Answer:
Step-by-step explanation:
For this case we have the following plot on the figure attached.
We know on this case that represent our radius for the square, since we need cross sections perpendicular to the y axis.
We find the intersection points like this:
Since we are assuming squares for the cross sections the area is given by where r = x= -2y+6.
Since our radius is on terms of x we can create a integral with limits on x in order to find the volume, And we can use the following integral in order to find the volume.
On the left part we are using the following property from algebra:
And after do the integral we got this:
Answer:
Inequality:
Set Notation:
Interval:
Step-by-step explanation:
Given
The Attached Number Line
Solving (a): The Inequality
i. On the number line, we notice that a thick line starts at number 3 and points to the right
ii. Also, there is a closed circle on number 3.
(i) & (ii) indicates that
Solving (b): Set Notation
The set notation that indicates is
Solving (c): The interval notation
The inequality implies that x starts from 3 and moves towards +infinity
The means that 3 is inclusive of the inequality
Hence:
The interval notation is
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1. < DCE=< DEC in the picture
⇒<ABC=<DEC=< DCE=<BCA ⇒ the triangle ABC is isosceles
2. ⇒<GFE=<DCE=<DEC=<FEG ⇒ the triangle EFG is isosceles
⇒ the triangles ABC and EFG have 2 angles equals ⇒ ABC~ EFG
5. ⇒ < ABC=<GEF =<DEC= < DCE=< BCA ⇒ the triangle ABC is isosceles
6. < GFE = < BCA= < ECD = <DEC = <FEG ⇒ the triangle EFG is isosceles
⇒ the triangles ABC and EFG have 2 angles equals ⇒ ABC~ EFG
Answer:
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Step-by-step explanation:
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