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3 years ago

Volume of a cube 3.8 ft 1.1 ft

Mathematics

1 answer:

balu736 [363]3 years ago

7 0

Where’s the photo? But I need to answer with a photo 3.8 ft and 1.1 ft equals 4.9 ft

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Find the exact value of cot(15degrees) using half angle formulas?

liubo4ka [24]

Double angle (or half angle, depending how you look at it) identities:

$\cos^2\dfrac x2=\dfrac{1+\cos x}2$

$\sin^2\dfrac x2=\dfrac{1-\cos x}2$

$\implies\cot^2\dfrac x2=\dfrac{\cos^2\frac x2}{\sin^2\frac x2}=\dfrac{1+\cos x}{1-\cos x}$

So we have

$\cot^215^\circ=\dfrac{1+\cos30^\circ}{1-\cos30^\circ}=\dfrac{1+\frac{\sqrt3}2}{1-\frac{\sqrt3}2}$

$\implies\cot^215^\circ=7+4\sqrt3$

$\implies\cot15^\circ=\sqrt{7+4\sqrt3}=2+\sqrt3$

Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know $\cos15^\circ>0$ and $\sin15^\circ>0$ , so it's also the case that $\cot15^\circ>0$ .

Also, the reason we have equality in the last step can be explained like so:

$7+4\sqrt3=4+4\sqrt3+3=4+4\sqrt3+(\sqrt3)^2=(2+\sqrt3)^2$

(not unlike the process used to complete the square)

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3 years ago

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On monday, deborah ran 3 2/5 miles and on tuesday she ran 4 1/5 miles how many miles did she run on these 2 days togehter

makkiz [27]

7 3/4.

i got this by adding 1/5+2/5=3/4 and then 4+3 which are the whole numbers.

7 0

3 years ago

Can I get some help with number 2 please :/

alexandr1967 [171]

Hello,

So the original temperature was 7 degrees Celsius.

Then, it went down 10 degrees.

7-10= -3

So, in this case, the answer is C) -3 degrees celsius

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2 years ago

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Help please It would mean a lot

Vera_Pavlovna [14]

the answer is 3/5

if that's not right I apologize

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2 years ago

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Lucas and Tayvan can paint a house in 1 hour working together. If Tayvan works alone, he can paint the house in 1.5 hours. How l

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