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tresset_1 [31]
3 years ago
5

Jackson is playing a video game that has 3 castles to conquer within each level. Jackson has completed 5 levels so far. If x rep

resents the number of remaining levels to complete, which of the following equations can be used to find the total number of castles Jackson will have conquered once he completes the final level?
Mathematics
1 answer:
pentagon [3]3 years ago
4 0
5 times 3 equals x then put x=15
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Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )
Zina [86]

Answer:

\purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

Step-by-step explanation:

\cos( \alpha ) =  \frac{ \sqrt{6} }{6}  =  \frac{1}{ \sqrt{6} }  \\  \\  \therefore \:  \sin( \alpha )  =  \sqrt{1 -  { \cos}^{2} ( \alpha ) }  \\  \\  =  \sqrt{1 -  \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} }  \\  \\ =  \sqrt{1 -  {\frac{1}{ {6} }}}  \\  \\ =  \sqrt{ {\frac{6 - 1}{ {6} }}}   \\  \\  \red{\sin( \alpha ) =  \sqrt{ { \frac{5}{ {6} }}} } \\  \\  \tan( \alpha ) =  \frac{\sin( \alpha ) }{\cos( \alpha ) }  =  \sqrt{5}  \\  \\ \sin( \beta )  =  \frac{ \sqrt{2} }{4}  \\  \\  \implies \: \cos( \beta )  =   \sqrt{ \frac{7}{8} }  \\  \\ \tan( \beta )  =  \frac{\sin( \beta ) }{\cos( \beta ) } =  \frac{1}{ \sqrt{7} }   \\  \\  \tan( \alpha  -  \beta ) =  \frac{ \tan \alpha  -  \tan \beta }{1 +  \tan \alpha .  \tan \beta}  \\  \\  =  \frac{ \sqrt{5} -  \frac{1}{ \sqrt{7} }  }{1 +  \sqrt{5} . \frac{1}{ \sqrt{7} } }  \\  \\  =  \frac{ \sqrt{35} - 1 }{ \sqrt{7}  +  \sqrt{5} }  \\  \\  \purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

8 0
3 years ago
Please I need help I can’t get a bad grade I try my best but I don’t understand
olya-2409 [2.1K]

Answer: What do you need, what grade are you in?

Step-by-step explanation:

3 0
3 years ago
What is the decimal multiplier to decrease by 30%?
sdas [7]
The decimal multiplier to decrease by 30 is .7
7 0
3 years ago
olive bought 36 potatoes plants. She planted them in her garden in 4 even rows. Wild animals ate a row. 5 plants were eaten by s
almond37 [142]
If there are 36 potato plants, and they are in 4 even rows, that means that there is 9 in each column because 9 x 4 is 36. Since 7 of them were eaten by the sheep and the goat, that means that there are 2 leftover in that row that the sheep and goat got to since 9-7 is 2.
5 0
3 years ago
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Which of the following expression expressions is equivalent to cos3x/sinxcosx?
77julia77 [94]
Correct Option:
Option B

Solution:
The given expression is:

\frac{cos(3x)}{sin(x)cos(x)}

cos(3x) can be written as cos(2x +x). Expanding it, we get:

cos(3x) = cos(2x+x) \\  \\ 
cos(3x) =cos(2x)sin(x)-sin(2x)cos(x)

Using this value of cos(3x) in given equation, we get:

\frac{cos(3x)}{sin(x)cos(x)} \\  \\ 
= \frac{cos(2x)sin(x)-sin(2x)cos(x)}{sin(x)cos(x)} \\  \\ 
= \frac{cos(2x)sin(x)}{sin(x)cos(x)}- \frac{sin(2x)cos(x)}{sin(x)cos(x)}  \\  \\ 
= \frac{cos(2x)}{cos(x)} - \frac{sin(2x)}{sin(x)} \\  \\ 
=sec(x)cos(2x)-csc(x)sin(2x)
8 0
3 years ago
Read 2 more answers
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