Write 4.63 x 10^-3 in standard notation

2<br> Do side lengths 23, 16, and 7 create a<br> triangle?<br> Show Your Work

Alexus [3.1K]

Answer:

what type? if right then

7^2+16^2=23^2

49+256=529

305≠529

so its not a right triangle

Step-by-step explanation:

7 0

3 years ago

HELP ME OUT PLEASE ITS DUE IN 5 MINS

mrs_skeptik [129]

The equation that can be used to find the number of wolves in the state on January 1 is w - 23 = 84

<h3>How to represent a situation with an equation?</h3>

A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier.

The equation that can be used to find the number of wolves in the state on January 1 can be calculated as follows:

where

w = number of wolves in the state January 1.

Therefore, the equation to represent the situation is as follows:

w - 23 = 84

learn more on equation here: brainly.com/question/7411234

#SPJ1

5 0

1 year ago

The value of a new car purchased for $20,000 decreases by 10% each year. Write an

Elena-2011 [213]

20000 x 90/100 = 18000

18000 x 90/100 = 16200

The value of the car after 2 years is $16200

6 0

3 years ago

Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 50% syrup?

zalisa [80]

He needs 2.5 lbs of sugar and 2.5 lbs of water

since 2.5 if 50% of 5 then thats how much sugar he needs.

6 0

3 years ago

Two solutions to y'' – 2y' – 35y = 0 are yı = e, Y2 = e -5t a) Find the Wronskian. W = 0 Preview b) Find the solution satisfying

pashok25 [27]

Answer:

a. $w(t)=-12e^{2t}$

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

Step-by-step explanation:

We have a differential equation

y''-2 y'-35 y=0

Auxillary equation

$(D^2-2D-35)=0$

By factorization method we are finding the solution

$D^2-7D+5D-35=0$

$(D-7)(D+5)=0$

Substitute each factor equal to zero

D-7=0 and D+5=0

D=7 and D=-5

Therefore ,

General solution is

$y(x)=C_1e^{7t}+C_2e^{-5t}$

Let $y_1=e^{7t} \;and \;y_2=e^{-5t}$

We have to find Wronskian

$w(t)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

Substitute values then we get

$w(t)=\begin{vmatrix}e^{7t}&e^{-5t}\\7e^{7t}&-5e^{-5t}\end{vmatrix}$

$w(t)=-5e^{7t}\cdot e^{-5t}-7e^{7t}\cdot e^{-5t}=-5e^{7t-5t}-7e^[7t-5t}$

$w(t)=-5e^{2t}-7e^{2t}=-12e^{2t}$

a. $w(t)=-12e^{2t}$

We are given that y(0)=-7 and y'(0)=23

Substitute the value in general solution the we get

$y(0)=C_1+C_2$

$C_1+C_2=-7$ ....(equation I)

$y'(t)=7C_1e^{7t}-5C_2e^{-5t}$

$y'(0)=7C_1-5C_2$

$7C_1-5C_2=23$ ......(equation II)

Equation I is multiply by 5 then we subtract equation II from equation I

Using elimination method we eliminate $C_1$

Then we get $C_2=-\frac{5}{2}$

Substitute the value of $C_2$ in I equation then we get

$C_1-\frac{5}{2}=-7$

$C_1=-7+\frac{5}{2}=\frac{-14+5}{2}=-\frac{9}{2}$

Hence, the general solution is

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

7 0

3 years ago