Rewrite the expression as a single logarithm and simplify the result. ln lcosxl +lnltanxl

1 answer:

6 0

Recall your logarithms rules

$\bf ln|cos(x)|+ln|tan(x)|\\\\
-----------------------------\\\\
log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\qquad thus\\\\
-----------------------------\\\\
ln|cos(x)tan(x)|\implies ln\left| cos(x)\cdot \cfrac{sin(x)}{cos(x)} \right|\implies 
ln|sin(x)|$

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The average distance from the sun to the planet Mercury is about 58,000,000 km. The diameter of a human hair is about 0.0025 cm.

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Answer:

Distance of Sun and Mercury = 58,000,000 km.

In Scientific notation, it would be: 5.8 × 10⁷ Km

Diameter of a human hair = 0.0025 cm

In scientific notation, it would be: 2.5 × 10⁻³ cm

Before Comparison, we need to bring to or vice-versa, so we can easily calculate then, here, we will go from cm to Km.

2.5 × 10⁻³ × 10⁻⁵ Km = 2.5 × 10⁻⁸

Now, we can compare the values,

5.8 × 10⁷ Km > 2.5 × 10⁻⁸

[ reason. - power of smaller number is in negative, it means, it is denominator, which would be very small as compared to other ]

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A store sells mugs. Each mug costs the same amount. During a sale, the store reduces the price of each mug by $1.75. Wen spends

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Answer:

$7.39

Step-by-step explanation:

Let the initial price be x

Then the reduced price is

x - 1.75

If 5 mugs cost $28.20, we have equation:

(x - 1.75)*5 = 28.20
x - 1.75 = 28.20/5
x - 1.75 = 5.64
x = 1.75 + 5.64
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Initial price for 1 mug was $7.39

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It takes 4 hours and 15 minutes to fly from Orlando, Florida, to Boston, Massachusetts. The distance between the two cities is 1

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Answer:

262.12mph and 419kph

Step-by-step explanation:

Given: It takes 4 hours and 15 minutes to fly from Orlando, Florida, to Boston, Massachusetts. The distance between the two cities is 1114 miles

To Find: the average speend of the plane in miles per hour, If every mile is approximately 1.6 kilometers, the speed of the airplane in kilometers per hour

Solution:

Distance between Orlando,Florida and Boston, Massachusetts $=1114$ $\text{miles}$