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3 years ago

The population of a town increased from 3500 in 2006 to 5350 in 2011. Find the absolute and relative (percent) increase.

Mathematics

1 answer:

a_sh-v [17]3 years ago

7 0

Answer:

15% increase per year

Step-by-step explanation:

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A rectangle has an area of 63 square inches. The width of the rectangle is 6 inches. What is the rectangle’s length, in inches?

atroni [7]

When you know the area and one side of a rectangle, divide the area by the known side to find the length of the other side.

Length = 63/6

Length = 10.5 inches

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2 years ago

How many lines of symmetry does a regular polygon with 32 sides have

Leya [2.2K]

32. 16 through opposite vertices and 16 through the centres of opposite sides

3 0

2 years ago

Use The four step process to find the slope of the tangent line to the graph of the given function at any point. ( simplify your

hodyreva [135]

Answer:

The answer to your question is: 16x + 3

Step-by-step explanation:

Step 1 : f(x) = 8x² + 3x

f(x +h) = 8(x + h)² + 3( x + h)

f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

f (x + h) = 8x² + 16xh + 8h² + 3x + 3h

Step 2 f(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

= 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x

= 16xh + 8h² + 3 h

Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h

= 16x + 8h + 3

Step 4 lim f(x + h) - f(x)/ h = lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3

h ⇒0 h ⇒0 h ⇒0

3 0

3 years ago

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 $c$ :

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

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3 years ago

What value in place of the question mark makes the polynomial below a perfect square trinomial? 9x2+?x+64

serg [7]

9x² + bx + 64
\/(9x²) = 3x
\/84 = 8
2*3x*8 = 48x
b = 48

4 0

3 years ago

Read 2 more answers