If an equation is a direct variation, then there is always something added or subtracted from the x term
1 answer:
Answer:
The given statement is false.
Step-by-step explanation:
Given statement:
"If an equation is a direct variation, then there is always something added or subtracted from the x term."
Consider 2 variables 'x' and 'y' such that 'y' varies directly with 'x'. Therefore, if two variables have direct variation, then they are related as:
, where, 'k' is a constant of proportionality.
Now, in the above relation, the variable 'x' is multiplied by 'k' but nothing is added or subtracted from the 'x' term.
If something is added to the 'x' term, then the relation is a linear variation and not a direct variation.
Thus, the given statement is FALSE.
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Given:
The largest circle has a radius of R=7 units.
Let x be the radius of the large shaded circle.
The small shaded circles have a radius of 1/5 of the large shaded circle.
=> the small shaded circles have a radius of r=x/5
By adding up radii, we have the equation
2(r+x+r)=2(x/5+x+x/5)=2R=2*7=14
Simplify:
7x/5=14/2
x=5
=> r=1
Area of outer circle =
Area of large shaded circle =
Area of 4 small shaded circles =
Total area of shaded circles =
Shaded area as a fraction of that of the outer circle
The largest circle has a radius of R=7 units.
Let x be the radius of the large shaded circle.
The small shaded circles have a radius of 1/5 of the large shaded circle.
=> the small shaded circles have a radius of r=x/5
By adding up radii, we have the equation
2(r+x+r)=2(x/5+x+x/5)=2R=2*7=14
Simplify:
7x/5=14/2
x=5
=> r=1
Area of outer circle =
Area of large shaded circle =
Area of 4 small shaded circles =
Total area of shaded circles =
Shaded area as a fraction of that of the outer circle