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3 years ago

Consider the parabola y = 6x − x2.

Mathematics

1 answer:

Assoli18 [71]3 years ago

8 0

Given expression is

$y= 6x -x^2$

And we have to find the slope of the tangent line at the point (1,5), and for that, first we find the derivative of the given expression, which is

$dy/dx = 6-2x$

And the derivative is the slope. And to find the slope at point (1,5), we put 1 for x in the expression of derivative, that is

$dy/dx = 6-2(1) = 4$

Hence, the slope of the tangent line to the parabola at the point (1, 5) is 4.

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A construction crew has just finished building a road. the road is 8 kilometers long. if the crew worked for 335 days, how many

elena-s [515]

8/335 km/day
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3 years ago

In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

4 0

3 years ago

Please help ASAP 25 pts + brainliest to right/best answer

Dmitry [639]

Answer:

Your answer is B

Step-by-step explanation:

The inverse is the opposite of something. Since the inverse of 1/3x is 3x, then we know that we have the multiply the equation by 3. Doing this results in 3x-15, or y=3(x-5)

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4 years ago

Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if

enyata [817]

Answer:

cosC = $\frac{7}{25}$

Step-by-step explanation:

cosC = $\frac{adjacent}{hypotenuse}$ = $\frac{BC}{AB}$ = $\frac{7}{25}$

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3 years ago

The sales tax rate is 5%. if the sales tax on 10-speed car is $6 what is the purchase price?

True [87]

Since the sales tax is 5% of the purchase price, we can just multiply it by $20 to get $120, the purchase price.
To get the total price, all we do is add $6 to $120, which is $126, the total price.

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3 years ago