Question

Work out the values of y that satisfy:

-2y^2 + 10y = 9

Give each answer as a decimal to 3.s.f.

Answer 1

Hi,

Step-by-step explanation:

To find the values of y that satisfy the equation −2y²+10y=9,

we can begin by rearranging the equation into the form of a quadratic equation,

2y²−10y+9=0.

We can then solve this quadratic equation using the quadratic formula:

`2y^2-10y+9=0 \\\\\Delta=(-10)^2-4*2*9=100-72=28=(2√(7))^2\\ \\{y=(10-2√(7))/(4) \ or\ y=(10+2√(7))/(4) }\\\\\\y=(5-√(7))/(2)\ or\ y=(5+√(7))/(2)\\`

Now we can find the values of y to three significant figures:

​​y≈3.823. or y=1.177

So, the values of y that satisfy the equation are approximately 3.823

and 1.177 to three significant figures.

Answer 2

To find the values of y that satisfy the equation -2y^2 + 10y = 9, we rearrange the equation and solve using the quadratic formula. The solutions are y = -0.1775 and y = 5.6775, rounded to 3 significant figures.

Step-by-step explanation:

To find the values of y that satisfy the equation -2y^2 + 10y = 9, we can rearrange the equation to get -2y^2 + 10y - 9 = 0. This is a quadratic equation that can be solved using the quadratic formula. The quadratic formula is given by:

y = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = -2, b = 10, and c = -9. Plugging in these values, we get:

y = (-10 ± √(10^2 - 4(-2)(-9))) / (2(-2))

y = (-10 ± √(100 - 72)) / (-4)

y = (-10 ± √28) / (-4)

y = (-10 ± 5.29) / (-4)

So the two solutions for y are y = -0.1775 and y = 5.6775, rounded to 3 significant figures.