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svlad2 [7]
4 years ago
12

Help me pleaseeeeeee ​

Mathematics
1 answer:
lions [1.4K]4 years ago
3 0

the answer is D

Step-by-step explanation:

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If a = √3-√11 and b = 1 /a, then find a² - b²​
Serga [27]

If b=\frac1a, then by rationalizing the denominator we can rewrite

b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8

Now,

a^2 - b^2 = (a-b) (a+b)

and

a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8

a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8

\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}

5 0
2 years ago
What is 8.7% of 5300? Round to the nearest hundredth.
ASHA 777 [7]

Answer:

Step-by-step explanation:

8.7% of 5300 is 461.1

Rounding up to the nearest hundredth gives your answer as

500

4 0
3 years ago
Please helppppppppppp
vichka [17]

Answer:

21.92

Step-by-step explanation:

division

87.68 ÷ 4

6 0
3 years ago
Read 2 more answers
A plane travels 236 miles in 1. 4 hours against the wind. On the return trip, it travels the same 236 miles in 1 hour. Find the
KIM [24]
Speed is given by the distance traveled divided by the time spent.

The net speed with which the plane traveled against the wind is given by \frac{236}{1.4} =168.57\ mi/hr while the speed with which the plane travelled in the return trip is given by \frac{236}{1} =236\ mi/hr 

Let the speed of the plane be v and the speed of the wind be w, then when the plane was traveling against the sun, we have, v - w = 168.57 and when the plane is travelling in the direction of the wind, we have, v + w = 236.

 Subtracting the first equation from the second equation, we have: 2w = 236 - 168.57 = 67.43

Thus, w = 67.43 / 2 = 33.715

Therefore, the speed of the wind is approximately 33.7 mi/hr.
5 0
3 years ago
Read 2 more answers
A beam of polarized light with intensity I0 and polarization angle θ0 strikes a polarizer with transmission axis θTA. What angle
11Alexandr11 [23.1K]

Answer:

θ^{TA} - θ^{0}

Step-by-step explanation:

According to the theory of Malus, when a completely plane polarized light is incident on an analyzer, the intensity 'I' of the light wave transmitted by the analyzer is proportional to the square of the cosine of angle between the transmission axes of the polarizer and analyzer. Therefore:

Using the theory of Malus, we need to estimate the angle between the transmission axis θ^{TA} and the polarization axis θ^{0}.

Thus:

angle θ = θ^{TA} - θ^{0}

4 0
3 years ago
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