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2 years ago

Find the derivative of x^2+6x+9 at the point (2,6).

1 answer:

4 0

The derivative of the function is 2x+6.
At the particular point (2,6), plug in the x coordinate for x.
2(2)+6 = 10

Hope this helps :)

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Mistery number . CLUES: -it has the digits 8,5 and 6 . - it is a odd number . - it has 8 in the hundreds place . WHAT IS THE MIS

Ipatiy [6.2K]

With digits 8, 5, and 6, an odd number must end in 5.
So far, we have _ _ 5.
The 8 is in the hundreds place.
Now we have 8_5.
The only place left for the 6 is the tens place.
The number is 865.

6 0

2 years ago

You want $5000 4 years from nowfor a down payment for a car. How much money must be deposited monetly into an account earning 4.

timama [110]

Answer:

$95.5090 must be deposited monthly

Step-by-step explanation:

From the information given:

The annual interest rate (r) = 4.2% = 0.042

Let assume that an amount Y is deposited, then after one month, it will increase to:

$Y ( 1+ \dfrac{0.042}{12})$

The total amount after 4 years will be:

$= Y ( 1+ \dfrac{0.042}{12})^{48}+Y ( 1+ \dfrac{0.042}{12})^{47} +Y ( 1+ \dfrac{0.042}{12})^{46} +...+ Y ( 1+ \dfrac{0.042}{12})$

$= Y ( 1.0035)^{48}+Y ( 1.0035)^{47} +Y( 1.0035)^{46} +...+ Y( 1.0035)$

Using the sum of a geometric progression:

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{(1.0035-1)}$

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{0.0035}$

The above amount is then equal to $5000

i.e

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{0.0035} = 5000$

$Y = \dfrac{5000\times 0.0035}{(1.0035)(1.0035^{48}-1)} \\ \\ \mathbf{Y = \$95.5090}$

8 0

2 years ago

Questions (no partial grades if you don't show your work) 1. In a group of 6 boys and 4 girls, four children are to be selected.

mariarad [96]

Answer:

Total number of ways will be 209

Step-by-step explanation:

There are 6 boys and 4 girls in a group and 4 children are to be selected.

We have to find the number of ways that 4 children can be selected if at least one boy must be in the group of 4.

So the groups can be arranged as

(1 Boy + 3 girls), (2 Boy + 2 girls), (3 Boys + 1 girl), (4 boys)

Now we will find the combinations in which these arrangements can be done.

1 Boy and 3 girls = $^{6}C_{1}\times^{4}C_{3}=6\times4$ =24

2 Boy and 2 girls= $^{6}C_{2}\times^{4}C_{2}=\frac{6!}{4!\times2!}\times\frac{4!}{2!\times2!}=15\times6=90$

3 Boys and 1 girl = $^{6}C_{3}\times^{4}C_{1}=\frac{6!}{4!\times2!}\times\frac{4!}{3!}=\frac{6\times5\times4}{3 \times2} \times4=80$

4 Boys = $^{6}C_{4}=\frac{6!}{4!\times2!} =\frac{6\times 5}{2\times1}=15$

Now total number of ways = 24 + 90 + 80 + 15 = 209

7 0

2 years ago

Simplify the next two expressions

prisoha [69]

1. 7x-40
2. 8x-30y-10

4 0

2 years ago

Raoul has to finish a 473-page book in a week. He decides to read the same number of pages each weekday and 30 extra pages on Sa

hodyreva [135]

Answer:

$59$ pages

Step-by-step explanation:

Variable:

x = number of pages he has to read on a weekday

x + 30 = The number of pages read on Saturday and Sunday

$5x+2(x+30) = 473$

$==> 5x + 2x + 60 = 473$

$==> 7x =413$

$==> x = 59$

Meaning that Raoul has to read 59 pages on Wednesday

6 0

2 years ago