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1 year ago

Simplify the following expression into the form a + bi, where a and b are rational numbers.

2 answers:

7 0

The answer is -16 - 10i.

Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²

Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i

Artyom0805 [142]1 year ago

3 0

Answer:

The simplified value of the given expression is -16-10i.

Step-by-step explanation:

The given expression is

$-2i(7-4i)+(3+i)(-2+2i)$

We need to convert the expression into the form a + bi, where a and b are rational numbers.

Using distributive property we get

$-2i(7)-2i(-4i)+3(-2+2i)+i(-2+2i)$

$-14i+8i^2+3(-2)+3(2i)+i(-2)+i(2i)$

$-14i+8i^2-6+6i-2i+2i^2$

Combine like terms.

$10i^2-10i+6$

Substitute $i^2=-1$ ,

$10(-1)-10i-6$

$-10-10i-6$

Combine like terms.

$-16-10i$

Therefore the simplified value of the given expression is -16-10i.

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A police helicopter is flying at 150 mph at a constant altitude of 0.5 mile above a straight road. The pilot uses radar to deter

natali 33 [55]

Answer:

a) (see attached picture)

b) d, h, velocity of helicopter, dd/dt

in the direction oposite to the movement of the helicopter.

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram that will represent the situation (see attached picture). As you may see, there is a right triangle being formed by the helicopter, the car and the graound. We can use this to build the equation we are going to use to model the problem.

$d^{2}=h^{2}+x^{2}$

we can use this equation to find the value of x at that very time, so we can do that by solving the equation for x, so we get:

$x=\sqrt{d^{2}-h^{2}}$

and substitute the given values:

$x=\sqrt{(1)^{2}-(0.5)^{2}}$

which yields:

x=0.866mi

we know that the height of the helicopter is going to be constant, so we rewrite the equation as:

$d^{2}=(0.5)^{2}+x^{2}$

$d^{2}=0.25+x^{2}$

Next, we can go ahead and differentiate the equation so we get:

$2d\frac{dd}{dt}=2x\frac{dx}{dt}$

which can be simplified to:

$d\frac{dd}{dt}=x\frac{dx}{dt}$

we can next solve the equation for dx/dt so we get:

$\frac{dx}{dt}=\frac{d}{x}*\frac{dd}{dt}$

so we can now substitue te provided values so we get:

$\frac{dx}{dt}=\frac{1}{0.866}*-190$

so we get:

$\frac{dx}{dt}=-219.40mph$

the negative sign means that the x-value is decreasing.

now, this problem deals with relative velocities, so we get that:

Velocity of car about the helicopter = Velocity of the car - Velocity of the helicopter. Or:

$V_{ch}=V_{c}-V_{h}$

so we can solve this for the actual velocity of the car, so we get:

$V_{c}=V_{ch}+V_{h}$

so we get:

$V_{c}=-219.40mph+150mph$

which yields:

$V_{c}=-69.4mph$

So it has a velocity of 69.4mph in a direction oposite to the helicopter's movement.

4 0

1 year ago

WILL GIVE BRAINLIEST!!!

timofeeve [1]

Answer:

$y=448-28x$

Step-by-step explanation:

Let x be the number of miles.

We have been given that Sully's car has an average fuel economy of 28 miles per gallon. The capacity of the fuel tank is 16 gallons.

Let us find the number of miles that Sully can drive with 16 gallons.

$\text{Number of miles Sully can drive}=\text{16 gallons}\times \frac{\text{28 miles}}{\text{gallon}}$

$\text{Number of miles Sully can drive}=\text{16}\times \text{28 miles}$

$\text{Number of miles Sully can drive}=448\text{ miles}$

This means that initially Sully's car has can drive 448 miles, so at x equals 0, y will be 448.

As the car consumes 1 gallon for each 28 miles driven, so the gallons of fuel consumed in traveling x miles will be 28x. As each gallon of fuel will decrease with each 28 miles traveled, so slope of our function will be -28.

Upon substituting slope and y-intercept in slope-intercept form (y=mx+b), we will get our function as:

$y=448-28x$

Therefore, our required function will be: $y=448-28x$ .

4 0

1 year ago

Read 2 more answers

Five friends bake ginger bread and subsequently meet up for a tasting session. Each one gives one of his ginger

GenaCL600 [577]

Answer:

The five friends had 10 fingers to start with; one had two each

Step-by-step explanation:

The statement says each gave one of not all of his ginger in the toasting session.

4 0

1 year ago

Alicia borrowed $15,000 to buy a car. She borrowed the money at 8% for 6 years. What is the interest she will pay for the loan ?

kykrilka [37]

The interest rate she would pay would be is $7,200

5 0

1 year ago

Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the rig

Serga [27]

Answer:

1.4in

Step-by-step explanation:

Length of Photo = 4in

Width of Photo = 3in

Unknown:

Value of X = ?

Solution:

Follow these steps:

Area of a rectangle = l x w

Since the photo is a rectangle; area of photo:

Area of photo = 4in x 3in = 12in²

For the area of the ad;

Length of ad = 4 + x

Width of ad = 3 + x

Given that,

the area of the photo = $\frac{1}{2}$ area of ad

12in² = $\frac{1}{2}$ area of ad

Area of ad = 24in²

Area of the ad;

(4 + x) (3 + x) = 24

12 + 4x + 3x + x² = 24

12 + 7x + x² = 24

x² + 7x = 24 - 12

x² + 7x = 12

x² + 7x - 12 = 0

Using the almighty formula where

a = 1, b = 7 and c = -12

x = $\frac{-b (+/-) \sqrt{b^{2} } - 4ac}{2a}$

x = $\frac{-7 + \sqrt[]{-7^{2} - 4x1x-12 } }{2x1}$ or $\frac{-7 - \sqrt[]{-7^{2} - 4x1x-12 } }{2x1}$

x = 1.4 or -8.4

therefore the answer is 1.4in

x is 1.4in

4 0

1 year ago