(1-x)y"-4xy'+5y=cosx

4 km = m help please

dybincka [34]

Answer:

4000m

Step-by-step explanation:

km to m --> multiply by 1000

4km * 1000 = 4000m

8 0

3 years ago

israel started to solve a radical equation in this way: square root of x plus 6 − 4 = x square root of x plus 6 − 4 4 = x 4 squa

agasfer [191]

Lets solve our radical equation $\sqrt{x+6}-4=x$ step by step.

Step 1 add 4 to both sides of the equation:

$\sqrt{x+6} -4+4=x +4$

$\sqrt{x} +6=x+4$

Step 2 square both sides of the equation:

$\sqrt{x+6} =x+4$

$\sqrt{x+6}^2 =(x+4)^2$

$x+6=(x+4)^2$

Step 3 expand the binomial in the right hand side:

$x+6=x^2+8x+16$

Step 4 simplify the expression:

$0=x^2+8x-x+16-6$

$x^2+7x+10=0$

Step 5 factor the expression:

$(x+2)(x+5)=0$

Step 6 solve for each factor:

$x+2=0$ or $x+5=0$

$x=-2$ or $x=-5$

Now we are going to check both solutions in the original equation to prove if they are valid:

For $x=-2$

$\sqrt{x+6}-4=x$

$\sqrt{-2+6}-4=-2$

$\sqrt{4}-4=-2$

$2-4=-2$

$-2=-2$

The solution $x=2$ is a valid solution of the rational equation $\sqrt{x+6}-4=x$ .

For $x=-5$

$\sqrt{x+6}-4=x$

$\sqrt{-5+6}-4=-5$

$\sqrt{1}-4=-5$

$1-4=-5$

$-3\neq -5$

Since -3 is not equal to -5, the solution $x=-5$ is not a valid solution of the rational equation $\sqrt{x+6}-4=x$ ; therefore, $x=-5$ is an extraneous solution of the equation.

We can conclude that even all the algebraic procedures of Israel are correct, he did not check for extraneous solutions.

An extraneous solution of an equation is the solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation. Is worth pointing out that extraneous solutions are particularly frequent in rational equation.

8 0

3 years ago

The edge of a cube measures 3.5 x 10 ^ -2 meters. What is the volume of the cube in cubic meters? WRITE Your ANSWERS IN SCIENTIF

Crank

The volume of given cube is: $4.29 * 10^{-5}$ cubic meters

Step-by-step explanation:

Volume of a cube is given by:

$V = a^3$

Given

Edge of the cube = $3.5*10^{-2}$

Putting the value of edge

$V = (3.5*10^{-2})^3\\V = 42.875 * (10^{-2})^3\\V = 42.9 * 10 ^{-2*3}\\V = 42.9 * 10^{-6}\\V = 4.29 * 10 * 10 ^{-6}\\V = 4.29 * 10^{-5}\ cubic\ meters$

The volume of given cube is: $4.29 * 10^{-5}$ cubic meters

Keywords: Volume, cube, scientific notation

Learn more about scientific notation at:

#LearnwithBrainly

7 0

4 years ago

Students make 71.5 ounces of liquid soap for a craft fair. They put the soap in 5.5 ounce bottles

Oxana [17]

Answer:

13 bottles of soap

Step-by-step explanation:

71.5/5.5=13

5 0

3 years ago

HELP ASAP

kow [346]

Answer:

C

Step-by-step explanation:

The distributive property says that

$a\cdot (b+c)=a\cdot b+a\cdot c$

Consider option C. In this option,

$(0.7\cdot 0.7)+(0.7\cdot 0.9)+(0.7\cdot 0.2)=0.7\cdot (0.7+0.9+0.2)$

The left part consists of three products

$(0.7\cdot 0.7)\\ (0.7\cdot 0.9)\\ (0.7\cdot 0.2)$

Each of these products has the factor $0.7.$ Usig the distributive property, we can write this factor before the brackets and all remaining factors write as the sum in the brackets:

$0.7\cdot (0.7+0.9+0.2)$

This is exactly the right part of equality from option C.

7 0

3 years ago