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3 years ago

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A cone has a radius of five feet and a height of 18 feet. If the radius of the cone is tripled but the volume but the volume rem

ains unchanged, what will be the new height of the cone

1 answer:

olasank [31]3 years ago

4 0

Volume of a cone is 1/3 of the area of the base times the height
v=(1/3)pi*5*5*18=(1/3)pi815*15*h
h=2

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A rectangle is 3 times as long as it is wide, and its perimeter is 80 centimeters. Find its dimensions

Free_Kalibri [48]

Say the width is W and the length is L

L=3W (and of course W=W)

Now you use the perimeter formula P=2L+2W

80=2(3W) + 2W)

80=6W+2W

80=8W Divide both sides by 8

W=10

Now that you know the width, substitute it back into L=3W to find the length

L=3(10)

L=30

The dimensions are length: 30 cm and width: 10 cm

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3 years ago

Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.

sergij07 [2.7K]

(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1$

For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:

$\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1$

which reduces to

<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2

(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

$\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678$

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3 years ago

Could someone help me with math? *spam answers not tolerated* THANKS WILL GIVE BRAINLIEST if you have an explanation! Thanks in

Andru [333]

Answer:

r = 3/2

Step-by-step explanation:

ratio (r) is the number that, when multiplied by the previous (n-1) term, gives the nth term of the geometric sequence (). To find the common ratio, we can take any term and divide it by its preceding term (rearrange the formula to get ). If we take 24 and divide it by 16, we get the common ratio of 3/2 (, ).

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3 years ago

Help! It says that I need to determine If both equations represent lines which are parallel, perpendicular, or none...

12345 [234]

  4x + 2y = 8   (1)
  8x + 4y = -4y (2)

A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
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y = -2x + 4

  (2) 8x + 4y = -4y
  <span>   </span>8x = -4y - 4y
y = $\frac{-8x}{-8}$
y = -x
<span>Thus the gradient of the two equations are different and as such    the two lines are not parallel
</span>
B) When two lines are perpendicular, the product of their gradient is -1
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p = (-2) * (-1)
p = 2
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Thus these lines are SKEWED LINES

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3 years ago

The graph below shows the function f(x)=x-3/x^2-2x-3 which statement is true

Ugo [173]

Answer:

The correct option is A.

Step-by-step explanation:

Domain:

The expression in the denominator is x^2-2x-3

x² - 2x-3 ≠0

-3 = +1 -4

(x²-2x+1)-4 ≠0

(x²-2x+1)=(x-1)²

(x-1)² - (2)² ≠0

∴a²-b² =(a-b)(a+b)

(x-1-2)(x-1+2) ≠0

(x-3)(x+1) ≠0

x≠3 for all x≠ -1

So there is a hole at x=3 and an asymptote at x= -1, so Option B is wrong

Asymptote:

x-3/x^2-2x-3

We know that denominator is equal to (x-3)(x+1)

x-3/(x-3)(x+1)

x-3 will be cancelled out by x-3

1/x+1

We have asymptote at x=-1 and hole at x=3, therefore the correct option is A....

4 0

3 years ago

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