All categories

2 years ago

What is the vertex of the parabola whose equation is y = (x + 1)^2 + 3?

1 answer:

5 0

The y-value of the vertex is positive 3, as shown by the +3 on the right hand side of the equation, and the x-value is -1, from the (x+1)^2 (remember, when the number is inside the brackets, flip the sign) The vertex would be (-1, 3)

If you are looking for a rigorous answer (calculus), we must find the mininum point of the equation: f(x) = (x+1)^2 + 3 f
f'(x) = 2(x+1) = 2x + 2
2x + 2 = 0
x = -1
f(1) = (-1 + 1)^2 + 3
f(1) = 0 + 3 = 3
(-1, 3)

You might be interested in

) Set up a double integral for calculating the flux of F=3xi+yj+zk through the part of the surface z=−5x−2y+2 above the triangle

Fynjy0 [20]

The surface (call it $S$ ) is a triangle with vertices at the points

$x=0,y=0\implies z=2\implies(0,0,2)$

$x=0,y=2\implies z=-2\implies(0,2,-2)$

$x=2,y=0\implies z=-8\implies(2,0,-8)$

Parameterize $S$ by

$\vec s(u,v)=(1-v)(2,0,-8)+v\bigg((1-u)(0,2,-2)+u(0,0,2)\bigg)=(2-2v,2v-2uv,-8+6v+4uv)$

with $0\le u\le1$ and $0\le v\le1$ . Take the normal vector to $S$ to be

$\vec s_v\times\vec s_u=(20v,8v,4v)$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^1\int_0^1\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^1\int_0^1(6-6v,2v-2uv,-8+6v+4uv)\cdot(20v,8v,4v)\,\mathrm du\,\mathrm dv$

$=\displaystyle8\int_0^1\int_0^1(11v-10v^2)\,\mathrm du\,\mathrm dv=\boxed{\frac{52}3}$

8 0

3 years ago

On a bicycle, Eddie can travel 20 miles in 4 hours. How many hours does it take Eddie to travel 1 mile?

Paul [167]

Answer:

1 mile = 0.2 hours

Step-by-step explanation:

Given that,

Eddie can travel 20 miles in 4 hours.

We need to find how many hours does it take Eddie to travel 1 mile.

20 mile = 4 hours

1 mile = (4/20) hours

= 0.2 hours

So, to travel 1 mile will take 0.2 hours.

3 0

2 years ago

Clara looked at the clock on her way to band practice.

Daniel [21]

Answer:

3:45 pm

Step-by-step explanation:

4 0

3 years ago

How many solutions does the system have?

omeli [17]

Answer:

B. No solutions

Step-by-step explanation:

8x+2y=14

8x+2y=4

These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y). The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.

7 0

2 years ago

Read 2 more answers

A bag contains 5 gray tiles and 2 blue tiles. Jenny reached into the bag and picked a tile randomly, and then without replacing

SpyIntel [72]

5/6 because she already picked a blue tile. it makes the grey tile to be picked.

8 0

3 years ago