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3 years ago

Evaluate the logarithm log10(1,000,000)

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

4 0

Answer:

Step-by-step explanation:

$log_{10} (1,000,000) \\ \\ = log_{10} (10^{6} ) \\ \\ = 6log_{10} (10) \\ \\ = 6 \times 1 \\ ( \because \: log_{10} (10) = 1) \\ \\ = 6$

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

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

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

Just need help with 4. Please

konstantin123 [22]

Answer:

11 3/5*9*12 1/2=1,305

1,305 cubic meters

Hope I helped.

Step-by-step explanation:

6 0

3 years ago

Write equivalent expression for 7× + 4× + 3-1

Mazyrski [523]

Answer: you just flip it. It would be the opposite.

Step-by-step explanation:

When you flip it, what’s the difference? It’s still the same.

6 0

3 years ago

In a shipment of airplane parts, 5% are known to be defective. If 21 parts are found to be defective, how many parts are in the

horrorfan [7]

We can use ratios and the cross-multiply-divide to find this.

The ratio 21:5 is avaliable via the question. We then need to compare that to the ratio x:100, the 100 being the percent and the x being the number of airplane parts.

21/5 = x/100

We can then solve for x to find the number of airplane parts. First we multiply by 100 on both sides to get 2100/5 = x. Therefore x = 420 and there are 420 airplane parts.

7 0

3 years ago

10d - 6d = 4 find what d equals

Nutka1998 [239]

Answer:

$\huge\boxed{\sf d = 1}$