What number goes in the box? 2 ^ ( ) = (2^7 ÷ 2^9)^3

Mathematics

1 answer:

navik [9.2K]2 years ago

4 0

Answer:

$x=-6$

Step-by-step explanation:

$(\frac{2^{7}}{2^{9}})^{3} \\(\frac{128}{512})^{3} \\(\frac{1}{4})^{3}\\(\frac{1}{4})*(\frac{1}{4})*(\frac{1}{4})\\\frac{1*1*1}{4*4*4} \\\frac{1^{3} }{4^{3} } \\\frac{1}{64} \\2^{x}=\frac{1}{64}\\log 2^x=log\frac{1}{64}\\x*(log(2))=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{log(2)} \\x=-6$

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4r+3=-18 please help me

lorasvet [3.4K]

Subtract three from either side. That will give you 4r=-21. Divide -21 by 4 and r will equal -5.25.

6 0

2 years ago

Verify cot x sec^4x=cotx +2tanx +tan^3x

Tanzania [10]

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

Verifying from left, we have

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { \tan}^{2} x )^{2}$

Expand the perfect square in the right:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { 2\tan}^{2} x + { \tan}^{4} x)$

We expand to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + \cot(x){ 2\tan}^{2} x +\cot(x) { \tan}^{4} x$

We simplify to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{2} x}{{ \cos}^{2} x} +\frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{4} x}{{ \cos}^{4} x}$