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Alika [10]
3 years ago
13

Find the zeros of each function. State the multiplicity of any multiple zeros. (Please show work)

Mathematics
1 answer:
Charra [1.4K]3 years ago
6 0
QUESTION 16

The given function is,

y = 3x {(x + 2)}^{3}

To find the zeroes of this function, we equate the function to zero to get,

3x {(x + 2)}^{3} = 0

We now apply the zero product principle to get,

3x = 0 \: or \: {(x + 2)}^{3} = 0

The second factor is repeating 3 times, therefore the root has a multiplicity of 3.

This implies that,

x = 0 \: or \: x = - 2
-2 has a multiplicity of 3.

QUESTION 17.

The given expression is

{x}^{4} - 8 {x}^{2} + 16 = 0

({x}^{2}) ^{2} - 8 {x}^{2} + 16 = 0

This is now a quadratic equation in x².

We split the middle term to get,

({x}^{2}) ^{2} - 4 {x}^{2} - 4 {x}^{2} + 16 = 0

We now factor to obtain,

{x}^{2} ( {x}^{2} - 4) - 4( {x}^{2} - 4) = 0

This implies that,

( {x}^{2} - 4)( {x}^{2} - 4) = 0

( {x}^{2} - 2^2)( {x}^{2} - 2^2) = 0

We apply difference of two squares here to get,

(x - 2)(x + 2)(x - 2)(x + 2) = 0

This is the same as,

(x - 2) ^{2} (x + 2) ^{2} = 0

This time both roots have a multiplicity of 2.

Applying the zero product property, we obtain,

(x - 2) ^{2} = 0 \: or \: (x + 2) ^{2} = 0

This implies that,

x = 2 \: or \: - 2

with a multiplicity of 2 each.
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Answer:

the answer to this question is $2,350

Step-by-step explanation:

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6 0
2 years ago
12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
never [62]

Answer:

<em>Part a) </em>Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) </em>Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c)  </em>Domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) </em>Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

<em>Part a) Determining the domain of f </em>

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) Determining the domain of g</em>

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c) Determining the domain of f+g</em>

<em>When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.</em>

<em>As,</em>

<em>      </em>Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

      Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

      Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

       Domain of g : {-1, 0, 1, 2, 3, 4}

<em>As</em> when <em>there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains</em>

So, the domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) List the ordered pairs of f-g</em>

As

    f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

    g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1)  = 14 - 4 = 10

(f - g)(x) = f(0) - g(0)  = 7 - 5 = 2

(f - g)(x) = f(1) - g(1)  = 4 - 6 = -2

(f - g)(x) = f(2) - g(2)  = 5 - 1 = 4

(f - g)(x) = f(3) - g(3)  = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords:  domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

#learnwithBrainly

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carbon-14 has a half-life of 5730 years. The formula f(t)=(1/2)^t/5730 give the percentage of carbon-14 left in the item after t
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Find the equation of the line tangent to the function at the given point f(x)=5x^2 at x=10
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f(x) = 5x²

f(10) = 5(10)²  = 5(100)  = 500

f'(x) = 10x

f'(10) = 10(10)   = 100  

Now, find the line that passes through (10, 500) and has a slope of 100

y - y₁ = m(x - x₁)

y - 500 = 100(x - 10)

y - 500 = 100x - 1000

        y = 100x - 500

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