What is the approximate difference in average daily miles between the two weeks?

The length of the hypotenuse of a 30-60 -90 triangle is 14 units. what is the length of the short leg

kifflom [539]

Recall that the short leg is the side opposite the 30 degrees angle. And the ratio of the short leg to the hypotenuse is 1:2.

Let the length of the short leg be x, then,

$\cfrac{x}{14}=\cfrac{1}{2}\\ \\\Rightarrow2x=14\\ \\\Rightarrow x=\cfrac{14}{2}=7$

6 0

3 years ago

At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 2y + 7z = 2? (if an answer does not

Nikitich [7]

If $f(x, y, z) = c$ represent a family of surfaces for different values of the constant $c$ . The gradient of the function $f$ defined as $\nabla f$ is a vector normal to the surface $f(x, y, z) = c$ .

Given the paraboloid

$y = x^2 + z^2$ .

We can rewrite it as a scalar value function f as follows:

$f(x,y,z)=x^2-y+z^2=0$

The normal to the paraboloid at any point is given by:

$\nabla f= i\frac{\partial}{\partial x}(x^2-y+z^2) - j\frac{\partial}{\partial y}(x^2-y+z^2) + k\frac{\partial}{\partial z}(x^2-y+z^2) \\ \\ =2xi-j+2zk$

Also, the normal to the given plane $3x + 2y + 7z = 2$ is given by:

$3i+2j+7k$

Equating the two normal vectors, we have:

$2x=3\Rightarrow x= \frac{3}{2} \\ \\ -1=2 \\ \\ 2z=7\Rightarrow z= \frac{7}{2}$

Since, -1 = 2 is not possible, therefore there exist no such point on the paraboloid $y = x^2 + z^2$ such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2.

4 0

3 years ago

A) how many ways are there to choose 10 players to take the field?

Kruka [31]

A. C(13, 10) = 13! = 13·12·11 = 13 · 2 · 11 = 286.C(13, 10) = 13! = 13·12·11 = 13 · 2 · 11 = 286.

B. P(13,10)= 13! =13! =13·12·11·10·9·8·7·6·5·4. (13−10)! 3!

C. f there is exactly one woman chosen, this is possible in C(10, 9)C(3, 1) =

10! 3!

9!1! 1!2! 10! 3!

8!2! 2!1! 10! 3!

7!3! 3!0!

= 10 · 3 = 30 ways; two women chosen — in C(10,8)C(3,2) =

= 45·3 = 135 ways; three women chosen — in C(10, 7)C(3, 3) =

= 10·9·8 ·1 = 120 ways. Altogether there are 30+135+120 = 285 1·2·3

possible choices.

5 0

3 years ago

which of the following are the exact same distance from a parabola? A.Locus and Directix B.Axis and vertex C.Directix and Focus

Softa [21]

Answer:

C. Directrix and Focus

Step-by-step explanation:

Given choices are :

A. Locus and Directrix

B. Axis and vertex

C. Directrix and Focus or

D. Vertex and Locus

Now we need to find about which of the above choices are the exact same distance from a parabola.

By definition of parabola, vertex lies at equal distance from directrix and focus.

Hence choice C. Directrix and Focus is correct.

6 0

3 years ago

Read 2 more answers

A cylindrical flower vase has a height of 8 inches and a radius of 2 inches what is the volume of the vase?

natta225 [31]

Answer:

1008.48 in ^2

Step-by-step explanation:

Given

Its a cylindrical vase .
Radius = 2 inches
height = 8 inches .

Formula

$\bold { \purple {volume = \pi \: {r}^{2}h \: }}$

Lets assume pi to be 3.14

$v = 3.14 \times {2}^{2} \times 8 \\ \\ \\ v = 3.14 \times 4 \times 8 \\ \\ \\ v = 3.14 \times 32 \\ \\ \\ v = 1008.48 {in}^{2}$

6 0

3 years ago