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2 years ago

I need help please!!

Mathematics

2 answers:

Usimov [2.4K]2 years ago

8 0

Answer:

Step-by-step explanation:

radius r = 5 cm

Height h = 5 cm

Volume of cylinder = πr²h

= π * 5 * 5 * 5

= 125π cm³

Rasek [7]2 years ago

7 0

Answer:

250π

Step-by-step explanation:

The formula for finding the volume of a cylinder is πr^2h

So, you just substitute the values:

π x 5^2 x 2(5)

Then simplify,

π x 25 x 10

To then get 250π

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Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check al

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Let's rewrite each equation in the Slope-Intercept Form of the Equation of a Line. First, let's start with the main equation:

$\bullet \ 5x-2y=-6 \therefore y=\frac{5}{2}x+3$

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$A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \therefore y=-\frac{2}{5}x-2 \\ \\ C) \ 2x-5y=-10 \therefore y=\frac{2}{5}x+2 \\ \\ D) \ y+4=-\frac{2}{5}(x-5) \therefore y=-\frac{2}{5}x-2 \\ \\ E) \ y-4=\frac{5}{2}(x + 5) \therefore y=\frac{5}{2}x+\frac{33}{2}$

For two perpendicular lines it is true that the product of its slopes is:

$m_{1}m_{2}=-1$

$m_{1}m_{2}=-1 \\ \\ m_{1} \ is \ the \ slope \ of \ y=\frac{5}{2}x+3, \ that \ is, \ m_{1}=\frac{5}{2} \\ \\ Then, \ the \ slope \ of \ a \ perpendicular \ line \ is: \\ \\ m_{2}=-\frac{2}{5}$

According to this, only A) B) and D) might be the perpendicular lines we are looking for. Notice that these lines are the same. The other condition is that the line must pass through the point (5, -4). By substituting this point in the equation, we have:

$y = -\frac{2}{5}x-2 \\ \\ -4=-\frac{2}{5}(5)-2 \\ \\ -4=-2-2 \\ \\ \boxed{-4=-4} \ True!$

Finally, the right answer are:

$A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \\ \\ D) \ y+4=-\frac{2}{5}(x-5)$

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