Counting from 1 to 100, how many 6s will you encounter?

Mathematics

1 answer:

Basile [38]3 years ago

4 0

6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 86, 96 so 20 6's

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A fast-growing vine is introduced into a small national park. The vine competes with the native plants in the park. Soon, the nu

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Remove the vine, it is causing the population to decrease. No amount of animals etc. will be able to take care of the vine if the population is already decreasing.

1. Remove the vine.

6 0

3 years ago

Read 2 more answers

I really really really need help!!!!

Yakvenalex [24]

For $f$ to be continuous at $x=1$ , you need to have the limit from either side as $x\to1$ to be the same.

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^-}(|x-1|+2)=2$
$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1^+}(ax^2+bx)=a+b$

If $a=2$ and $b=3$ , then the limit from the right would be $2+3=5\neq2$ , so the answer to part (1) is no, the function would not be continuous under those conditions.

This basically answers part (2). For the function to be continuous, you need to satisfy the relation $a+b=2$ .

Part (c) is done similarly to part (1). This time, you need to limits from either side as $x\to2$ to match. You have

$\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2^-}(ax^2+bx)=4a+2b$
$\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2^+}(5x-10)=0$

So, $a$ and $b$ have to satisfy the relation $4a+2b=0$ , or $2a+b=0$ .

Part (4) is done by solving the system of equations above for $a$ and $b$ . I'll leave that to you, as well as part (5) since that's just drawing your findings.

8 0

3 years ago

A cone has a volume 12 pie cubic inches it’s height 4 inches what is the radius?

insens350 [35]

Answer:

Step-by-step explanation:

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have V = 12π in³ and H = 4 in. Substitute:

$12\pi=\dfrac{1}{3}\pi(r^2)(4)\qquad\text{multiply both sides by 3}\\\\36\pi=4\pi r^2\qquad\text{divide both sides by}\ 4\pi\\\\9=r^2\to r=\sqrt9\to r=3$