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3 years ago

5

Given the following two statements, is the compound statement valid? p: Two angles are congruent. q: The angles are vertical Com

pound statement: If two angles are congruent then the angles are vertical.

1 answer:

maw [93]3 years ago

5 0

No, this is not valid. In the picture below, $\angle a$ is a vertical angle with $\angle b$ . But $\angle a$ is not $\cong \angle b$

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Step-by-step explanation:

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Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7.

madam [21]

Answer:

$y = 3x - 13$

Step-by-step explanation:

The equation of parallel line differ only by their constant.

Hence, the equation of the line parallel to $y = 3x + 7$ is nothing but $y = 3x + c$ .

When a point passing through this line is given we can substitute the point in this line and get the value for $c$ .

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3 years ago

A right triangle whose hypotenuse is StartRoot 18 EndRoot18 m long is revolved about one of its legs to generate a right circula

skelet666 [1.2K]

Answer:

V = $\frac{1}{3}$ π(8 - $\frac{8}{3}$ ) $\sqrt{\frac{8}{3} }$ = 9.11 $m^{3}$

r = 4 $\frac{\sqrt{3} }{3}$

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Step-by-step explanation:

Given that the right triangle whose hypotenuse is $\sqrt{8}$

Let r is the radius of the cone
Let h is the height of the cone

We know that:

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<=> $r^{2} = 8 - h^{2}$

The volume of the cone is:

V = π $r^{2} \frac{1}{3} h$

<=> V = π $\frac{1}{3}(8 - h^{2} )h$

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For maximum/minimum: $\frac{dV}{dh}$ = 0

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<=> $h^{2}$ = $\frac{8}{3}$

<=> h = $\sqrt{\frac{8}{3} }$

=> $r^{2}$ = $\frac{16}{3}$

<=> r = 4 $\frac{\sqrt{3} }{3}$

So the volume of the cone is:

V = $\frac{1}{3}$ π(8 - $\frac{8}{3}$ ) $\sqrt{\frac{8}{3} }$ = 9.11 $m^{3}$

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