Given that y varies directly with x, and y = 15 when x = 8 , what is the proportionality constant, k? Round your answer to the h
1 answer:
The proportionality constant "k" is 1.88
<h3><u>Solution:</u></h3>Given that y varies directly with x
y = 15 when x = 8
To find: proportionality constant "k"
Direct variation means that increase/decrease in one quantity also causes increase/decrease in other quantity.
⇒ y varies directly with x
This means,
Can also be written as:
y = kx
Where "k" is the proportionality constant
Substituting the given values of "x" and "y"
15 = k(8)
k = 1.875
On rounding to nearest hundredths place we get 1.88
Thus the proportionality constant is 1.88
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Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means: