Four points are coplanar sometimes? always or never

Two nimbers have a product of 90 and a sum of 19. What are the two numbers?

bulgar [2K]

Answer:

9 + 10 = 19 product is 9 x 10 = 90 9^2 + 10^2 = 181

6 0

2 years ago

What is the equation for a 75 90 15 triangle

vladimir1956 [14]

Answer:

30,60,90 triangle, which is the lengths 1 √ 3 , and 2 respectively. This is what I have got so far: Using the 30-60-90 Ratio

Step-by-step explanation:

4 0

3 years ago

Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. Th

xenn [34]

Answer:

The solutions are linearly independent because the Wronskian is not equal to 0 for all x.

The value of the Wronskian is $\bold{W=-3e^{7x}}$

Step-by-step explanation:

We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

$W = \left|\begin{array}{cc}y&z\\y'&z'\end{array}\right|$

Thus replacing the functions of the exercise we get:

$W = \left|\begin{array}{cc}e^{5x}&e^{2x}\\5e^{5x}&2e^{2x}\end{array}\right|$

Working with the determinant we get

$W = 2e^{7x}-5e^{7x}\\W=-3e^{7x}$

Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.

3 0

3 years ago

Pls help with 29..tank you

trapecia [35]

Answer:

See below

Step-by-step explanation:

Let the 2 roots be A and A^2.

Then A^3 = c/a and A + A^2 = -b/a.

Using the identity a^3 b^3 = (a + b)^3 - 3ab^2 - 3a^2b:-

A^3 + (A^2)^3 = ( A + A^2)^3 - 3 A.A^4 - 3 A^2. A^2

= (A + A^2)^3 - 3A*3( A + A^2)

Substituting:-

c/a + c^2/a^2 = (-b/a)^3 - 3 (c/a)(-b/a)

Multiply through by a^3:-

a^2c + ac^2 = -b^3 + 3abc

Factoring:-

ac(a + c) = 3abc - b^3

This is not the formula required in the question but let's see if the formula in the question reduces to this. If it does we have completed the proof.

a(c - b)^3 = a(c^3 - 3c^2b + 3cb^2 - b^3) = ac^3 - 3ac^2b + 3acb^2 - ab^3

c(a - b)^3 = c(a^3 - 3a^2b + 3ab^2 - b^3) = ca^3 - 3a^2bc + 3acb^2 - cb^3.

These are equal so we have

ca^3 - 3a^2bc + 3acb^2 - cb^3 = ac^3 - 3abc^2 + 3acb^2 - ab^3

The 3acb^2 cancel out so we have:-

a^3c - ac^3 = 3a^2bc - 3abc^2 + b^3c - ab^3

ac(a^2 - c^2) = 3abc( a - c) + b^3(c - a)

ac(a + c)(a -c) = 3abc(a - c) - b^3 (a - c)

Divide through by (a - c):-

ac(a + c) = 3abc - b^3 , which is the result we got earlier.

This completes the proof.

3 0

3 years ago

Read 2 more answers

An initial amount of 250 grows at a rate of 10% every year. Write an

Bingel [31]

Answer:

10% of 250 = 25.

When getting an increase, (using ^ for this example) add 25 to 250, getting 275. That's one increase of 10%. For an increase of 5 years (x = 5) divide 250/10=25, then multiply 25x5=125. That is the increase number. Add 125+250=375. Y=375

X = 5, Y = 375

7 0

3 years ago

Four points are coplanar sometimes? always or never​

Four points are coplanar sometimes? always or never