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3 years ago

Will is packing cubes with side lengths that are

Mathematics

2 answers:

earnstyle [38]3 years ago

6 0

Step-by-step explanation:

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fgiga [73]3 years ago

5 0

Answer:

Step-by-step explanation:4545

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Please help it’s the last question

Mrac [35]

Answer:

$y=$ $-\frac{5}{6}x - 1$ is the answer

Step-by-step explanation:

Equation of the line: y = 6/5x + 1

= 5y = 6x + 5

= 6x - 5y + 5

Equation of the perpendicular line: bx - ay + k = 0

= -5x -6y + k = 0

Equation passes through (6,-6),

-5(6) -6(-6) + k = 0

-30 + 36 + k = 0

6 + k = 0

k = -6

Substituting,

-5x -6y + k = 0

-5x -6y -6 = 0

-6y = 5x + 6

$y=$ $-\frac{5}{6}x - 1$ (Slope-Intercept form)

6 0

3 years ago

A model for the population in a small community after t years is given by P(t)=P0e^kt.

LUCKY_DIMON [66]

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}$

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}$

$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t$

b)

A = 10,000, t = 3

$\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I$

3 0

4 years ago

Graph the line that contains the point (o,3) and has a slope of 1/2

Katyanochek1 [597]

Answer:

Step-by-step explanation:

y-3=1/2(x-0)=1/2 x

2y-6=x

2y-x=6

3 0

3 years ago

A cuboid with dimensions 45 cm by 16 cm by 12 cm is cut to form smaller cubes of

LenKa [72]

Answer:

<u>135 cubes</u>

Step-by-step explanation:

Volume of cuboid :

45 x 16 x 12
720 x 12
8,640 cm³

Volume of a small cube :

(4)³
64 cm³

Number of cubes :

n = 8,640/64
n = <u>135 cubes</u>

4 0

2 years ago

If T is the midpoint of SU find the values of x, ST and SU.

Nitella [24]

Answer: The required values are

x = 12 units, ST = 60 units and SU = 120 units.

Step-by-step explanation: Given that T is the midpoint of SU, where

ST = 5x and TU = 3x + 24.

We are to find the values of x, ST and SU.

Since T is the midpoint of SU, so we get

$ST=TU\\\\\Rightarrow 5x=3x+24\\\\\Rightarrow 5x-3x=24\\\\\Rightarrow 2x=24\\\\\Rightarrow x=\dfrac{24}{2}\\\\\Rightarrow x=12.$

So, the value of x is 12.

Therefore,

$ST=5\times12=60$

and

$SU=5x+3x+24=8x+24=8\times12+24=96+24=120.$

Thus, the required values are

x = 12 units, ST = 60 units and SU = 120 units.

8 0

3 years ago

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