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3 years ago

Is 7/45 a repeating or terminating

Mathematics

1 answer:

timurjin [86]3 years ago

8 0

I believe that 7/45 is a repeating decimal

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The Park family was traveling to Disney World on vacation. They drove 487.5 miles in 7.5 hours. At this rate, how many miles did

andrew-mc [135]

They drove 65 miles per hour

7 0

3 years ago

EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 9z on the curve of intersection of the plane x − y + z =

geniusboy [140]

The Lagrangian,

$L(x,y,z,\lambda,\mu)=x+2y+9z-\lambda(x-y+z-1)-\mu(x^2+y^2-1)$

has critical points where its partial derivatives vanish:

$L_x=1-\lambda-2\mu x=0$

$L_y=2+\lambda-2\mu y=0$

$L_z=9-\lambda=0$

$L_\lambda=x-y+z-1=0$

$L_\mu=x^2+y^2-1=0$

$L_z=0$ tells us $\lambda=9$ , so that

$L_x=0\implies-8-2\mu x=0\implies x=-\dfrac4\mu$

$L_y=0\implies11-2\mu y=0\implies y=\dfrac{11}{2\mu}$

Then with $L_\mu=0$ , we get

$x^2+y^2=\dfrac{16}{\mu^2}+\dfrac{121}{4\mu^2}=1\implies\mu=\pm\dfrac{\sqrt{185}}2$

and $L_\lambda=0$ tells us

$x-y+z=-\dfrac4\mu-\dfrac{11}{2\mu}+z=1\implies z=1+\dfrac{19}{2\mu}$

Then there are two critical points, $\left(\pm\frac8{\sqrt{185}},\mp\frac{11}{\sqrt{185}},1\pm\frac{19}{\sqrt{185}}\right)$ . The critical point with the negative $x$ -coordinates gives the maximum value, $9+\sqrt{185}$ .

8 0

3 years ago

X + p = q

expeople1 [14]

X=q-p
What you have to do is to rearrange the formula
x+p=q
All you have to do is to move “+q” to the other side of the formula. Doing so you also have to change the sign from “+” to “-“ so that your equation could be balanced
Hope this helps!!!!

5 0

2 years ago

A square has the sides length 2k-1 units. An equilateral triangle has the sides of the length k+2 units. the square and the tria

AlladinOne [14]

I think that you assumed that:
2k - 1 = k + 2

However we can't do this, because a square has 4 sides whilst a triangle only has 3 sides.
This means that we can say
4(2k - 1) = 3(k + 2)

We multiply by 4 due to 4 sides of the square, and by 3 due to the 4 sides of the triangle.

Lets expand the brackets, and solve it:

4(2k - 1) = 3(k + 2)
8k -4 = 3k + 6
5k -4 = 6 ( subtract both sides by 3x to collect the x values)
5k = 10 (add both sides by 4 to get the x's alone)
k = 2 (divide both sides by 5 to get what just x is)

So k = 2 units

8 0

3 years ago

Write the solution to the given inequality in interval notation.

DIA [1.3K]

Option A: $[4, \infty)$ is the solution

Explanation:

The solution of the given inequality is the set of all the possible values of x.

The graph shows the number line in which the shaded region is from the right of -4 and the arrow of solution goes to infinity.

Also, There is a closed circle at the point -4.

This means that -4 is included in the solution set.

The solution to the inequality is the set of all the real values which are greater than or equal to -4.

Thus, the solution is x ≥ -4

Hence, the solution is $[4, \infty)$

4 0

3 years ago