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3 years ago

Solve the diﬀerential equation x^3y"'− 3x^2 y" 6xy'−6y = 0.

1 answer:

3 0

Equation at the end of step 1 : (((x3)•y)-(((3x2•y6)•x)•y))-6y = 0 Step 2 :Step 3 :Pulling out like terms :

3.1 Pull out like factors :

 -3x3y7 + x3y - 6y = -y • (3x3y6 - x3 + 6)

Trying to factor a multi variable polynomial :

3.2 Factoring 3x3y6 - x3 + 6

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Equation at the end of step 3 : -y • (3x3y6 - x3 + 6) = 0 Step 4 :Theory - Roots of a product :

4.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2 Solve : -y = 0

Multiply both sides of the equation by (-1) : y = 0

You might be interested in

Someone helpp !! I don’t understand this at all

Naddika [18.5K]

Answer:

∠AB=9

Step-by-step explanation:

the pyagrothyes therom= $a^{2}$ + $b^{2}$ = $c^{2}$

to find ∠AB we need to find the height of the triangle.

replace the variables:

$a^{2}$ + $6^{2}$ = $9^{2}$

= $9^{2}$ - $6^{2}$ = $a^{2}$

simplify:

81-36= $\sqrt{45}$

now we solve for ∠AB

replace the variables:

$6^{2}$ + $\sqrt{45}$ = $c^{2}$

simplify:

36+45= $\sqrt{81}$

$\sqrt{81}$ =9

I hope this helps you!!

have a nice day!!

4 0

2 years ago

Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of

Shalnov [3]

Answer:

$Owl= 67.14ft$

Step-by-step explanation:

See comment for complete question.

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

$(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})$

$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

The height of the owl is:

$Owl= H + 5$

$Owl= 62.14 + 5$

$Owl= 67.14ft$

7 0

2 years ago

A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solv

Vladimir79 [104]

Hey there,

Your question states: A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.

So, I will do 94.75 minus 11.50 because he bought nice scrubs so that would be 83.25.

I will do 83.25 divided by 9 because that's the number that person bought, each scrub will end up to be 9.25.

Hope this helps.

~Jurgen

6 0

3 years ago

Read 2 more answers

When multiplying numbers in scientific notation you blank the coefficients and substract the exponents?

34kurt

For the sake of example, let's multiply the two numbers $2.3 \times 10^5$ and $3.5 \times 10^7$ together. Altogether, we have:

$2.3\times10^5\times3.5\times10^7$

Rearranging the expression, we can group the exponents and coefficients together:

$2.3\times3.5\times10^5\times10^7$

Multiplying each out, we notice that since $10^5$ and $10^7$ have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:

$2.3\times3.5\times10^{5+7}=8.05\times10^{12}$

The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and adding its exponents.

8 0

3 years ago

7. A magnifying glass shows you an image of an object that is 7 times the object's actual size. An ant is 0.2 cm in length. What

Bess [88]

#1) (b)
#2) (d)
#3) (d)

My explanations are the same as your previous questions.

4 0

3 years ago