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2 years ago

Write -2i + (9 − 3i) − (6 − 10i) as a complex number in standard form.

Mathematics

2 answers:

vovikov84 [41]2 years ago

8 0

Answer:

5i+3

Step-by-step explanation:

Given the expression

-2i + (9 − 3i) − (6 − 10i)

Where i² = -1 (complex number rule)

Therefore,

-2i + 9-3i-6+10i

Collecting like terms gives

5i+3

Vika [28.1K]2 years ago

6 0

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Step-by-step explanation:

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2 years ago

A player shoots a basketball from a height of 6 feet. The equation, h = -16t^2 + 25t + 6, gives the height, h , of the basketbal

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Answer:

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Step-by-step explanation:

We are given this function for the height (h) after t seconds:

$h=-16t^2+25t+6$

Seconds is t and we want to find the height after 1.5 seconds. Plug 1.5 in for t.

$h= -16(1.5)^2+25(1.5)+6$

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve the exponent first.

(1.5)²= 1.5*1.5=2.25

$h= -16(2.25)+25(1.5)+6$

Multiply.

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$h= -36+37.5+6$

Add.

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This is already rounded to the nearest tenth, so it is the answer.

After 1.5 seconds, the basketball is at a height of 7.5 feet.

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2 years ago

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3 years ago

2. Ariana has created a paper airplane for her physics class at school where all the students will be testing their planes by se

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Answer:

2. The airplane will crash into the ground after 5 seconds.

3. The domain of the function is [0,30] and range of the function is $[-\infty,900]$ .

Step-by-step explanation:

Ariana initial attempt is modeled by the function,

$h(x)=x^2-12x+35$

where, h is the height in feet and x is the time in seconds of the paper airplanes path.

If airplane crash into the ground, then $h(x)=0$ ,

$0=x^2-12x+35$

$0=x^2-7x-5x+35$

$0=x(x-7)-5(x-7)$

$0=(x-7)(x-5)$

Equate each factor equal to 0.

$x=5,7$

Therefore the airplane will crash into the ground after 5 seconds.

The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.

$h(t)=-4t^2+120t$

The value of t must be positive because time can not be negative.

Find the zeros of the function.

$0=-4t(t-30)$

$t=0,30$

The leading coefficient is negative, so the it is a downward parabola. Since the zeros of the function are 0 and 30, therefore the function is negative before 0 and after 30.

The height can not be negative, so the domain of the function is

$0\leq t\leq 30$

The vertex of a downward parabola is the maximum point.

Vertex of a parabola,

$(\frac{-b}{2a},h(\frac{-b}{2a}))$

$(\frac{-120}{2(-4)},h(\frac{-120}{2(-4)}))$

$(15,h(15))$

Put t=15 it in the equation.

$h(15)=-4(15)^2+120(15)=900$

$(15,900)$

The range of the function is

$[-\infty,900]$

Therefore the domain of the function is [0,30] and range of the function is $[-\infty,900]$ .

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2 years ago