All categories

2 years ago

The complex number -5i has the complex trigonometric form of 5(cos 270° + isin 270)

Mathematics

1 answer:

Verizon [17]2 years ago

5 0

Answer:

True , -5i = 5*(0 - i) = 5*( cos 3π/2 + i*sin 3π/2) = 5*(cos 270 + i*sin 270)

Step-by-step explanation:

5*( cos 3π/2 radians + i*sin 3π/2 radians) = 5*(cos 270 degrees + i*sin 270 degrees)

You might be interested in

HELP WILL GIVE BRAINLIEST

lianna [129]

Answer:

Tank A is filling faster

Step-by-step explanation:

On the graph, You can see that the line of tank A is rising far faster than tank B.

8 0

2 years ago

Read 2 more answers

The lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1 hour. There

KIM [24]

Answer:

If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1

Sample size = 4

Total lifetime of 4 batteries = 40 hours

We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling:

$\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1}{\sqrt4} = 0.5$

We have to find the value of x such that the probability is 0.05

P(X > x) = 0.05

$P( X > x) = P( z > \displaystyle\frac{x - 40}{0.5})=0.05$

$= 1 -P( z \leq \displaystyle\frac{x - 40}{0.5})=0.05$

$=P( z \leq \displaystyle\frac{x - 40}{0.5})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 40}{0.5} = 1.64\\x = 40.825 \approx 40.83$

Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

8 0

3 years ago

△EFG≅△JKL.<br><br> What is m∠L?

snow_lady [41]

M∠E ≅ m∠J
m∠F ≅ m∠K
m∠G ≅ m∠L

So, m∠ L is 58.

4 0

2 years ago

Read 2 more answers

Using the given information, give the vertex form equation of each parabola.

Amanda [17]

Answer:

The equation of parabola is given by : $(x-4) = \frac{-1}{3}(y+3)^{2}$

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:( $\frac{47}{12}$ ,-3)

The general equation of parabola is given by.

$(x-h)^{2} = 4p(y-k)$ , When x-componet of focus and Vertex is same

$(x-h) = 4p(y-k)^{2}$ , When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

For value of p:

p= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

p= $\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}$

p= $\sqrt{(\frac{1}{12})^{2}}$

p= $\frac{1}{12}$ and p= $\frac{-1}{12}$

Since, Focus is left side of the vertex,

p= $\frac{-1}{12}$ is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p= $\frac{-1}{12}$

$(x-h) = 4p(y-k)^{2}$

$(x-4) = 4(\frac{-1}{12})(y+3)^{2}$

$(x-4) = \frac{-1}{3}(y+3)^{2}$

8 0

2 years ago

"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."

Marizza181 [45]

An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.

Basing from the graph, we can actually see that the interval is:

10 <span>Fahrenheit degrees</span>

6 0

2 years ago