PLEASE HELP MY GRADES!!! Select the correct answer from the drop-down menu. Shapes I and II are _____ .

Mathematics

1 answer:

mel-nik [20]4 years ago

3 0

Answer:

Similar but not congruent

Step-by-step explanation:

They look to be the same shape, but they aren't the same exact size so they cant be congruent. To be congruent they would have to be the same size and shape, but they are only the same shape, different sizes.

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An ice cream shop sells cones at the volume of 94.2 cubic meters they want to double the volume of the cones without changing th

marin [14]

The volume of a cone is $V=\pi r^2\frac{h}3$ where r = radius and h = height. If the cone has a volume of 94.2 cm³ (I assume you didn't mean m³ because that would be ridiculously huge) and a height of 10 cm, we can plug these values into the formula to find the radius. Don't do any rounding.

$94.2 = \pi r^2\frac{10}3 \\ 282.6 = \pi r^2 *10 \\ 28.26 = \pi r^2 \\ 8.99543738355 = r^2 \\ 2.99923946752=r$

Now we know that's going to be the radius of our <em>new </em>cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.

$188.4 = \pi (2.99923946752)^2\frac{h}3 \\ 188.4 = \pi(8.99543738355)\frac{h}3 \\ 188.4 = 28.26\frac{h}3 \\ 565.2 = 28.26h \\\\ \boxed{h = 20, r\approx 3}$

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Clim_%7Bh%20%5Cto%20%5C116%7D%20x-16%2F%5Csqrt%7Bx%7D%20-4" id="TexFormula1" title="\lim_{h

Evgen [1.6K]

Answer:

$\displaystyle 8$

Step-by-step explanation:

we would like to compute the following limit

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right)$

if we substitute 16 directly we'd end up

$\displaystyle = \frac{16 - 16}{ \sqrt{16} - 4}$

$\displaystyle = \frac{0}{ 0}$

which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right)$