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Sholpan [36]
3 years ago
14

If -10x – 9y = -7 is a true equation, what would be the value of -30x – 27y?

Mathematics
1 answer:
Tpy6a [65]3 years ago
8 0

Answer:

-30x-27y = -21

Step-by-step explanation:

We know that;

-30x-27y = 3(-10x-9y)

Recall, -10x-9y = -7

Thus; -30x-27y = 3(-7) = -21

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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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A major baseball diamond is a square with side lengths of 90 feet.
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Answer: \bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}

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Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square.  Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

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