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2 years ago

F(x)= -5x-1 and g(x)= 2x^2solve (f+g)(x)

Mathematics

2 answers:

Georgia [21]2 years ago

8 0

$f(x)=-5x-1;\ D_f:x\in\mathbb{R}\\\\g(x)=2x^2;\ D_g:x\in\mathbb{R}\\\\D_f=D_g\ then\ (f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=-5x-1+2x^2=2x^2-5x-1$

madam [21]2 years ago

7 0

$\{f + g \}(x) = (-5x - 1 )\ +\ 2 x^{2} \\\\= 2 x^{2} -5x - 1\ \ Answer$

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Amiraneli [1.4K]

Answer:

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dolphi86 [110]

Answer:

(a)

Distance from player should be 13.82 feet or 36.2 feet

(b)

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Step-by-step explanation:

we are given

The ball follows a path given by the equation

$y=-0.01x^2+0.5x+3$

where

x and y are measured in feet and the origin is on the court directly below where the player hits the ball

(a)

net height is 8 ft

so, we can set y=8

and then we can solve for x

$8=-0.01x^2+0.5x+3$

$8\cdot \:100=-0.01x^2\cdot \:100+0.5x\cdot \:100+3\cdot \:100$

$800=-x^2+50x+300$

$-x^2+50x-500=0$

$x^2-50x+500=0$

we can use quadratic formula

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

$x=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-500\right)}}{2\left(-1\right)}$

$x=5\left(5-\sqrt{5}\right),\:x=5\left(5+\sqrt{5}\right)$

$x=13.82,x=36.2$

So, distance from player should be 13.82 feet or 36.2 feet

(b)

we can plug x=30 and check whether y=8 ft

$y=-0.01(30)^2+0.5(30)+3$

$y=9ft$

we know that

height of net is 8 ft

so, the ball will go over the net

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