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3 years ago

List out all of the angles that are vertical and all of the angles that are adjacent. Find the missing angles measures

Mathematics

1 answer:

mr_godi [17]3 years ago

8 0

Answer:

∠BXY = 150

∠BXZ = 30

∠AXZ = 150

Step-by-step explanation:

∠AXY and ∠BXY are adjacent angles

∠AXY + ∠BXY = 180 {linear pair}

30 + ∠BXY = 180

∠BXY = 180 - 30 = 150

∠AXZ = ∠BXY {Vertically opposite angles}

∠AXY = 150°

∠BXZ = ∠AXY {Vertically opposite angle}

∠BXZ = 30°

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miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is $\dfrac{4}{3}\pi r^3$

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Solution A)

The given curve, $y=3+3e^{-5x}$ rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

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$V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)$

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Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

$x^2+y^2=r^2$

$y=\sqrt{r^2-x^2}$

The solid form is sphere of radius r.

Using disk method, to find volume of solid

$V=\int_a^b\pi R^2dx$

where, a = -r, b = r , $R=y=\sqrt{r^2-x^2}$ and dx is thickness of disk.

$V=\int_{-r}^r\pi (r^2-x^2)dx$

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$V=\pi(2r^3-\dfrac{2r^3}{3})$

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Step-by-step explanation:

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