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Lady bird [3.3K]
4 years ago
7

How do you expand ln(2x^2) & log2(sqrt8x^2)

Mathematics
1 answer:
olga2289 [7]4 years ago
5 0
㏑(2x²)
㏒(2x²)/㏒(e)  Change from the natural logarithm to logarithm divided by a logarithm.
2㏒(2x)/㏒(e) Change from ㏒(2x²) to 2㏒(2x)
(2㏒(2) + 2㏒(x))/㏒(e) Factor 2㏒(2x).


㏒₂(√(8x²))
㏒₂(2x√2) Change √8x² to 2x√2.
㏒₂(2x) + ㏒₂(√2) Factor ㏒₂(2x√2).
㏒₂(2) + ㏒(x) + 0.5 Change ㏒₂(2) to 0.5.
1 + ㏒(x) + 0.5 Change from ㏒₂(2) to 1.
1 + 0.5 + ㏒(x) Add 1 and 0.5.
1.5 + ㏒(x)
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HELP!
emmasim [6.3K]

A) Divide the total height by the average height:

26.4 / 1.2 = 22 total boys.


B) Divide total feet by total time:

440 feet / 20 seconds = 22 feet per second.\

Because the submarine is diving the rate would become negative 22 feet per second.

7 0
3 years ago
Answer question! I really need help
emmasim [6.3K]
I can't answer it the problem
6 0
3 years ago
Determine if these values form a right triangle. E
LekaFEV [45]

Answer:

They do not.

Step-by-step explanation:

a² + b² = c²    c is the hypotenuse

9² + 12² = 17²

81 + 144 = 289

225  ≠  289

4 0
3 years ago
Sue makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 1:4. Yellow paint is s
Lostsunrise [7]

Answer:

Sue's percentage profit = 9% on each tin of green paint she sells.

Step-by-step explanation:

Litres of green paints mixed = 50 litres

Ratio of litres of yellow paint and litres of blue paint = 1:4.

To determine the litres of yellow paint, we say:

yellow \: paint =  \frac{1}{4}  \times 50 = 10 \: litres

To determine the litres of blue paint, we say:

blue \: paint =  \frac{4}{5}  \times 50 = 40 \: litres

Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76

Similarly,

Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232

Total cost of yellow and blue paints = £232 + £76

= £308

Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.

Thus, selling price of the green paint = £446.60

profit \: \% =  \frac{selling \: price - cost \: price}{cost \: price}  \times  \frac{100}{1}

profit \: \% =  \frac{446.60 - 308}{308}  \times  \frac{100}{1}

profit \: \% =  \frac{138.60}{308} \times  \frac{100}{1}

profit \: \% = 0.45 \times 100

profit \: \% = 45\%

Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:

profit \: \% \: on \: each \: green \: tin =  \frac{45}{5}  = 9\%

Hence, Sue's percentage profit for selling each tin of green paint is 9%.

Proof

9% × 5 tins of green paint = 45%

4 0
4 years ago
-7 = z/-6 <br><img src="https://tex.z-dn.net/?f=%20-%207%20%3D%20%20%5Cfrac%7Bz%7D%7B%20-%206%7D%20" id="TexFormula1" title=" -
lara [203]
-7 = z/-6
-7 (-6) = z
42 = z

Z = 42
4 0
4 years ago
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