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3 years ago

Can somebody please help me with this one thanks so muchhhh.

Mathematics

1 answer:

Nesterboy [21]3 years ago

7 0

Answer:

y=0

Step-by-step explanation:

look at 6 on the x=axis, sine the line falls on the x-axis at 6, the y value is 0

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Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side

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Answer:

cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = $-\frac{1}{3}$

cos(b) = $-\frac{1}{4}$

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = $-\sqrt{1-(-\frac{1}{3})^2}$ [Since, sin(a) = $\sqrt{(1-\text{cos}^2a)}$ ]

= $-\sqrt{\frac{8}{9}}$

= $-\frac{2\sqrt{2}}{3}$

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.

sin(b) = $-\sqrt{1-(-\frac{1}{4})^2}$

= $-\sqrt{\frac{15}{16}}$

= $-\frac{\sqrt{15}}{4}$

By substituting these values in the identity,

cos(a + b) = $(-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})$

= $\frac{1}{12}-\frac{\sqrt{120}}{12}$

= $\frac{1}{12}(1-\sqrt{120})$

= $\frac{1}{12}(1-2\sqrt{30})$

Therefore, cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

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3 years ago

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Answer:

Total number of tables of first type = 23.

Total number of tables of second type = 7

Step-by-step explanation:

It is given that there are 30 tables in total and there are two types of tables.

Let's call the two seat tables, the first type as x and the second type as y.

∴ x + y = 30 ......(1)

Also a total number of 81 people are seated. Therefore, 2x number of people would be seated on the the first type and 5y on the second type. Hence the equation becomes:

2x + 5y = 81 .....(2)

To solve (1) & (2) Multiply (1) by 2 and subtract, we get:

y = 7

Substituting y = 7 in (1), we get x = 23.

∴ The number of tables of first kind = 23

The number of tables of second kind = 7

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