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3 years ago

Help please thank you

Mathematics

1 answer:

svp [43]3 years ago

8 0

Answer:

The third is an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence means we add the same amount each time as n increases by 1

In the first, we add -6 then -12, then -24 so it is not arithmetic

In the second we add 2 then 4 then 6 then 8

In the third, we add -1.4 each time

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Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term s

nignag [31]

Answer:

$(1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8$

Step-by-step explanation:

Given

$(1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)$

Required

Solve

We have:

$(1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)$

Collect like terms

$1.3t^3 + 0.6t^2 + 0.4t^2 - 24t- 18t + 8$

$1.3t^3 + t^2 -42t + 8$

So:

$(1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8$

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Let $x,y$ be the dimensions of the rectangle. We know the equations for both area and perimeter:

$A=xy=36$

$P=2(x+y)=36 \iff x+y=18$

So, we have the following system:

$\begin{cases}xy=36\\x+y=18\end{cases}$

From the second equation, we can deduce

$y=18-x$

Plug this in the first equation to get

$xy=x(18-x)=-x^2+18=36$

Refactor as

$x^2-18x+36=0$

And solve with the usual quadratic formula to get

$x=9\pm3\sqrt{5}$

Both solutions are feasible, because they're both positive.

If we chose the positive solution, we have

$x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}$

If we choose the negative solution, we have

$x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}$

So, we're just swapping the role of $x$ and $y$ . The two dimensions of the rectangle are $9+3\sqrt{5}$ and $9-3\sqrt{5}$

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