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LUCKY_DIMON [66]
3 years ago
7

A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the con

e? Use 3.14 for pi. Round your answer to the nearest hundredth. 5.81 inches 6.57 inches 7.89 inches 8.89 inches
Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
7 0
\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.4\\
V=35
\end{cases}\implies 35=\cfrac{\pi (2.4)^2 h}{3}\implies 105=5.76\pi h
\\\\\\
\cfrac{105}{5.76\pi }=h\implies 5.805467091295 \approx h\implies 5.81 \approx h
stepan [7]3 years ago
6 0
Let's look at the formula used to find the volume of a cone.
πr²(h/3)=V
Let's fill in what we know. The volume is 35 and the radius is 2.4. Also, we're using 3.14 for pi. Let's fill this in.
2.4²(3.14)(h/3)=35
Let's find 2.4 squared.
5.76(3.14)(h/3)=35
18.0864(h/3)=35
Let's divide both sides by 18.0864.
H/3=1.93708353
Let's multiply both sides 3.
H=5.81125058
H≈5.81
So, the height is 5.81 inches.
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3 0
2 years ago
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3 years ago
Let <img src="https://tex.z-dn.net/?f=i" id="TexFormula1" title="i" alt="i" align="absmiddle" class="latex-formula"> be the imag
VLD [36.1K]

Hey~freckledspots!\\----------------------

We~will~solve~for~i^{425}!

Rule~of~exponent: a^{b + c} = a^ba^c\\Apply:~i^{425}~=~i^{424}i\\ \\Rule~of~exponent: a^{bc} = (a^{b})^c\\Apply: i^{424} = i(i^2)^{212} \\\\Rule~of~imaginary~number: i^2 = -1\\Apply: i(i^2)^{212} = -1^{212}i\\\\Rule~of~exponent~if~n~is~even: -a^n = a^n\\Apply: -1^{212}i = 1^{212}i\\\\Simplify: 1^{212}i = 1i\\Multiply: 1i * 1 = i\\----------------------\\

Now~let's~solve~1^{14}!\\\\Rule~of~exponent: a^{b + c} = a^ba^c\\Apply: i^{14} = (i^2)^7\\\\Rule~of~imaginary~number: i^2 = -1\\Apply: (i^2)^7 = -1^7\\\\Rule~of~exponent~if~n~is~odd: (-a)^n = -a^n\\Apply: -1^7 = -1^7\\\\Simplify: -1^7 = -1\\----------------------\\Now,~we~have: i-1+i^{-14}+i^{44}\\----------------------

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Answer:\\\large\boxed{-1+i}\\----------------------

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8 0
3 years ago
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