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3 years ago

the tangent line to the curve y=x^3-6x^2-34x-9 has slope 2 at two points on the curve. find the two points

1 answer:

7 0

$\bf y=x^3-6x^2-34x-9\implies \cfrac{dy}{dx}=3x^2-12x-34
\\\\\\
\stackrel{\textit{slope of 2}}{2}=3x^2-12x-34\implies 0=3x^2-12x-36
\\\\\\
0=x^2-4x-12\implies 0=(x-6)(x+2)\implies x=
\begin{cases}
6\\
-2
\end{cases}\\\\
-------------------------------\\\\
\stackrel{y}{f(6)}=(6)^3-6(6)^2-34(6)-9\implies f(6)=-213\\\\\\ (\stackrel{x}{6}~,~\stackrel{y}{-213})
\\\\\\
\stackrel{y}{f(-2)}=(-2)^3-6(-2)^2-34(-2)-9\implies f(-2)=27\\\\\\ (\stackrel{x}{-2}~,~\stackrel{y}{27})$

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PtichkaEL [24]

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a silkworm winds its cocoon out of one long silk fiber. to make silk thread, 3 to 10 of these silk fibers are unwound from their

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Answer:

Possible lengths of the silk fibre 'x' are 100, 75, 60, 50 and 30 yards respectively.

Step-by-step explanation:

Let the length of the silk fiber = x yards.

Let the number of silk fibres = a.

It is given that the silk fibers between 3 to 10 yards are combined to form a silk thread of 300 yards.

So, we get the equation,

$ax=300$ , where $3\leq a\leq 10$

i.e. $x=\frac{300}{a}$ , $3\leq a\leq 10$

So, the possible values of 'a' are 3, 4, 5, 6 an 10.

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3 years ago

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3 years ago

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At smith lake boat rentals it costs $25 per hour to rent a boat plus one time charge for cleaning. The bengal family rented a bo

vesna_86 [32]

Answer: the Jones family paid $164

Step-by-step explanation:

Let x represent the one time charge that smith lake boat rentals charge for cleaning.

The bengal family rented a boat from 11 am- 6:30pm and paid $226.50. This means that the number of hours for which they rented the boat is

11 - 6:30/= 7.5 hours

Therefore,

25 × 7.5 + x = 226.5

187.5 + x = 226.5

x = 226.5 - 187.5

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If the jones family rented a boat from 8am-1pm, the number of hours would be 5 hours.

The amount that they paid is

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3 years ago

Jocelyn is training for a race by running several miles each day. she tracks her progress by recording her average speed in minu

Luden [163]

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To find the equation, we need to insert the points (x,y) in the calculator.

Researching the problem on the internet, the values of x and y are given as follows:

Values of x: 1, 2, 3, 4, 5, 6.

Values of y: 8.2, 8.1, 7.5, 7.8, 7.4, 7.5.

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More can be learned about regression equations at brainly.com/question/25987747

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