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3 years ago

Find the 13th term of the arithmetic sequence -3x+7, -5x+3, -7x-1, ...

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

3 0

Answer:

a₁₃ = - 27x - 41

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3x + 7

d = a₂ - a₁ = - 5x + 3 - (- 3x + 7)

= - 5x + 3 + 3x - 7

= - 2x - 4

Then

a₁₃ = - 3x + 7 + 12(- 2x - 4)

= - 3x + 7 - 24x - 48

= - 27x - 41

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

Find the area of each figure

jeka94

Answer:

50.74 yds^2

Step-by-step explanation:

7 0

3 years ago

How much of a spice that is 30% salt should be added to 175 ounces of a spice that is 65% salt in order to make a spice that is

klasskru [66]

$\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{30\% spice}&x&0.30&0.30x\\
\textit{65\% spice}&175&0.65&(175)(0.65)\\
-----&-----&-------&-------\\
mixture&x+175&0.50&(x+175)(0.50)
\end{array}$

so.. as you can see, we use the decimal notation for the percentages... 65% is just 65/100 and 50% is just 50/100 and so on

so.. whatever the salted amounts are, we know they'll add up to (x+175)(0.50)

thus (0.30x) + (175)(0.65) = (x+175)(0.50)

solve for "x"

5 0

3 years ago

2. The graph of a certain geometric sequence can be described as a curve increasing from left to right. Which sequence would hav

kozerog [31]

Answer:

0 (-1,2,-4, 8, -16) that should help you

Step-by-step explanation:

8 0

3 years ago

Can you all help me pls. Thanks.

Nataliya [291]

Answer:

Step-by-step explanation:

6 0

3 years ago

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