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3 years ago

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter

Mathematics

1 answer:

Citrus2011 [14]3 years ago

5 0

9 times 16 = 144
2(9+16)= 50
smallest possible perimeter is 50(whatever unit you're doing)

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What is the graph of this equation

OverLord2011 [107]

Answer:

Look at attached image

Step-by-step explanation:

8 0

3 years ago

Determine the formula for the nth term of the sequence:<br>-2,1,7,25,79,...

rodikova [14]

A plausible guess might be that the sequence is formed by a degree-4* polynomial,

$x_n = a n^4 + b n^3 + c n^2 + d n + e$

From the given known values of the sequence, we have

$\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}$

Solving the system yields coefficients

$a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4$

so that the n-th term in the sequence might be

$\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}$

Then the next few terms in the sequence could very well be

$\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}$

It would be much easier to confirm this had the given sequence provided just one more term...

* Why degree-4? This rests on the assumption that the higher-order forward differences of $\{x_n\}$ eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of $\{x_n\}$ by $\Delta^{k}\{x_n\}$ . Then

• 1st-order differences:

$\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}$

• 2nd-order differences:

$\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}$

• 3rd-order differences:

$\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}$

• 4th-order differences:

$\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}$

From here I made the assumption that $\Delta^4\{x_n\}$ is the constant sequence {15, 15, 15, …}. This implies $\Delta^3\{x_n\}$ forms an arithmetic/linear sequence, which implies $\Delta^2\{x_n\}$ forms a quadratic sequence, and so on up $\{x_n\}$ forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.

5 0

2 years ago

What is the measure of the complement of 20°

Vesnalui [34]

Answer:

So if you have an angle that is 20 degrees, then the complement angle measures 70 degrees.

6 0

2 years ago

What is x over 5 equals 8 over 9?

julia-pushkina [17]

X/5 = 8/9
this is a proportion, so we cross multiply
(9)(x) = (5)(8)
9x = 40
x = 40/9 or 4 4/9

3 0

2 years ago

What is the value of the exponential expression 36 1/2

garik1379 [7]

For this case we have an exponential expression of the form:
$36^{ \frac{1}{2}}$
We can rewrite the exponential expression using power properties.
We have then:
$\sqrt{36}$
From here, we take the square root of 36.
We have then:
$\sqrt{36} = 6$
Answer:
The exponential function is given by:
$36^{ \frac{1}{2}}=6$

4 0

2 years ago

Read 2 more answers