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erastova [34]
2 years ago
11

The steps to derive the quadratic formula are shown below:

Mathematics
1 answer:
Georgia [21]2 years ago
3 0

Answer: x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

\left(x+\frac{b}{2a} \right)^2

So, taking the square root of both sides,

x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}

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How 7,5,6 and 3 equal 75
____ [38]
Well first you do 7+5 to equal 12, and then you multiply 12 by 6 and get 72, then you add the 3 to get 75. 6(7+5)+3=75. Hope this helps!!
4 0
3 years ago
(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2
SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0
3 years ago
Choose the correct proportions.
cestrela7 [59]

Answer:

Options A, B and C are CORRECT PROPORTIONS

Step-by-step explanation:

Option A

3:5 = 6:10

The LHS must equal the RHS

3:5 is in it's lowest term.

6/10 will be in it's lowest term by dividing the numerator and denominator by 2.

6/10 = 3/5

Option B

3/6 and 5/10.

Diving 3/6 fractions by 3

= 1/2

Dividing 5/10 fraction by 5

= 1/2

Option C

Dividing 6/3 by 3 = 2

Dividing 10/5 by 5 = 2

Thats how you work through equivalent proportional fractions

6 0
3 years ago
Convert 15/9 to a decimal. A. 1.64 B. 1.67 C. 1.66 D, 1.69
Travka [436]
15/9 = 1.6666... (where 6 repeats infinitely)

If we're rounding to 2 decimal places, 6 will round up to 7

Therefore, B. 1.67 is your answer
7 0
3 years ago
A website offers a coupon such that each customer has a 15% chance of getting the coupon every day they visit. Aya visits the we
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Dkajnsuzhsisnsmeskms
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3 years ago
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