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umka21 [38]
2 years ago
11

Find x. \/3 1.5 3 \/3 2

Mathematics
2 answers:
Mnenie [13.5K]2 years ago
7 0

Answer:

x = \sqrt{3}

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{3}{x} = \sqrt{3} ( multiply both sides by x )

3 = x × \sqrt{3} ( divide both sides by \sqrt{3} )

\frac{3}{\sqrt{3} } = x , then rationalising the denominator

x = \frac{3}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{3\sqrt{3} }{3} = \sqrt{3}

serg [7]2 years ago
3 0

x = \sqrt{3}

Step-by-step explanation:

Given:

\sin(ABC) =  \frac{AC}{AB}

=  >  \sin(60) =  \frac{3}{AB}

=  >AB= 2 \sqrt{3}

Now by Pythagoras theorem,

AC^{2} + BC^{2} = AB^{2}

Substituting values,

{3}^{2} +  {x}^{2} = (2 \sqrt{3})^{2}

=  >  {x} =  \sqrt{3}

Hence, value of x is \sqrt{3}

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Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate
salantis [7]
The population Pa of insect A after t years is given by the equation 
     Pa = 1.3(1-0.038)^t 
while the population Pb of insect B after t years is 
     Pb = 2.1(1-0.046)^t

We equate the above expressions to find the number of years t it will take the two populations to be equal: 
     Pa = Pb
     1.3(1-0.038)^t  = 2.1(1-0.046)^t
     1.3(0.962)^t  = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.

We can now solve for t:
     (0.962)^t / (0.954)^t = 2.1/1.3
     (0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
     t = log (2.1/1.3) / log (0.962/0.954)
     t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
8 0
3 years ago
Read 2 more answers
Please help!! I'm really confused
chubhunter [2.5K]

Answer:

(-4,3)

Step-by-step explanation:

G is plotted 4 units left and 3 units up

:) ur welcome

8 0
3 years ago
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Please solve the following question!!
Komok [63]
2(21x − 7) + 4(3x + 2) = 6(2x + 9) + 3
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4 0
3 years ago
Round to the nearst tenth
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Answer:

Step-by-step explanation:

4 0
3 years ago
Values of k for which the quadratic equation 2x - kx + k 0 has equal roots is
WARRIOR [948]

Answer:

The answer is D.

Step-by-step explanation:

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D =  {b}^{2}  - 4ac

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0 =  {k}^{2}  - 4(2)(k)

{k}^{2}  - 8k = 0

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4 0
3 years ago
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