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Pepsi [2]
3 years ago
9

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

Mathematics
1 answer:
NNADVOKAT [17]3 years ago
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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Tom throws a Frisbee into the air from a height of 4 feet with
siniylev [52]

Answer:

68 feet

Step-by-step explanation:

Vertical motion model:

h = -16t² + vt + s

Given v = 64 and s = 4:

h = -16t² + 64t + 4

This is a parabola.  The maximum of a parabola is at the vertex.

For y = ax² + bx + c, the vertex is at x = -b/(2a).

Therefore, the time to reach the maximum height is:

t = -64 / (2 × -16)

t = 2

And the maximum height is:

h = -16(2)² + 64(2) + 4

h = 68

So the Frisbee reaches a maximum height of 68 feet.

5 0
3 years ago
Mike hiked to a lake in 4.5 hours at an average rate of 2
aleksandrvk [35]

Answer:

It took Pedro  <em>3.81 hours</em> to reach the lake.

Step-by-step explanation:

Time taken by Mike to hike a lake = 4.5 hours

Average rate of Mike while hiking the lake = 2\frac{1}{5}\ miles/hr

Formula for distance can be seen as:

Distance = Speed\times Time

Distance traveled by Mike = 4.5 \times 2\frac{1}{5} = 4.5\times \frac{11}{5} = 9.9\ miles

Rate of Pedro while hiking the same distance = 2\frac{3}{5}\ miles/hr = \frac{13}{5}\ miles/hr

Given that, Pedro also travels the same distance.

And we have to find the Time.

Time = \dfrac{Distance}{Speed}

Time = \dfrac{9.9}{\frac{13}{5}}\\\Rightarrow Time = \dfrac{9.9\times 5}{13} = \bold{3.81\ hours}

It took Pedro  <em>3.81 hours</em> to reach the lake.

6 0
2 years ago
C. Find the value of x below:<br> 15.r + 5<br> -2 + 16.
nydimaria [60]

Answer:

7

Step-by-step explanation:

(15x + 5) and (-2 + 16x) represents the measures of corresponding angles.

Measures of corresponding angles are equal.

Therefore,

- 2 + 16x = 15x + 5

16x - 15x = 5 + 2

x = 7

5 0
3 years ago
Tom drives a truck. His regular trip is a distance of 280 km. He drives at an average speed of 80 km/h. For safety reasons Tom’s
kakasveta [241]
Cost of fuel = 30% of $400 000 = 30/100 x 400000 = $120 000

Fuel amount = $120 000/$1.5 = 80 000 liters
new cost of fuel = 80000 x $1.6 = $144 000

increase in cost = 144000 - 120000 = $24000

So the increase in petrol price increases the operating cost by $24000
5 0
3 years ago
Read 2 more answers
Brainliest if correct
Westkost [7]

Answer:

2y+6

Step-by-step explanation:

distribute

4 0
2 years ago
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