A right cubic prism has edges of 3 1/4 inches. How many cubes with side lengths of 1/4 inches would be needed to fill the prism?

Please help! What is -9/5 - (-9/5)? A. 0 B.2 C. 18/5 D. -18/5

Pie

Answer:6

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

How many months does it take for $700 to double at simple interest of 14%?

aleksandrvk [35]

It will approximately take 7 months to double $700 at a %14 interest rate.
700•.14=98
98 divided into 700= 7.14

3 0

3 years ago

Can I get help with this???

exis [7]

5x + 13 + 3x + 7 = 180

8x +20 = 180

8x = 160

x = 20

7 0

3 years ago

The distance a vehicle travels can be found by using the formula d = rt, where d is the total distance traveled, r is the rate o

stellarik [79]

Answer:

She spends 2 hours driving.

Step-by-step explanation:

The formula given is:

$d = rt$

In which d is the distance traveled, r is the rate of speed, and t is the amount of time spent traveling.

Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour.

This means that $d = 80, r = 50$

To the nearest hour, how many hours does she spend driving?

We have to find t. So

$d = rt$

$50t = 80$

$t = \frac{80}{50}$

$t = 1.6$

Rounding to the nearest hour

She spends 2 hours driving.

4 0

4 years ago

A complex number, represented by z = x + iy, may also be visualized as a 2 by 2 matrix

Marat540 [252]

Answer:

Step-by-step explanation:

A) Suppose that we have the complex numbers

$z= x + iy \quad \text{and} \quad \\\\ \tilde{z}=\tilde{x} + i \tilde{y}$

Remember that to sum complex numbers, we sum the real parts of the two numbers to get the real part and the imaginary parts of the two numbers to get the imaginary part. Hence,

$z+\tilde{z} = (x + i y) + (\tilde{x} + i \tilde{y}) = (x + \tilde{x})+i (y+\tilde{y})$

On the other hand, if we sum the matrix visualizations of $z \quad \text{and} \quad \tilde{z}$ we get

$\left[\begin{array}{cc}x &y\\-y&x\end{array}\right] + \left[\begin{array}{cc}\tilde{x}&\tilde{y}\\ -\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x + \tilde{x}& y + \tilde{y}\\-(y+\tilde{y})&x+\tilde{x}\end{array}\right]$

which is the matrix visualization of $z + \tilde{z}$ .

To multiply two complex numbers, we use the distributive law to multiplly and then separete the real part from the imaginary part

$z \cdot \tilde{z}= (x + iy) \cdot (\tilde{x} + i \tilde{y})=(x \tilde{x} + i x \tilde{y} + i \tilde{x} y - y\tilde{y} ) = (x\tilde{x}-y\yilde{y})+i(x\tilde{y}+\tilde{x}y)$

Again, if we multiply the matrix visualizations of $z \quad \text{and} \quad \tilde{z}$ we get

$\left[\begin{array}{cc}x&y\\-y&x\end{array}\right]\left[\begin{array}{cc}\tilde{x}&\tilde{y}\\-\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x\tilde{x}-y\tilde{y}&x\tilde{y}+y\tilde{x}\\-y\tilde{x}-x\tilde{y}&x\tilde{x}-y\tilde{y}\end{array}\right]$

which is the matrix viasualization of $z\cdot\tilde{z}.$

B) Since the usual matrix operations are consisten with the usual addition and multiplication rules in the complex numbers, we can use them to find the multiplicative inverses of a complex number $z=x+iy$ .

We are looking for the complex number $z^{-1}=(x+iy)^{-1}$ which in terms of matrices is equivalent to find the matrix

$\left[\begin{array}{cc}x&y\\-y & x\end{array}\right]^{-1}= \dfrac{1}{x^{2}+y^{2}} \left[\begin{array}{ccc}x&-y\\y&x\end{array}\right]$

Hence,

$z^{-1}=\dfrac{1}{x^2 +y^2} (x-iy)=\dfrac{1}{|z|^2}(x-iy)$

6 0

3 years ago