Sara claims that a sequence of transformations carries rectangle 1 onto rectangle 2. Which of the following sequences of transfo
rmations can be used to support Sara’s claim?
Answer choices
A.) A reflection over the Y axis followed by a reflection over the X axis.
B.) A translation of 7units to the left, followed by a translation of 8
units up.
C.) A reflection of the X-axis, followed by translation of 4 units to the right.
D.) A rotation of 270° clock wise about the origin, followed by a reflection over the y-axis
Answer choices
A.) A reflection over the Y axis followed by a reflection over the X axis.
B.) A translation of 7units to the left, followed by a translation of 8
units up.
C.) A reflection of the X-axis, followed by translation of 4 units to the right.
D.) A rotation of 270° clock wise about the origin, followed by a reflection over the y-axis
1 answer:
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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: