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mote1985 [20]
3 years ago
6

Show that log√7 + log√20 - log√14 = 1/2

Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

Alright, lets get started.

log \sqrt{7}  + log \sqrt{20}  - log\sqrt{14} = \frac{1}{2}

We could write this square root as \frac{1}{2}

log7^{\frac{1}{2}} + log20^{\frac{1}{2}}- log14^{\frac{1}{2}}

Using the property of logm^{n } = n log (m)

\frac{1}{2}log 7 + \frac{1}{2} log 20 - \frac{1}{2} log14

\frac{1}{2} is common in each term, so

\frac{1}{2}(log7 + log 20 - log 14)

Using property of log m  + log n = log(mn)

\frac{1}{2}(log 140 - log 14)

Using property of log m - log n = log\frac{m}{n}

\frac{1}{2}log\frac{140}{14}

\frac{1}{2} log 10

log 10 value is 1 , hence

\frac{1}{2} * 1 = \frac{1}{2} : Answer

Hope it will help :)

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Lapatulllka [165]

Let's go through the choices.

A. HL, hypotenuse-leg. Yes we have a right triangle with congruent hypotenuse and leg which gives us congruent triangles, CHECK

B. HA, hypotenuse actute. Yes we have a right triangle witha congruent hypotenuse and acute angle, so congruent triangles, CHECK.

C. LL. leg leg. We don't know HL=PE so we can't use this theorem here. NO.

D. SAS, side angle side. For this one we first have to prove angle HEL is congruent to angle PME which is easily done with the Triangle Angle theorem (two congruent angles means three congruent angles) and then we can use SAS because then we have congruent sides and a congruent included angle. This one's a judgement call, I'll say NO because of the two steps.

E. AAS. Angle Angle Side, yes we have two congruent angles and a side. CHECK

F. ASA. Again we need an additional step before we conclude two angles and an included side are congruent. So again a judgement call, we'll go with NO.

7 0
3 years ago
Water is launched straight up out of a fountain so that the water droplets return to the ground after about 6 s. What is the ini
Reptile [31]

Answer:

The initial velocity is 314.88 ft/s

The maximum height reached is 144 meter.

Step-by-step explanation:

The total time period is 6 seconds for the raindrop.

Using the equation of motion by differentiating h(t) to give v(t),

<em>v(t) = -32(t) + 96</em>

<em>at t=0, v(0) = 96 m/sec = 314.88 ft/sec</em>

It is given that,

h(t) = (-16)(t^{2}) + 96t

differentiating we get

<em>v(t) = -32(t) + 96</em>

at highest point, v=0;

thus gives us highest point achieved at t=3 seconds.

Height at t=3 seconds is,

<em>h(t) = (-16)(t^{2}) + 96t =  (-16)(3^{2}) + 96(3) = 144 m</em>

3 0
3 years ago
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Step-by-step explanation:

4x + 2xy=

4×4 + 2×4×-3

= 16 + (-24)

= - 8

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timofeeve [1]

duh-

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Answer:

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Step-by-step explanation:

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