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4 years ago

What is the value of (7 + 2i)(3 - i)?

1 answer:

7 0

There are two ways to work this out: normal variables or using "imaginary" numbers.

Normal variables:
$(7+2i)(3-i)\\(7*3)+[7*(-i)]+(3*2i)+[2i*(-i)]\\21-7i+6i-2i^{2}\\\\21-i-2i^{2}$

Imaginary numbers:
Using the result from earlier:
$21-i-2i^{2}$
Now since $i = \sqrt{-1}$ , then the expression becomes:
$21-i-2i^{2}\\21-i-2(\sqrt{-1})^{2}\\21-i+(-2)(-1)\\21-i+2\\\\23-i$

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Element X is a radioactive isotope such that every 81 years, its mass decreases by half. Given that the initial mass of a sample

jasenka [17]

Answer:

15?

Step-by-step explanation:

3 0

3 years ago

Which of the sets of ordered pairs represents a function?

iogann1982 [59]

(x,y)
if x repeats with a differnt y then it is not a function

A. none of them repeat, it's a function
B. none of them repeat, it's a function

both of them are functions

5 0

3 years ago

write equation that has base of 3 stretched vertically by factor of 2/3 reflected in y axis, asymptote of y=2 and passes through

madam [21]

The exponential equation is $y = \frac23(3)^{-x+0.74} + 2$

<h3>How to determine the equation?</h3>

An exponential function is represented as:

$y = b^x$

The base is 3.

So, we have:

$y = 3^x$

It is stretched vertically by 2/3.

So, we have:

$y = \frac23(3)^x$

When reflected over the y-axis, we have:

$y = \frac23(3)^{-x}$

An asymptote of y = 2, makes the function becomes

$y = \frac23(3)^{-x} + 2$

Lastly, it passes through the point (0, 3.5).

So, we have:

$y = \frac23(3)^{-x+h} + 2$

This gives

$3.5 = \frac23(3)^{-0+h} + 2$

$3.5 = \frac23(3)^{h} + 2$

Subtract 2 from both sides

$1.5 = \frac23(3)^{h}$

Multiply by 3/2

$2.25 = (3)^{h}$

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in $y = \frac23(3)^{-x+h} + 2$

$y = \frac23(3)^{-x+0.74} + 2$

Hence, the exponential equation is $y = \frac23(3)^{-x+0.74} + 2$

Read more about exponential equation at

brainly.com/question/23729449

#SPJ1

3 0

2 years ago

The function y=−16x2+36 represents the height y (in feet) of an apple x seconds after falling from a tree. Find and interpret th

Lapatulllka [165]

Answer:

A. x-intercept=x=1.5 , y-intercept=y=36

B.the apple will hit the ground after x=1.5 seconds.

Step-by-step explanation:

A. X-intercept and Y-intercept:

X-intercept:

the point where the line passes through X-axis i.e. point where y=0

Y-intercept:

the point where the line passes through Y-axis i.e. point where x=0

Given Equation:

$y=-16x^2+36$

Finding X-intercept:

to find x-intercept, put y=0 in the given equation as

$0=-16x^2+36\\$

adding $-16x^2$ to both sides of the equation, we get

$16x^2=36$

dividing both sides by 16, we get

$x^2=\frac{36}{16}\\x^2=2.25$

taking√ on both sides of the equation, we get

$x=\sqrt{2.25}\\ x=1.5$

Finding Y-intercept:

to find y-intercept, put x=0 in the given equation

$y=-16(0)^2+36\\y=36$

thus x-intercept $=x=1.5$

and y-intercept $=y=36$

B.when will the apple hit the ground after x seconds?

In the given equation if x represent the time in seconds then y represents the height of the tree from which the apple is fallen down

so if the apple hits the ground, at this stage the height is zero so y=0, thus we get x as

$0=-16x^2+36\\$

dividing both sides by 16, we get

$x^2=\frac{36}{16}\\x^2=2.25$

taking√ on both sides of the equation, we get

$x=\sqrt{2.25}\\ x=1.5$

the apple will hit the ground after x=1.5 seconds.

8 0

3 years ago

Joshua spends 25 minutes of each day reading. He reads d days a week. Let m represent the number total minutes of reading a week

Rasek [7]

Answer:

25 x D = Y

Step-by-step explanation:

Example: Say he reads for three days a week.

25 x 3 = 75

or 6 days

25 x 6 = 150

or 4

25 x 4 = 100

4 0

3 years ago