All categories

2 years ago

What is the pattern in the values as the exponents increase?

Mathematics

2 answers:

Troyanec [42]2 years ago

6 0

Divide the previous value by 3

brilliants [131]2 years ago

4 0

Answer:

Multiply the previous value by 3.

Step-by-step explanation:

The correct pattern in the values as the exponents increase is - Multiply the previous value by 3.

We can see, that $3^{-1}$ is $\frac{1}{3}$

And in the next step, $3^0$ is $\frac{1}{3}\times3=1$

In the next step, $3^1$ is $1\times3=3$

In the last step, $3^2$ is $3\times3=9$

So, at each step, 3 is multiplied to the previous product/value.

Therefore, the correct answer is last option.

You might be interested in

Find the volume of the rectangular prism. Write your answer as a fraction.

suter [353]

Answer:

V = 8/125 cubic units

Step-by-step explanation:

This prism is actually a cube of side length 2/5.

The volume of a cube of side length s is V = s^3.

Here, the volume of the cube (rectangular prism) is V = (2/5)^3, or

V = 8/125 cubic units

8 0

2 years ago

Given z=4+3i evaluate z

DerKrebs [107]

Answer:

Step-by-step explanation:

Assuming we want to evaluate |z|, given that, z=4+3i.

Then, by definition of modulus,

$|x + yi| = \sqrt{ {x}^{2} + {y}^{2} }$

$|4+ 3i| = \sqrt{ {4}^{2} + {3}^{2} }$

$|4+ 3i| = \sqrt{ 16+ 9 } \\ |4+ 3i| = \sqrt{25 } \\ |4+ 3i| = 5$

Therefore the modulus be of the given complex number is 5 units

5 0

3 years ago

Solve for x in the equation shown below

baherus [9]

Answer:

x = 14

Step-by-step explanation:

Step 1: First, Simplify the fraction.

$\frac{4x}{7} =8$

Step 2: Next, Multiply both sides by 7.

4x = 8 × 7

Step 3: Simplify 8 × 7 to 56.

4x = 56

Step 4: Then, Divide both sides by 4.

$x=\frac{56}{7}$

Step 5: Lastly, Simplify the fraction and you're done!

x = 14

3 0

3 years ago

Multiply: (5x2y – 3xy2)(3xy2 + 5x2y)<br> Please help I need to get this one right!

Aliun [14]

Answer:

(1): "*-5x2y" was replaced by "*(-5x2y)".

(2): "x2" was replaced by "x^2". 1 more similar replacement(s).

STEP

Equation at the end of step 1

(3x • (y2)) • (0 - (5x2 • y))

STEP

Equation at the end of step

3xy2 • -5x2y

STEP

Multiplying exponential expressions :

3.1 x1 multiplied by x2 = x(1 + 2) = x3

Multiplying exponential expressions :

3.2 y2 multiplied by y1 = y(2 + 1) = y3

I believe the answer is ( -3•5x3y3)

6 0

3 years ago

Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

4 0

3 years ago