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Rus_ich [418]
3 years ago
13

dennis mowed his next door neighbors lawn for a handful of dimes and nickels, 80 coins in all. upon completing the job he counte

d out the coins and it came to 6.60. how many of each coin did he earn?
Mathematics
1 answer:
Serggg [28]3 years ago
7 0

Answer:

52 dimes and 28 nickels

Step-by-step explanation:

n = number of nickels

d = number of dimes

n+d = 80   the number of coins he got

Multiply the number of nickels times .05 plus the number of dimes times .10 to equal the amount of money he got

.05n + .10d = 6.60

Divide this equation by .05

.05n/.05  + .10/.05 = 6.60/.05

n + 2d = 132

n+d = 80

Multiply by -1

-n-d=-80

Add this to n+2d = 132

n+2d=132

-n-d=-80

-------------------

d = 52

Now we need to solve for n

n+d = 80

n+52 = 80

Subtract 52 from each side

n+52-52= 80-52

n = 28


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a. v.v' = v₁v₂ -  v₁v₂ = 0 b.  (20, -21)/29 and  (-20,21)/29

Step-by-step explanation:

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= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)

= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

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So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j  

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= v₁v₂ - v₂v₁

=  v₁v₂ -  v₁v₂ = 0

So, v.v' = 0

b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).

So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.

A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29

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