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Effectus [21]
3 years ago
15

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t^2 + cos(t) and v(0) = 2.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0
\bf \displaystyle a(t)=3t^2+cos(t)\implies \stackrel{velocity}{\int~ [3t^2+cos(t)]dt}\\\\\\ t^3+sin(t)+C=~~~v(t)
\\\\\\
\begin{cases}
v(0)=2\\
v=2\\
t=0
\end{cases}\implies 0^3+sin(0)+C=2\implies C=2
\\\\\\
\boxed{t^3+sin(t)+2=v(t)}
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Two different families pay for entry into a water park.
icang [17]

Answer:

Adult ticket: $7

Child ticket: $2

Step-by-step explanation:

Set up a system of equations where a represents the cost of one adult ticket and c is the cost of one child ticket:

2a + 3c = 20

a + 4c = 15

Solve by elimination by multiplying the bottom equation by -2:

2a + 3c = 20

-2a -8c = -30

Add them together:

-5c = -10

c = 2

Now, we can plug in 2 as c to find the value of a:

2a + 3c = 20

2a + 3(2) = 20

2a + 6 = 20

2a = 14

a = 7

6 0
3 years ago
5x−6=3x+10 PLSPLS HELP
vichka [17]

Answer:

x = 8

Step-by-step explanation:

Let's solve your equation step-by-step.

5x−6=3x+10

Step 1: Subtract 3x from both sides.

5x−6−3x=3x+10−3x

2x−6=10

Step 2: Add 6 to both sides.

2x−6+6=10+6

2x=16

Step 3: Divide both sides by 2.

2x /2 = 16/ 2

x=8

3 0
3 years ago
Read 2 more answers
Curtis plays a trivia game he earns 2 points for each correct answer and loses 0.25 points for each incorrect answer he get 21 c
Maslowich

Answer:

41

Step-by-step explanation:

Curtis is playing a trivia game.

Number of points earned for each correct answer = 2

Number of points lost for each correct answer = 0.25

Given that:

Number of correct answers given by Curtis = 21

Number of wrong answers given by Curtis = 4

To find:

Total score of the game by Curtis?

Solution:

First of all, let us find the points earned by correct answers.

Points earned by correct answers = Number of correct answers multiplied by Points earned on one correct answer.

Points earned by correct answers = 21 \times 2 = 42

Now, let us find the points to be lost by wrong answers.

Points lost by wrong answers = Number of wrong answers multiplied by Points lost on one correct answer.

Points lost by wrong answers = 4 \times 0.25 = 1

The score of the game can be calculated by subtracting the points lost from the points earned.

Score = 42 - 1 = <em>41</em>

3 0
2 years ago
I will mark you the brainiest for the correct answer, please be correct, Have a good day and take care, thanks. ( VIEW THE IMAGE
makkiz [27]

Mistake in Line 2 : Was in the determining the values for a ,b,c

Mistake in Line 4 : Not taking the square roots of both sides.

Step-by-step explanation:

{a}^{2}  +  {b}^{2}  =  {c}^{2}

First Mistake : Line 2

a = x \\ b = 6 \\ c = 10

Second Mistake : Line 4

136 =  {x}^{2}  \\ not \\ 136 = x

Correct Solution :

{x}^{2}  +  {6}^{2}  =  {10}^{2}  \\  {x}^{2}  =  {10}^{2}  -  {6}^{2}  \\  {x}^{2}  = 100 - 36 \\

{x}^{2}  = 64 \\  \sqrt{ {x}^{2} }  =  \sqrt{64}  \\ x = 6

3 0
3 years ago
2p - 3q - 4r + 6r -2q + p
sergejj [24]

2p - 3q - 4r + 6r - 2q + p = 0

2p + p - 3q - 2q - 4r + 6r = 0

3q - 5q + 2r = 0

7 0
3 years ago
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