\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Hence, the logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Learn more on Simplifying logarithms here: brainly.com/question/17851187

#SPJ1

8 0

1 year ago

A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22 mi/h. Find the speed and direc

Minchanka [31]

Answer: The speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

Step-by-step explanation:

Since we have given that

Speed at which woman walks due west = 3 mi/hr

Speed at which ship moving due north = 22 mi/hr

Now it forms "Pythagorus theorem":

So, it becomes,

$H^2=B^2+P^2\\\\H^2=3^2+22^2\\\\H^2=9+484\\\\H^2=493\\\\H=\sqrt{493}\\H=22.20\ mi/hr$

And the direction of the woman relative to the surface of the water is given by

$\theta=\sin^{-1}x(\dfrac{3}{22.2})=7.76\approx 8^\circ$

Hence, the speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

5 0

3 years ago

Plz help!!<br> Consider the given right triangle.

aalyn [17]

Answer:

b = 8

c = 16

Step-by-step explanation:

From the given right triangle,

a = $8\sqrt{3}$ , m(∠B) = 30°

By applying sine rule in the given triangle,

cos(B) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

cos(B) = $\frac{BC}{AB}$

cos(30°) = $\frac{8\sqrt{3}}{c}$

$\frac{\sqrt{3} }{2}= \frac{8\sqrt{3} }{c}$

c = 16

Further we apply tangent rule,

tan(B) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(30°) = $\frac{b}{a}$

$\frac{1}{\sqrt{3}}=\frac{b}{8\sqrt{3} }$

b = 8

4 0

2 years ago

What is a statistical question

77julia77 [94]

If Boonk steals everyday for 2 items each day how many items will Boonk have stole for 4 months

3 0

3 years ago

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How many millimeters are in 15 centimeters

finlep [7]

1 centimeter is equivalent to 10 millimeters. So 15x10=150 millimeters.
Hope this helped! :D

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2 years ago

Read 2 more answers