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3 years ago

Which complex number has an absolute value of 5? –3 + 4i 2 + 3i 7 – 2i 9 + 4

Mathematics

1 answer:

Ugo [173]3 years ago

4 0

Answer:

Step-by-step explanation:

-3 + 4i

value = square( (-3)^2 + (4i)^2 ) = sqr(9 + 16) = sqr(25) = 5

The absolute value is like the Pythagoras theorem

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Yuri [45]

Answer:

Step-by-step explanation:

8 0

3 years ago

An investment of $8,000 earns interest at an annual rate of 7% compounded continuously. Complete parts (A) and (B) below. Click

Sergeeva-Olga [200]

Answer:

A. $\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}$

B. $\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }$

Step-by-step explanation:

Given that:

An investment of Amount = $8000

earns at an annual rate of interest = 7% = 0.07 compounded continuously

The objective is to :

A) Find the instantaneous rate of change of the amount in the account after 2 year(s).

we all know that:

$A = Pe^{rt}$

where;

$A = (8000) \ e ^{0.7t}$

The instantaneous rate of change = $\dfrac{dA}{dt}$

$\dfrac{dA}{dt} = \dfrac{d}{dt}(8000 \ e ^{0.07t} )$

$= 8000 \dfrac{d}{dt}e^{0.07 \ t}$

$\dfrac{dA}{dt}= 8000 (0.07)e^{0.07 \ t}$

$\dfrac{dA}{dt}= 560 e^{0.07 \ t}$

At t = 2 years; the instantaneous rate of change is:

$\dfrac{dA}{dt}|_{t=2}= 560 e^{0.07 \times 2}$

$\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}$

(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000.

Here the amount = 12000

$12000 = (8000)e^{0.07 \ t}$

$\dfrac{12000 }{8000}= e^{0.07 \ t}$

$1.5= e^{0.07 \ t}$

㏑(1.5) = 0.07 t

0.405465 = 0.07 t

t = 0.405465 /0.07

t = 5.79

$\dfrac{dA}{dt}= 560 e^{0.07 \ t}$

At t = 5.79

$\dfrac{dA}{dt}|_{t = 5.79}= 560 e^{0.07 \times 5.79}$

$\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }$

7 0

3 years ago

2. Find tan A for the right triangle below:

Andreyy89

Answer:

$tan A=\frac{8}{15}$

Step-by-step explanation:

According to the trigonometric ratios the tangent of an angle is the ratio of perpendicular to base, i.e.

$tan\theta=\frac{Perpendicular}{Base}$

In the provided triangle the perpendicular is 8 and base is 15.

Compute value of tan <em>A</em> as follows:

$tan\theta=\frac{Perpendicular}{Base}\\tanA=\frac{8}{15}\\$

Thus, the value of tan <em>A</em> is $\frac{8}{15}$ .

8 0

3 years ago

Will give Brainly if you solve 4

aivan3 [116]

Answer:

Step-by-step explanation:

it will be criss cross

8 0

3 years ago

Read 2 more answers

In a sample of 1000 adults, 150 said they are very confident in the nutritional information on restaurant menus. for us adults a

lions [1.4K]

There are 150 confident adults out of 1000.
Selecting four at random withOUT replacement
Probability that all four are confident
=(150/100*149/999*148/997*147/996)
=150!/146! / (1000!/996!)
= 7301/14925090
= 0.00048918

(check: answer < (150/1000)^4=0.00050625, ok)

6 0

3 years ago