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3 years ago

Express the complex number z = -4+3i in polar form: r(cos⁡(θ)+i sin(θ)).

Mathematics

1 answer:

kirill [66]3 years ago

8 0

Answer:

5( cos(- 0.64)+ $i$ sin(-0.64))

Step-by-step explanation:

Given:

z = -4+3i

$r=\sqrt{(-4)^2+3^2}= 5$

θ= $tan^-^1(\frac{3}{-4} ) = -0.64$

Polar form=r(cosθ+ $i$ sinθ)=> 5( cos(- 0.64)+ $i$ sin(-0.64))

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

Timothy is filling fish bowls with pebbles at his fish store. He wants to have $\frac{1}{6}$ of a pound of pebbles in each fish

Luba_88 [7]

Answer:

Step-by-step explanation:

Given that:

Each fish bowl to have pebbles of weight equivalent to = $\frac{1}{6}$

Total pounds of pebbles that Timothy can use = $2\frac{1}{3}$

To find:

The greatest value of Total number of fish bowls that Timothy can fill ?

Solution:

First of all, we need to convert mixed fraction into a fractional number and then we also need to see division of two fractions.

Formula:

$1. \ p\dfrac{q}{r} = \dfrac{p\times r+q}{r}\\2. \ \dfrac{\frac{a}{b}}{\frac{c}d}=\dfrac{a\times d}{b\times c}$

Now, the given mixed fraction can be converted to fractional number as:

$2\dfrac{1}{3} = \dfrac{2\times 3+1}{3} = \dfrac{7}{3}$

Now, To find the total number of fish bowls that can be filled, we need to divide the total number of pounds with number of pounds of pebbles in each fish bowl.

So, the answer is:

$\dfrac{\frac{7}{3}}{\frac{1}{6}}\\\Rightarrow \dfrac{7\times 6}{3\times 1}\\\Rightarrow \dfrac{42}{3}\\\Rightarrow \bold{14}$

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3 years ago

Please help. I don't understand it. HELP ASAP....

Vladimir [108]

Answer:

$\large\boxed{x\leq-27}$

Step-by-step explanation:

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3 years ago

Which statement is true about the end behavior of the graphed function?

tatyana61 [14]

The correct answer is:

A) as the x-values go to positive infinity, the functions values go to negative infinity.

Explanation:

We can see in the graph that the right hand portion continues downward to negative infinity. The right hand side of the graph is "as x approaches positive infinity," since x continues to grow larger and larger. This means as x approaches positive infinity, the value of the function approaches negative infinity.

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3 years ago

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