All categories

2 years ago

Make c the subject: x=-b+(b²-4ac) divided by 2a The brackets mean square root

1 answer:

7 0

$x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\
2ax=-b+\sqrt{b^2-4ac}\\
\sqrt{b^2-4ac}=2ax+b\\
b^2-4ac=(2ax+b)^2\\
-4ac=4a^2x^2+4abx+b^2-b^2\\
-4ac=4a^2x^2+4abx\\
c=-ax^2-bx$

You might be interested in

Line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints an M1 (2,16) and M2 (-3,5

Arisa [49]

Answer:

12.1

Step-by-step explanation:

The dashed line joining M₁ and M₂ is the hypotenuse of a right triangle as shown in red below.

The base of the triangle is

x₂ - x₁ = 2 - (-3) = 2+ 3 = 5

The height of the triangle is

y₂ - y₁ = 16 - 5 = 11

We can now use Pythagoras' theorem to calculate distance between the two midpoints.

x² = 5² + 11² = 25 + 121 = 146

x = √146 = 12.1

The distance between M₁ and M₂ is 12.1.

8 0

3 years ago

Find the radius of a circle in which a central angle of StartFraction pi Over 7 EndFraction radian determines a sector of area 7

QveST [7]

Answer:

Step-by-step explanation:

The formula for determining the the area of a sector is expressed as

Area of Sector = θ/360 × πr²

Where

θ represents the central angle.

π is a constant whose value is 3.14

r represents the radius of the circle.

From the information given,

The central angle is π/7 radian. Converting to degrees, it becomes

π/7 × 180/π = 180/7 = 25.714 degrees.

Area of sector = 77 square meters

Therefore

77 = 25.714/360 × 3.14 × r²

77 = 0.2243r²

r² = 77/0.2243 = 343.29

r = √343.29 = 18.53 meters

5 0

3 years ago

The daily revenues of a cafe near the university are approximately normally distributed. The owner recently collected a random s

lbvjy [14]

Answer:

The sample size to obtain the desired margin of error is 160.

Step-by-step explanation:

The Margin of Error is given as

$MOE=z_{crit}\times\dfrac{\sigma}{\sqrt{n}}$

Rearranging this equation in terms of n gives

$n=\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2$

Now the Margin of Error is reduced by 2 so the new M_2 is given as M/2 so the value of n_2 is calculated as

$n_2=\left[z_{crit}\times \dfrac{\sigma}{M_2}\right]^2\\n_2=\left[z_{crit}\times \dfrac{\sigma}{M/2}\right]^2\\n_2=\left[z_{crit}\times \dfrac{2\sigma}{M}\right]^2\\n_2=2^2\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2\\n_2=4\left[z_{crit}\times \dfrac{\sigma}{M}\right]^2\\n_2=4n$