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3 years ago

9

Given the following linear function, sketch the graph of the function and find the domain and range. f(x)=2/3-3

1 answer:

Darina [25.2K]3 years ago

5 0

Answer:

f(x)= 2/3-3 is undefined.

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Find intergral (e^xcos(3x)dx

ArbitrLikvidat [17]

Answer:

Hello,

Step-by-step explanation:

Here is an other method than classical:

$I=\int {e^x*cos(3x)} \, dx =e^x*(k_1/cos(3x)+k_2*sin(3x) )\\\\Let's\ derivate:\\\\e^xcos(3x)=e^x(k1*cos(3x)+k_2*sin(3x))+e^x*(k_1*(-sin(3x))*3+k_2*cos(3x)*3)\\\\By\ identification:\\\\\left\{\begin{array}{ccc}k_1+3k_2&=&1\\-3k_1+k2&=&0\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}k_1&=&\dfrac{1}{10}\\k2&=&\dfrac{3}{10}\\\end{array}\right.\\\\\\\boxed{I=e^x(\dfrac{1}{10}*cos(3x)+\dfrac{3}{10}*sin(3x))}\\$

8 0

2 years ago

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2

butalik [34]

Answer:

The correct answer is A) 5n = 3d and 3n + 6 = 2d + 4

Step-by-step explanation:

hope this is right...

6 0

4 years ago

Find the vertex of the parabola given by the following equation y=x2+10x+33

vovikov84 [41]

$\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\

\begin{array}{llccll}
y = &{{ 1}}x^2&{{ +10}}x&{{ +33}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

6 0

4 years ago

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop

Anettt [7]

Answer:

a. $\frac{1}{15}$

b. $\frac{2}{5}$

c. $\frac{14}{15}$

d. $\frac{8}{15}$

Step-by-step explanation:

Given that there are two laptop machines and four desktop machines.

On a day, 2 computers to be set up.

To find:

a. probability that both selected setups are for laptop computers?

b. probability that both selected setups are desktop machines?

c. probability that at least one selected setup is for a desktop computer?

d. probability that at least one computer of each type is chosen for setup?

Solution:

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

a. Favorable cases for Both the laptops to be selected = $_2C_2$ = 1

Total number of cases = 15

Required probability is $\frac{1}{15}$ .

b. Favorable cases for both the desktop machines selected = $_4C_2=6$

Total number of cases = 15

Required probability is $\frac{6}{15} = \frac{2}{5}$ .

c. At least one desktop:

Two cases:

1. 1 desktop and 1 laptop:

Favorable cases = $_2C_1\times _4C_1 = 8$

2. Both desktop:

Favorable cases = $_4C_2=6$

Total number of favorable cases = 8 + 6 = 14

Required probability is $\frac{14}{15}$ .

d. 1 desktop and 1 laptop:

Favorable cases = $_2C_1\times _4C_1 = 8$

Total number of cases = 15

Required probability is $\frac{8}{15}$ .

8 0

4 years ago

School x and y are in a comepetition. School x has 8 more points than school y and 3 times more points as school y . How many po

lara [203]

Answer: School Y has 4 points and School X has 12 points.

Explanation:

Let the number of points School Y has be x

Let the number of points School X has be 3x

According to question, we get

$3x-x=8\\\\2x=8\\\\x=\frac{8}{2}\\\\x=4$

So, the number of point School Y has 4.

and number of points School X has

$3x=3\times 4=12$

Hence, School Y has 4 points and School X has 12 points.

6 0

3 years ago