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Hoochie [10]
2 years ago
13

Last tuesday evening, Aaron, the car wash owner, found he had 90% more quarters than dimes. If the combined value of Aaron's qua

rters and dimes is $69, how many times did he have
Mathematics
1 answer:
Alex Ar [27]2 years ago
4 0

Aaron the car wash owner had 228 quarters and 120 dimes.

<h3>Equation</h3>

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the number of quarters and y represent the number of dimes. Hence:

x = 90% of y + y

x = (0.9y) + y

x - 1.9y = 0   (1)

Also:

0.25x + 0.1y = 69   (2)

From both equations:

x = 228, y = 120

Aaron the car wash owner had 228 quarters and 120 dimes.

Find out more on Equation at: brainly.com/question/13763238

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Answer:

x (max) = 26760 m

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Step-by-step explanation:

Equations to describe the projectile shot movement are:

a(x)  =  0     V(x)  =  V(₀) *cos α                  x  =  V(₀) *cos α  * t

a(y)  = -g     V(y)  =  V(₀) * sin α  - g*t         y  =   V(₀) * sin α *t  - (1/2)*g*t²

a ) What is the range of the projectile.   α  =  30°

then  sin 30° = 1/2     cos  30° = √3 /2   and     tan 30° = 1/√3

x  maximum occurs when in the equation of trajectory  we make  y  = 0

Then

y  =  x*tan α  -  g*x / 2*V(₀)²*cos²  α

x*tan α  =  g*x /  2* V(₀)²*cos²  α

By subtitution

1/√3    =   9.8* x(max)  / 2* (550)²*0.75

(1/√3) * 453750 / 9.8  = x (max)

x (max) = 453750 / 16.95   meters

x (max) = 26760 m

The maximum height is when V(y) = 0

We compute t in that condition

V(y)  =  0  =  V(₀) * sin α - g*t

t  =   V(₀) * sin α / g       ⇒   t  =  550* (1/2) / 9.8

t  =  28.06 sec

Then  h (max)  =   y(max)  =  V(₀) sin α * t  - 1/2 g* t²

y (max)  =  550* (1/2)*28.06 - (1/2)* 9.8 * (28.06)²

y (max)  =  7717  -  3858  

y (max)  = 3859  meters

What is the speed when the projectile hits the ground

V  =  V(x)  + V (y)    and   t  =  2* 28.06         t  =  56.12 sec

mod V  =√ V(x)²  + V(y)²

V(x)  =  V(₀) cos α    =  550 * √3/2

V(x)  = 475.5  m/sec       V(x)²   =  226338 m²/sec²

V(y) =  550*1/2   -  9.8* 56.12     ⇒  V(y) = 275  -  549.98

V(y) =  - 274.98          V(y) ²   =  

V =  √ 226338 + 75614     ⇒  V = 549.5  m/sec

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