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oksano4ka [1.4K]
3 years ago
15

6. f(x) = x ^ 2 + 2x g(x) = 3x ^ 2 - 1

Mathematics
1 answer:
AVprozaik [17]3 years ago
7 0

Answer:

3x^2+1

Step-by-step explanation:

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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
sashaice [31]

Answer:

f(x) = x^3  -sinx +Cx+D

Step-by-step explanation:

Given that:

f ''(x)= 6x +sinx

We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.

We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C

\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx  + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\

Now, integrating it again to find f(x):

f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx  -\int{cosx} \, dx  +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3}  -sinx +Cx+D\\\Rightarrow x^3  -sinx +Cx+D\\\\\therefore f(x) = x^3  -sinx +Cx+D

5 0
4 years ago
Find the point on the line y = 4x + 3 that is closest to the origin.
umka21 [38]
That point will be where the perpendicular line through the origin intersects the given line.
.. (-1/4)x = 4x +3
.. -3 = (17/4)x
.. -12/17 = x

The point on the given line that is closest to the origin is (-12/17, 3/17).

4 0
3 years ago
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.19 a p
SSSSS [86.1K]

Answer:

Yes, it is worth the extra drive, going to the further store is cheaper.

The cheaper option saves you $0.89.


Step-by-step explanation:

1.) Neighborhood store

It is 2.4 miles away

The car averages about 25 miles per gallon, then you would need:

2.4 miles / (25 miles/gallon) = 0.096 gallons of gas < 13 gallons (Ok)

The gas is about $3.89/gallon, then the gas would cost:

0.096 gallons * ($3.89/gallon) = $0.37344 = $0.37

The chicken is sold for $3.49 a pound, and you need 6 pounds, then you would pay:

6 pounds * ($3.49/pound) = $20.94

In total you would need:

$0.37 (gas) + $20.94 (chiken) = $21.31 if you buy the chicken in the neiborhood store

2.) Store acroos town

It is 8.2 miles away

The car averages about 25 miles per gallon, then you would need:

8.2 miles / (25 miles/gallon) = 0.328 gallons of gas < 13 gallons (Ok)

The gas is about $3.89/gallon, then the gas would cost:

0.328 gallons * ($3.89/gallon) = $1.27592 = $1.28

The chicken is sold for $3.19 a pound, and you need 6 pounds, then you would pay:

6 pounds * ($3.19/pound) = $19.14

In total you would need:

$1.28 (gas) + $19.14 (chiken) = $20.42 if you buy the chicken in the store across town


$20.42 < $21.31, then it is worth the extra drive, going to the further store is cheaper.

The cheaper option saves you: $21.31-$20.42=$0.89


8 0
3 years ago
Hi, I need help. The sheet is homework. If you help, thank you
Paul [167]

Answer:

1.  Solution

2.  Distributive Property

3.  Multiplying

4.  Area model

5.  Properties of equality

6.  Expanded form

Step-by-step explanation:

Hope this helps!

sorry if I got any wrong one

7 0
3 years ago
Read 2 more answers
What is 14% of $59.99 and how do I figure this problem?
serious [3.7K]
Is/of =%/100 so x/59.99=14%/100 Cross multiply to get the answe
4 0
3 years ago
Read 2 more answers
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