Write two expressions (with at least two terms each) that when added together have a sum of -4n + 6.

Question 3 Unsaved

bazaltina [42]

Answer:

Step-by-step explanation:

DE given is

y''+8y'+15y=0, y(0)=0, y'(0)=1

Take Laplace on the DE

We get

$s^2 Y(s) -sY(0) -y'(0)+8(sY(s)-y(0))+15Y(s) =0\\s^2 Y(s) -s(0) -1+8(sY(s)-0)+15Y(s) =0\\Y(s)(s^2+8s+15)-1=0\\Y(s) = \frac{1}{s^2+8s+15}$

Simplify to get

Y(s) = $\frac{1}{2}[ {\frac{1}{s+3} -\frac{1}{s+5} }]$

Take inverse

$y(t) = \frac{e^{-3t} -e^{-5t}}{2}$

8 0

2 years ago

Find an equation of the plane that contains (3, 4, −9) and is parallel to x + y − 5z = 1. (Use x, y, and z for coordinates.)

emmainna [20.7K]

Answer:

x + y - 5z = 52

Step-by-step explanation:

Given data:

Point on the plane (3,4,-9)

parallel to x + y -5z = 1

Finding the normal vector

(1 , 1 , -5)(x, y , z) = 1

the normal vector is (1 , 1 , -5)

formula for finding equation the plane given the normal vector (a,b,c) and point (m,n,o) is as

a(x - m) + b(y - n) + c(z-o)=0

Substituting the data we have

1(x-3) + 1( y- 4) - 5(z+9) =0

x-3 +y -4 -5z -45 = 0

x + y - 5z = 45 +4 +3

x + y - 5z = 52

6 0

2 years ago

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below

jok3333 [9.3K]

Answer:

The value of the test statistic = 2.58

Test statistic Z = - 4.805

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

There is significant difference between in the mean number of times men and women send a Twitter message in a day

Step-by-step explanation:

Step(i):-

Sample size of men n₁ = 25

mean of the first sample x₁⁻ = 20

Standard deviation of the first sample σ₁ = 5

Sample size of women n₂ = 30

mean of the second sample x₂⁻ = 30

Standard deviation of the first sample σ₂ = 10

Level of significance ∝= 0.01

Step(ii):-

Null Hypothesis : H₀: There is no significant difference between in the mean number of times men and women send a Twitter message in a day

Alternative Hypothesis :H₁:There is significant difference between in the mean number of times men and women send a Twitter message in a day

Test statistic

$Z = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S.D_{1} ^{2} }{n_{1} }+\frac{ S.D_{2} ^{2}}{n_{2} } } }$

$Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2} }{25 }+\frac{ (10)^{2} }{ 30} } }$

Z = $\frac{-10}{2.081} = - 4.805$

The value of the test statistic = 2.58 C

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

Conclusion:-

There is significant difference between in the mean number of times men and women send a Twitter message in a day

7 0

2 years ago

19

const2013 [10]

Answer:

10:2:3

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

8 0

2 years ago

Read 2 more answers

Select the correct answer.

MatroZZZ [7]

Answer:

A

Step-by-step explanation:

x+y=34 (add the seperate hours together to get the total amount of hours)

10x+15y=410 (multiply the money made each hour by the hours worked and add them together to get the amount of money joy made)

5 0

2 years ago