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2 years ago

Log(2)-log(8) check all that apply

Mathematics

1 answer:

Serggg [28]2 years ago

3 0

Answer: -2log(2) or -0.60206

Explanation:

log(1/4)
= log(2^2)
= - 2log(2)

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Differentiate respect to x, (3x²+2)³

galina1969 [7]

Answer:

3(3×2x + 0)(3x²+2)² = 18x(3x²+2)²

3 0

3 years ago

12. 17g + 149-69 +g =

Kitty [74]

Answer:

12. 18g+80

13. 13x+13

14. 17s

15. 3t

Step-by-step explanation:

On each you just combine the like terms and simplify the equations.

(Add/subtract all of the common numbers)

6 0

3 years ago

How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

3 years ago

Q(x)=2 −2+? please solve this huhu

Free_Kalibri [48]

Answer:

I mean it would just be q(x) = 0

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The function f(x) varies directly with x, and f(x) = 45 when x = 9.

Paladinen [302]

Answer:

Option C = 15

Step-by-step explanation:

In principle when a function f(x) varies directly with x it suggests that any changes in x results in the equivalent changes in f(x). If we have two variables, i.e. y representing f(x) and x representing itself, any increment/decrement in x will result to the same increment/decrement in y by a factor a, thus we can say that y = ax, implying y and x have the same ratio.

In the given question we know that $f(x) = 45$ when $x=9$ , which translates as