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Tanya [424]
3 years ago
14

Pls can someone help me

B2%7D%20-%20%20log10%20%5Csqrt%7B7%7D%20" id="TexFormula1" title=" log10 \sqrt{36} + log10 \sqrt{2} - log10 \sqrt{7} " alt=" log10 \sqrt{36} + log10 \sqrt{2} - log10 \sqrt{7} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0

Answer:

= log_{10}(\frac{6\sqrt{2} }{\sqrt{7} } )

Step-by-step explanation:

Given the expression log10\sqrt{36} + log10\sqrt{2}  - log10\sqrt{7} \\

According to the law of logarithm;

loga + log b = log(ab) and log a - log b = log(a/b)

The given expression becomes;

log10\sqrt{36} + log10\sqrt{2}  - log10\sqrt{7} \\= log_{10}(\frac{\sqrt{36} \times \sqrt{2} }{\sqrt{7} })\\= log_{10}(\frac{6\sqrt{2} }{\sqrt{7} } )

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What is the length of missing side JK? Round Answer to nearest tenth please.
zvonat [6]

Given:

Triangle LJK.

LJ = 89 in, LK = 28 in and m∠L = 42°

To find:

The length of missing side JK.

Solution:

LJ = k = 89

LK = j = 28

JK = l = ?

Using law of cosine:

l^{2}=j^{2}+k^{2}-2 jk \cdot \cos L

Substitute the given values.

l^{2}=28^{2}+89^{2}-2 \cdot 28 \cdot 89 \cdot \cos 42^\circ

l^{2}=784+7921-4984 \cdot (0.7)

l^{2}=784+7921-4984 \cdot (0.7431)

l^{2}=784+7921-3703.6

l^{2}=5001.4

Taking square root on both sides.

l=70.7

The length of the missing side is 70.7 in.

4 0
3 years ago
A thermometer reading 7 °C is brought into a room with a constant temperature of 34°C. If the thermometer reads 14 °C after 4 ​m
never [62]
For this case we are going to define the following variable:
 x: time in minutes
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 t (x) = (14/4) x + 7
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 For x = 11 we have:
 t (11) = (14/4) * (11) + 7
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Mumz [18]

Answer:

<h2>1. x = 4</h2><h2>2. x = 20</h2>

Step-by-step explanation:

1.

ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:

\dfrac{AC}{AJ}=\dfrac{AB}{AK}

We have:

AC = 1 + 4 = 5

AJ = 1

AB = 1 + x

AK = 1

Substitute:

\dfrac{5}{1}=\dfrac{1+x}{1}

5=1+x           <em>subtract 1 from both sides</em>

4=x\to x=4

2.

ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:

\dfrac{VU}{VM}=\dfrac{VT}{VN}

We hve:

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Substitute:

\dfrac{x+8}{x}=\dfrac{49}{35}              <em>cross multiply</em>

35(x+8)=49x          <em>use the distributive property a(c + b) = ab + ac</em>

35x+280=49x              <em>subtract 35x from both sides</em>

280=14x         <em>divide both sides by 14</em>

20=x\to x=20

3 0
3 years ago
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