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3 years ago

Jack's brother is 14 years older than him. In six years 'time, Jack's brother will be twice as old as him. How old is Jack now?

Mathematics

2 answers:

Sedaia [141]3 years ago

6 0

Answer: 23

Step-by-step explanation:

zhuklara [117]3 years ago

3 0

Answer:

Step-by-step explanation:

Jacks age: x-14

Jack's brothers age: x

In 6 years time:

Jack's age: x-8

Jack's brother's age: x + 6

Given that:

x+6 = 2(x-8)

Simplify:

x+6 = 2x-16

x+22 = 2x

2x = x+22

x = 22

we mentioned earlier that Jack's brother's age was x. but Jack's age was x-14.

So, Jack's age: 22-14 = 8

Hope this helps.

Good Luck

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The complete question in the attached figure

we have that
tan a=7/24 a----> III quadrant
cos b=-12/13 b----> II quadrant
sin (a+b)=?

we know that
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step 1
find sin b
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step 2
Find sin a and cos a
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tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325

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