PLEASE HELP (30 POINTS)

Please help me with this AP Calculus question!!

Temka [501]

9514 1404 393

Answer:

B. 3

Step-by-step explanation:

If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.

dy/dx = 3 at x = 4

__

The derivative of the expression can be found from the quotient formula:

d(u/v) = (du·v -u·dv)/v²

y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2

= (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2

= (x^2 -4x +12)/(x -2)^2

= ((x -4)x +12)/(x -2)^2

Then for x=4, we have ...

y' = 12/4 = 3

dy/dx = 3 at x = 4

7 0

3 years ago

The pyramid shown has a square base that is 12 centimeters on each side. The slant height is 18 centimeters. What is the surface

iogann1982 [59]

A = 576 cm2 hope that helps ;)

8 0

3 years ago

Read 2 more answers

Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

3 years ago

Janet drove 300 miles in 4.5 hours. Write and equation to find the rate at which she was traveling.

Kobotan [32]

If you would like to know the rate at which she was travelling, you can calculate this using the following steps:300 miles ... 4.5 hoursx miles = ? ... 1 hour300 * 1 = 4.5 * x300 = 4.5 * xx = 300 / 4.5x = 200 / 3x = 66.67 miles per hour Janet was travelling at the rate 66.67 miles per hour.

Read more on Brainly.com - brainly.com/question/1927497#readmore

7 0

3 years ago

How many times will the digit "3" appear if we write all whole numbers from 1-9999?

Marysya12 [62]

Answer:

4000

Step-by-step explanation:

from 1 - 1000 = 300

1's = 100

10's = 100

100's = 100

1000's = 0

300 * 10 = 3000

then add in all the 3000's (ie 3001,3002, etc ) that adds one more thousand

3000 + 1000 = 4000

5 0

3 years ago