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3 years ago

What is (f⋅g)(x)?

1 answer:

7 0

(f * g)(x) is equal to f(x) * g(x).

Plug in f(x) and g(x) for f(x) * g(x).

(x^2 - 2x + 3) * (x^3 - 4) = x^5 - 2x^4 + 3x^3 - 4x^2 + 8x - 12

Answer:
(f*g)(x) = x^5 - 2x^4 + 3x^3 - 4x^2 + 8x - 12

You might be interested in

(Picture Included) 20 points - can someone solve 11, 12, 13, and 15?

slavikrds [6]

11. 3(5) + 2(4)

15 + 8 = 13

12. x= -12

13. -30

15. x = 44

6 0

4 years ago

What is the period and midline?

OverLord2011 [107]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\

\end{array}\qquad$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{ A}}|\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\
\bullet \textit{vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\


\end{array}$

$\bf \begin{array}{llll}
\bullet \textit{function period}\\
\qquad \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\
\qquad \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)
\end{array}
$

so if you notice yours $\bf \begin{array}{llll}
3.2cos&\left( \frac{5}{3}\theta \right)+&6.1\\
&\ \uparrow&\uparrow \\
&B&D 
\end{array}$

now.. normally the function $\bf 3.2cos&\left( \frac{5}{3}\theta \right)$
has a D value of 0, or no vertical shift, and the amplitude and the period simply make the wave taller and thinner, but the midline is still the x-axis

now, with D = 6.1, that moves the midline up vertically that much

now.. the period, well, B = 5/3, normal period of cosine is $2\pi$
so, the new period will be $\bf \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{5}{3}}\implies \cfrac{6\pi }{5}$

notice the picture below
the vertical shift by the D component, or 6.1, moved the midline to y = 6.1 :)

6 0

3 years ago

The first term of an Ap is - 504 while<br>the sum of its 9 terms is-126 find<br>Sum of its 30 terms

frozen [14]

Answer:

The sum of its 30 terms is 38167.5

Step-by-step explanation:

Given:

The First term in the AP is -504

The Sum of its 9 terms is -126

To Find:

The sum of its 30 terms = ?

Solution:

The sum of n terms of an AP:

$S_n = (\frac{n}{2} ) [ 2 a_1 + ( n - 1 ) d ]$

The sum of 9 terms of an AP:

$S_9 = (\frac{9 }{2} ) [ 2(-504) + ( 9 - 1 )d ]$

$S_9 = (4.5 )[ 2 (-504)+ ( 8 ) d ]$

$(4.5 )(2)(-504) + (4.5) 8 d = - 126$

(-4536) +36d = -126

36 d = -126+4536

36 d= 4410

$d= \frac{4410}{36}$

d = 122.5

The sum of its 30 terms is

$S_{30} = ( \frac{30 }{2 }) [ 2 (-504) + ( 30-1)(122.5) ]$

$S_{30} =(15) [ 2 (-504) + ( 29)(122.5) ]$

$S_{30} = [ 2 (-504)(15) + ( 29)(122.5)(15) ]$

$S_{30} = [ -15120 + 53287.5 ]$

$s_{30} = 38.167.5$

6 0

4 years ago

A draw scaling of a parking lot has a width of four inches. If the scale is 1 inch = 8 feet. What is the actual width of the par

IgorLugansk [536]

Answer: 32 feet

Step-by-step explanation:

Since 1 inch equals 8 feet and the parking lot has a width of 4 inches we multiply 8 times 4 giving you an answer of 32, so the parking lot's width is 32 feet.

4 0

3 years ago

Tammy drove 715 miles in 11 hours. at the same rate, how long would it take her to drive 845 miles?

Alex787 [66]

Answer:

Step-by-step explanation:

So we have direct proportions here.

715=11

845=x

845*11/715

x=13

To check our work.

715/11=65

65*13=845.

Basically, in this formula, you use cross multiplication. So A*B=B*A. B and B go together and A and A go together/

So we can use the formula x = b*b/a. Since A is one of the A's and the other value of A is missing, we can use this formula to find it.

Hope this helped, ask me if you have any questions.

8 0

3 years ago