All categories

3 years ago

Does the function g(x) = -2x2 + 10x + 2 have a minimum or a maximum? Identify its value. +

Mathematics

1 answer:

Hitman42 [59]3 years ago

3 0

Answer:

(5/2, 29/2), and this represents a maximum

Step-by-step explanation:

g(x) = -2x^2 + 10x + 2 is a quadratic function with coefficients {-2, 10, 2}.

The formula for the axis of symmetry (which passes through the vertex) is

x = -b/ [2a]. Here, a = -2; b = 10. Therefore, the axis of symmetry is

x = -10/ [2(-2)] = -10/(-4) = 5/2

Evaluate the function g(x) = -2x^2 + 10x + 2 at x = 5/2 to determine the y-coordinate of the vertex:

g(5/2) = -2(5/2)^2 + 10(5/2) + 2, or

g(5/2) = -2(25/4) + 25 + 2, or

g(5/2) = -25/2 + 27, or

g(5/2) = 14.5

The vertex is thus (5/2, 29/2), and this represents a maximum, because the coefficient of the x^2 term is negative (the curve opens downward).

You might be interested in

Use the GCF to factor:<br>25 + 40

Nookie1986 [14]

The answer would be the number 5

5 0

3 years ago

A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

Darina [25.2K]

Answer:

$100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy$ ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving $y=x^2$ about y axis in the interval $0\leq x\leq 3$ .

Density of the fluid in the tank, $D=100\ lbs/ft^3$

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, $y(0)=0^2=0$

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in $x=3$ in the parabolic equation . This gives,

$H=3^2=9\ ft$

So, the height of top of tank is, $y(3)=H=9\ ft$

Now, 5 ft above 'H' means $H+5=9+5=14$

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

$\Delta y=(14-y)$ ft

Now, area of cross section of the tank is given as:

$A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section$

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, $y=x^2$

So, $x=\sqrt y$

Therefore, radius, $r=\sqrt y$

Now, area of cross section is, $A(y)=\pi (\sqrt y)^2$

Work done in pumping the contents to 5 feet above is given as:

$W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy$

Plug in all the values. This gives,

$W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}$

7 0

3 years ago

What is -12=2+5v+2v

Xelga [282]

2+5y+2y=-12

2+7v=-12

2+7y-2=-12-2

7y=-14

7y/7=-14/7

y=-2

6 0

3 years ago

Read 2 more answers

A librarian surveyed her reading club. Of those surveyed, 7 favored mysteries, 4 favored fantasy, 3 favored science fiction, and

blsea [12.9K]

answer:

338 out of 520

step by step:

13 out of 20 dont favor mystery

13:20

? :520

520÷20=26

13×26= 338

338 students out of 520 do not favor mysteries

7 0

3 years ago

I really need help on 16 and 18 I'm super confused problem because I'm tired but I really need help

Bogdan [553]

Answer:

Hello,

Step-by-step explanation:

16)

Area of the square= 5²=25 (unit of square)

17)

Volume of the cube =3^3 =27 (unit of volume)

18)

side of the cube =5 (unit of lenght)

Volume of the cube = (5 (unit of lenght)) ^3

=125 * (unit of lenght)^3 =125 (unit of volume)

5 0

1 year ago