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Karo-lina-s [1.5K]

3 years ago

5

in finding the solutions of differential equations by P, Q, method (dy/dx +Py = Q) , when the integrating factor = e ( to the po

wer , integration of P.dx) is it necessary that Q must be in terms of x variable only? Or can terms with y variable be also present?

1 answer:

Amanda [17]3 years ago

8 0

Yes. Q must be in terms of v variables or a constant. It cannot be in terms of y variables.

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What are the period and phase shift for f(x) = 3 tan(4x + π)?

Y_Kistochka [10]

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

\end{array}$

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

$\bf \begin{array}{llll}


\bullet \textit{vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\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}$

now.. with that template above in mind, let's see yours

$\bf \begin{array}{lllllll}
f(x)=&3tan(&4x+&\pi )\\
f(x)=&3tan(&4x+&1\pi )&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

7 0

3 years ago

What is 9 wholes3/8 - 8 wholes7/8?

love history [14]

Result: 1 2/3 : 4 3/8 = 821 ≅ 0.3809524 ... subtraction fractions: 2/3 - 1/2 • multiplying a fraction by another fraction - multiplication: 7/8 * 3/9 ... multiplying a fraction by a whole number: 6 * 3/4

3 0

3 years ago

Use Cramer's rule to solve the following system of equations.

sp2606 [1]

5x + 3y = 7> (4) 5x + (4) 3y = (4) 7 4x + 5y = 3> (-5) 4x + (-5) 5y = (-5) 3 20y + 12y = 28 -20x -25y = -15 (X's cross out) 12y - 25y = 28 -15 -13y = 13 Y = -1 (Plug in for y) 5x + 3(-1) = 7 5x -3 =7 (add 3 to 7) 5x = 10 (divide by 5) X= 2 Ordered Pair= (2, -1)

4 0

3 years ago

The surface area of a cylinder is 408.2 square feet. The area of one of the bases is 78.5 square feet. Find the height of the cy

Phantasy [73]

Answer: The height of the cylinder is 8 feet.

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

The area of one of the bases is 78.5 square feet. This means that

78.5 = 3.14 × r²

r² = 78.5/3.14 = 25

r = √25 = 5

The formula for determining the surface area of a cylinder is expressed as

Surface area = 2πr² + 2πrh

The surface area of a cylinder is 408.2 square feet. Therefore,

408.2 = 2 × 3.14 × 5² + 2× 3.14 × 5 × h

408.2 = 157 + 31.4h

31.4h = 408.2 - 157

31.4h = 251.2

h = 251.2/31.4

h = 8 feet

6 0

4 years ago

Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews

maks197457 [2]

Answer:

Step-by-step explanation:

The given information can be tabulated as follows.

Success type High Moderate Low Total

0.40 0.35 0.25 1

Good reviews 0.95 0.60 0.10

Combined prob 0.4*0.95 0.35*0.6 0.25*0.1

0.38 0.21 0.025 0.6125

A) the probability that a product attains a good review

=Prob it it successful and gets good review + Prob it is moderate successful and gets good review +Prob it it low successful and gets good review

= 0.6125

B) If a new design attains a good review, the probability that it will be a highly successful product= $\frac{0.38}{0.6125} \\=0.6204$

C) Prob that does not attain a good review =(0.40*0.05)+0.35(0.4) +(0.25)*0.9

= 0.385

Prob for successful not getting good review = 0.40(0.05) = 0.02

Reqd prob = $\frac{0.02}{0.385} \\=0.05195$

8 0

4 years ago