Find all values of m so that the function y = e^mx
is a solution of the given differential equation. y' + 9y = 0

Answers

Answer 1

Answer: Hello,

y=e^(mx)
y'=m*e^(mx)

0=y'+9y=m*e^(mx)+9*e^(mx)
==> e^(mx)*(m+9)=0
This must be exact for every value of ,so
m=-9

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If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answers

The correct answers are:
1) sin(x) = $( √(3) )/(2)$
2) tan(x) = $√(3)$

Explanation:
Given:
$cos(x) = (1)/(2)$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( (1)/(2) )^2 = 1 \n sin^2(x) + (1)/(4) = 1 \n sin^2(x) = (3)/(4)$

Step 3:
Take square-root on both sides:
$√(sin^2(x)) = \sqrt{(3)/(4)}$

sin(x) = $( √(3) )/(2)$

Now to find the tan(x), we would use the following formula:

tan(x) = $(sin(x))/(cos(x))$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $( ( √(3) )/(2) )/( (1)/(2) )$

Hence tan(x) = $√(3)$

Answer:

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

Step-by-step explanation:

Given = $\cos x=(1)/(2)$

To find : $\sin x=?$ and $\tan x=?$

Solution:

We know that, if the cosine function of an angle is $(1)/(2)$ then the angle is equal to the 60°.

$\cos x=(1)/(2)$

x = 60°

The value of the :

$\sin x=\sin 60^o=(√(3))/(2)$

We know that ratio of sine function to the cosine function is equal tto the tangent

$\tan x=(\sin x)/(\cos x)=((√(3))/(2))/((1)/(2))=√(3)$

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

Choose the correct sum of the polynomials (2x3 − 5x − 1) + (4x3 + 8x + 3).a2x3 − 3x − 4
b6x3 + 3x + 2
c2x3 + 3x + 2
d6x3 − 3x − 2

Answers

Answer:

Option (b) is correct.

Step-by-step explanation:

Given: Polynomial $2x^3-5x-1$ and $4x^3+8x+3$

We have to find the sum of given polynomial and choose the correct option from given options.

Consider the given Polynomial $2x^3-5x-1$ and $4x^3+8x+3$

We have to find the sum that is $2x^3-5x-1+(4x^3+8x+3)$

Apply plus minus rule $+(-a)=-a$

We have,

$2x^3-5x-1+4x^3+8x+3$

Now adding like terms, we have,

Like terms are terms having same variable with same degree.

$(4+2)x^3+(8-5)x-1+3$

Simplify , we have,

$6x^3+3x+2$

Thus, option (b) is correct.

(2x3 − 5x − 1) + (4x3 + 8x + 3)
=6x^3 +3x +2

answer is b. 6x3 + 3x + 2

Someone Pliz help me

Answers

Answer:

midpoint= (1,1)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

If Dave runs 1.3 kilometers in 10 minutes what is his average rate?Adapting and Using Formulas

Answers

1.3km = 10 minutes

speed * time = distance

speed = distance divided by time

His speed = 1.3/10 = 0.13 km/h

The perimeter of a rectangle is 90 centimeters. The width of the rectangle can be represented by (x + 2), and its length can be represented by (3x - 5). What are the dimensions of this rectangle in centimeters?A With = 10 and length = 25
B With = 12 and length = 29
C With = 14 and length = 31
D With = 16 and length = 32

Answers

Perimeter of a rectangle=2lenght + 2width
In this case:
Perimeter=90 cm
width=(x+2)
lenght=(3x-5)
Then:

2(x+2)+2(3x-5)=90
2x+4+6x-10=90
2x+6x=90+10-4
8x=96
x=96/8
x=12

with=(x+2)=12+2=14
lenght=(3x-5)=3*12-5=31

Answer: C width=14 and lenght=31.

A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the number of adults. The number of female students was half the number of male students. If the total number of people who went on the trip is 82, find the numbers of male students and female students.

Answers

Given:
adults = x
male = 7x + 1
female = (7x + 1)/2
total number of people = 82

x + (7x + 1) + [(7x +1)/2] = 82
2x/2 + (14x + 2)/2 + (7x + 1)/2 = 82
2x + 14x + 2 + 7x + 1 = 82 * 2
23x + 3 = 164
23x = 164 - 3
23x = 161
x = 161/23
x = 7

adults = x = 7
males = 7x + 1 = 7(7) + 1 = 49 + 1 = 50
females = (7x+1)/2 = 50/2 = 25

7 + 50 + 25 = 82

Answer:

50 males, 25 females

Step-by-step explanation:

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