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2 years ago

I Need Help!!!!

Mathematics

1 answer:

vagabundo [1.1K]2 years ago

8 0

Answer:

6^27

Step-by-step explanation:

To answer this, we are going to use one of the laws of indices

We have this as;

(a^b)^c = a^(b * c) = a^bc

we are going to apply same here

(6^-3)^-9 = 6^(-3 * -9) = 6^27

You might be interested in

Roberto wants to display his 18 sports cards in an album . Some pages hold 2 cards and others hold 3 cards .

nexus9112 [7]

Answer:

Step-by-step explanation:

Assuming Roberto wants to completely fill each page that he puts cards in, this function describes the number of 2-card pages, a, and 3-card pages, b.

2a + 3b =18

Ricardo can fill up 9 2-card pages, and 6 3-card pages.

a=9, b=0

We must add 2 3-card pages at a time,so that we have an even number for the 2-card pages:

a=6, b=2

Add 2 to b once more:

a=3, b=4

One more time:

a=0, b=6:

Thus, Ricardo can display his figures in the following page combinations:

a=9, b=0

a=6, b=2

a=3, b=4

a=0, b=6

Remember that a= number of 2-card pages and b=number of 3-card pages

There are 4 different ways that Ricardo can arrange his figures in terms of what kind of pages he uses.

3 0

3 years ago

Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The

geniusboy [140]

B

3x6=18
4x6=24
16x6=96
The second picture is 6 times bigger than the first so it's 1 to 6

8 0

2 years ago

Read 2 more answers

6 points

kodGreya [7K]

Answer:

$y=-2\,(x+3)^2-3$

Step-by-step explanation:

Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex $(x_v,y_v)$ in the expression:

$y-y_v=a\,(x-x_v)^2\\y=a\,(x-x_v)^2+y_v$

we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter $a$ :

$y=a\,(x-x_v)^2+y_v\\y=a\,(x+3)^2+(-3)\\y=a\,(x+3)^2-3\\-5=a\,(-2+3)^2-3\\-5=a\,(1)-3\\a=-5+3\\a=-2$

So, now we can write the full expression for the parabola:

$y=a\,(x+3)^2-3\\y=-2\,(x+3)^2-3$

8 0

3 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

Highest (-3,-3)

Lowest (2,2)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

\dfrac{1}{2} - 60\% - 25\% = 2 1 −60%−25%

Helen [10]

Answer:

the answer is -85%

.........

7 0

2 years ago