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serious [3.7K]
3 years ago
9

HELP PLEASE URGENT!!!!

Mathematics
1 answer:
loris [4]3 years ago
4 0
<span>Equations:
g + b + 0 = 1500
g + 0 + r = 750
g + b + r = 2000
============
</span><span>g = 250
b = 1250
r = 500
============
Happy Valentines :)</span>
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Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)
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Answer:

f(x)=\frac9{x+1}\\ f'(x)=-\frac9{(x+1)^2}\\ f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\\ |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\\ x_1=2\ \vee\ x_2=-4\\ f(x_1)=f(2)=\frac9{2+1}=3\\ f(x_2)=f(-4)=\frac9{-4+1}=-3

First tangent line:

y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5

Second tangent line:

y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7


Notice: slope of -1 means that both f'(x_1), \ f'(x_2) are equal to -1, so f'(x_1)=-1 \ and \ f'(x_2)=-1


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Which of the following is not a factor of x^3 – 3x^2 – 4x + 12?
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Answer:

c. (x + 3)

Step-by-step explanation:

using factor theorem

if x - 3 is a factor then p(a) = 0

p(a)= x^3 - 3x^2 - 4x + 12

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p(3) = (3)^3 - 3(3)^2 - 4(3) + 12

= 27 - 27 - 12 + 12

= 0

therefore x-3 is a factor

b.(x + 2)

p(-2) = (-2)^3 - 3(-2)^2 - 4(-2) + 12

= -8 -12 + 8 + 12

,= 0

therefore x + 2 is a factor

c.(x + 3)

p(-3) = (-3)^3 - 3(-3)^2 - 4(-3) + 12

= -27 -27 + 12 + 12

= -30

therefore x + 3 is not a factor

d.(x-2)

p(2) = (2)^3 - 3(2)^2 - 4(2) + 12

= 8 -12 - 8 + 12

= 0

therefore x - 2 is a factor

4 0
3 years ago
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