3. Rectangle J is 6 feet wide and 9 feet long.

Mathematics

1 answer:

Furkat [3]2 years ago

8 0

Answer:

No it's not!

Step-by-step explanation:

because the length (long) of J and K are totally different whereas the breadth(width) of J and K is also different which does make similar in sense

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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

maria [59]

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

5 0

3 years ago

HELP ON GEOMETRY!!! PHOTO ATTACHED

Dvinal [7]

Answer:

q = 3 units

Step-by-step explanation:

$In\: \triangle GFH \: and\; \triangle GJI\\\angle GFH \cong \angle GJI..(each\: 90\degree)\\\angle FGH \cong\angle JGH..(common\: angles)\\\therefore \triangle GFH \sim \triangle GJI..(by \: AA\: postulate)\\\\\therefore \frac{GF}{GJ}=\frac{HF}{IJ}..(By\: c.s.s.t.)\\\\\therefore \frac{4}{8}= \frac{q}{6}\\\\\therefore \frac{1}{2}= \frac{q}{6}\\\\q =\frac{6}{2}\\q= 3 \: units$