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AfilCa [17]
3 years ago
14

Use log4(2) = 0.5 to approximate the value of log4(32)

Mathematics
1 answer:
shepuryov [24]3 years ago
4 0

log4(32) = 2.5

Step-by-step explanation:

Given that,

log4(2) = 0.5

To find: log4(32)

32 can be written as 2 power 5

log4(32) = log4(2^5)

= 5 log4(2)

In the logarithms if there is a power it is multiplied and only the log is applied to the base of the powered term.

Hence,

log4(32) = 5log4(2)

We know that log4(2) = 0.5

So,

log4(32) = 5(0.5)

log4(32) = 2.5

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You purchase a pair of jeans online. You will be charged 6% sales tax on the jeans and an additional shipping charge of $8.95, w
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3 years ago
A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. at w
Katena32 [7]

The height of broken part of tree from ground is 5.569m.

Justification:

Let BD is a tree of height 12 m.

<u>Suppose it got bent at a point C and let the part CD take the position CA, meeting the ground at A</u>.

i.e., CD = AC = h m

<u>Broken part makes 60° angle from ground</u>

So, ∠BAC = 60°

<u>Now, height of remaining part of tree</u> = (12 – h)m.

In right angled ∆ABC,

sin 60° = BC/AC

⇒ √3/2 = (12 - h)/h

⇒ √3h = 2(12 – h)

⇒ √3h = 24 – 2h

⇒ √3h + 2h = 24

⇒ h(√3 + 2) = 24

⇒ h(1.732 + 2) = 24

⇒ h(3.732) = 24

⇒ h = 24/3.732 = 6.4308 m

<u>Hence, height of broken tree from ground</u>

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<u>Hence, tree is broken 5.569 m from ground</u>.

<u>Note</u>: See attached picture.

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3 years ago
8. A rectangle's sides are measured to be 6.2 cm and 9.3 cm. What is the
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3 years ago
#1. The area of a square tile is 53.4cm^2. find the length of one side of the tile, rounded to the nearest 10th.
andrey2020 [161]

Problem 1

<h3>Answer: 7.3</h3>

Explanation: Apply the square root to the area to get the side length. This only applies to areas that are squares (hence the name).

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

Problem 2

<h3>Answer:  C) 1.3</h3>

Explanation: Use your calculator to find that choices A,B,D plugged into the square root function yield terminating decimal values. "Terminating" means "stop". This implies that they are perfect squares (though not perfect squares in the sense of whole number perfect squares which you may be used to). Choice C is the only value that has a square root that leads to a non-terminating decimal. The digits of this decimal go on forever without any pattern. The value is irrational.

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  • sqrt(1.3) = 1.140175425 keeps going forever without any pattern
  • sqrt(0.09) = 0.3 terminating decimal

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

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<h3>Answer:  23.6 feet approximately</h3>

Explanation: Apply the square root to 15.5 to get roughly 3.937; this is the approximate side length of one square. Six of these tiles placed together will lead to a total length of roughly 6*3.937 = 23.622 which rounds to 23.6 feet. Like with problem 1, the square root being used like this only works for square areas.

5 0
3 years ago
Read 2 more answers
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