A laser beam moves along a straight line so that its velocity is given by v(t)=r²-4 feet/sec. What is the total distance, in feet, that the laser beam will have traveled between t=1 and t=3 seconds?

Answers

Answer 1

Answer:

4

Step-by-step explanation:

I used a calculator. I put integral values of 3 and 1 and then entered the equation inside absolute value bars

Answer 2

The total distance traveled by the laser beam in the given time interval is required.

The total distance traveled by the laser in the given time interval is 4 feet.

Equation of motion

The given equation is

[tex]v(t)=t^2-4[/tex]

The given time interval is from t = 1 to t = 3 seconds.

In order to find the distance traveled we need to integrate the equation with respect to time and between the given intervals.

[tex]0=t^2-4\\\Rightarrow t=\pm 2=+2[/tex]

The laser will change the direction at [tex]t=2[/tex]

[tex]\int_1^3 v(t)=\int_1^2t^2-4 dt+\int_2^3t^2-4 dt\\\Rightarrow \int_1^3 v(t)=\dfrac{t^3}{3}-4t|_1^2+\dfrac{t^3}{3}-4t|_2^3\\\Rightarrow \int_1^3 v(t)=\left|\dfrac{2^3}{3}-4\times 2-(\dfrac{1^3}{3}-4)+\dfrac{3^3}{3}\right|-\left|4\times 3-(\dfrac{2^3}{3}-4\times2)\right|\\\Rightarrow \int_1^3 v(t)=\dfrac{5}{3}+\dfrac{7}{3}\\\Rightarrow \int_1^3 v(t)=\dfrac{12}{3}\\\Rightarrow \int_1^3 v(t)=4\ \text{m}[/tex]

Since, here distance is asked the absolute value of each integral is used.

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Related Questions

I NEEDS HELP WITH THIS

Answers

Answer:

you answer will be ∠JKH=129°

Step-by-step explanation:

hope it helps..

have a great day!!

Find the surface of this triangular prism please

Answers

Answer:

270cm²

Step-by-step explanation:

The formula is given as

S = bh × l (s1 + s2 + h)

l = 7cm

h = 5cm

s1 = 12 cm

s2 = 13cm

b = 12 cm

Surface Area = 12 cm × 5 cm × 7 cm(12 cm+ 13 cm+ 5cm)

= 60cm² × 7 cm(30 cm)

= 60cm² + 210 cm²

= 270 cm²

Si X es una variable aleatoria de tipo continuo… ¿Es posible definir el índice de asimetría de Fisher? ¿Por qué?

Answers

Answer:

Primero, para un caso discreto, el índice de asimetría de Fisher se calcula como:

[tex]\frac{\sum(xi - M)*n_i}{N*S_x}[/tex]

Donde:

xi son los i-esimos distintos valores de nuestro conjunto de datos.

M es la media

N es el numero de datos

ni es la frequencia absoluta de cada xi

Sx es la desviacion tipica

Podemos ver que en el caso discreto, escribimos el coeficiente con una sumatoria, lo cual realmente no podemos hacer para una variable continua.

Lo que si podemos hacer para una variable continua, es una integral, donde como esta vez tenemos una variable continua, podemos definir una función:

f(X) = frequencia absoluta para X.

Y escribir el coeficiente como:

[tex]\frac{\int\limits^a_b {(X - M)*f(x)} \, dx }{N*S_x}[/tex]

Entonces si, es posible definir el índice.

PLS HELP... 10 POINTS ASAP
Coach Jackson has a ratio of 1 girls to 3 boys in his classroom. If there are 6 girls in his class, what is the total number of students in Coach Jackson's class?
a. 18
b. 24
c. 12
d. 2

Answers

Answer:

b, 24

Step-by-step explanation:

b

1:3

6:18

6+18=24

I GOTCHU HOMIE

Answer:

The answer is 18.

Step-by-step explanation:

6 x 3 x 1 = 18

Tabitha's truck gets between 21 and 24 miles
Per gallon. The truck's fuel tank holds 20 gallons
of
gas.
What farthest reasonable distance that
Tabitha can expect to drive on a full tank of gas?
A) 350 miles
B) 400 miles
C) 450 miles
D) 500 miles

Answers

Start by finding the mean of the gas range:
21+24/2= 22.5
Multiply 22.5 by 20
22.5 x 20= 450

Your answer is 450 miles

Please help me ASAP!!!!!!

See pic attached

Answers

Hope this helps you.

Solve by factoring

2n^2+12n+18

Answers

Answer:

Step-by-step explanation:

d/dn(2 n^2 + 12 n + 18) = 4 (n + 3)

Indefinite integral:

integral(18 + 12 n + 2 n^2) dn = (2 n^3)/3 + 6 n^2 + 18 n + constant

Global minimum:

min{2 n^2 + 12 n + 18} = 0 at n = -3


Danielle's pool table is 5 feet wide and 8 feet long. Danielle wants to replace the felt on
the pool table. The felt costs $2.20 per square foot. How much would it cost in total to
replace the felt on the pool table?

Answers

Answer:

$88

Step-by-step explanation:

cost to replace the felt = Area of a rectangle x felt cost per square foot

Area = length x width

5 x 8 = 40

cost of replacement = 40 x 2.2 = 88

I need help I hate math whoever helps thx and nobody put a scam link that’s annoying I’m not falling for it.

Answers

Answer:

y≤46

it's the third one. hope it helps

PLEASE HELP 15 POINTS HURRY!!!!!

Answers

Answer:

B. A. D.

Step-by-step explanation:

Help please. No links

Answers

Answer:

C

Step-by-step explanation:

The question is asking which one is equal to the absolut value of 12. The absolute value of -12 equals 12, so it is the same as the absolute value of 12.

An eight minute phone call cost $3.36. What rate describes the cost for each minute?

Answers

Answer:

0.46 a minute or 46 cents a minute

Step-by-step explanation:

$3.36 divided by 8 is 0.46 or 46 cents

whats the the midpoint between (2, -1) and (-6, 0).

Answers

Answer:

X Midpoint -2   Y Midpoint -0.5

Answer:

(-2, -.5)

Step-by-step explanation:

2-6=-4                                           -1+0=-1

-4/2=-2                                           -1/2=-.5

Liam measures 5 kg of rice. One kilogram is approximately equal to 2.2 pounds. Which measurement is closest to the number of pounds of rice?
2.5 pounds
7 pounds
11 pounds
14 2 pounds

Answers

Answer:
11 pounds

Step by step:
5x2.2=11

Answer:

11

Step-by-step explanation:

To convert kg to pounds you would multiply 5×2.205 which would equal 11.02500. If we round it would be 11

Nick was thinking of a number. Nick adds 11, then divides by 6 to get an answer of -7. What was the original number?

Answers

Answer:

-53/6

Step-by-step explanation:

x + 11 / 6 = -7

Subtract 11/6 from both sides to isolate x.

x = -53/6

HELP ME WITH THIS PLEASE.
THANKS LOVE U GUYS SO MUCH.

Answers

Answer:

48.

Step-by-step explanation:

1). <C = 74 because it forms a supplemetary angle 180- 106 = 74.

2). We know that the sum of all the angles in a triangle is 180 so we need to add them.

3). 4y + 3y +22 + 74= 180

4). simplify 7y +96=180

5). isolate y so we must subtract 96 from either side.

6). 7y= 84 now divide by 7 on each side. 84/7 = 12.

7). Now we know y = 12 and that angle A is equal to 4y.

8). <A = 4(12) now distrubute

9). <A= 48 degrees

GOD, BLESS!!!

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Answers

Answer:

D trust me look

Step-by-step explanation:

Hope This Helped

Answer:

The answer is D

Step-by-step explanation:

8x6 is 48

-3x6=18-

-4x6=24-

-7x6=42-

A maple tree is 16 yards tall and its shadow is 12 yards long. A nearby observation tower is 12 yards tall. How long is the observation tower's shadow? Write your answer as a whole number or a decimal. Do not round.

Answers

Answer: 9 yards

Step-by-step explanation:

Given

The maple tree is 16 yards tall and its shadow is 12 yards tall

Suppose the angle made by the maple tree is x

[tex]\Rightarrow \cos x=\dfrac{12}{16}[/tex]

For the tower also, the angle made by the tower and its shadow is x

Suppose the length of the shadow is y

[tex]\Rightarrow \cos x=\dfrac{y}{12}[/tex]

Substitute the value of [tex]\cos x[/tex]

[tex]\Rightarrow \dfrac{y}{12}=\dfrac{12}{16}\\\\\Rightarrow y=9\ \text{yards}[/tex]

Choose the student who combined like terms correctly to write an equivalent expression. 5 + C + C + C -4. Melvin's work Sabrina's work Sudesha's work Zisel's work 5 + C + C + C - 4 5 + C + C + C-4 O 5 + C + C + C - 4 5+ C + C + C - 4 = 90 = 30 +1 = 4c = c + 1 ​

Answers

Answer:

Sabrinas work

Step-by-step explanation:

5+c+c+c-4

5+3c-4

=3c+1

Find the 75th term of the following arithmetic sequence.
6, 11, 16, 21,

Answers

Answer:

The 75th term in the sequence is 16

Step-by-step explanation:

The 75th term of a sequence can be considered as the term that is in the position at 75% along the sequence. This is assuming that the sequence has been sorted already from lowest value to highest value

In this sequence, which has 4 terms, we can find the 75th term by finding what term is at 75% (or three-quarters) along the sequence.

To find the 75th term:

Multiply the number of terms by 0.75 (or 75%/100%) :

             0.75*4 terms= 3

Then, we find the value of the term that is at position 3 from the left (lowest number)

In this case, the term that is at the 3rd position from the left is 16

Thus, the 75th term in the sequence is 16

write an equation for a function that has vertical asymptotes at x=3 & x=-10

Answers

Answer:

[tex] \frac{5}{ {x}^{2} + 7x - 30} [/tex]

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

[tex]0 - x = 3[/tex]

[tex]0 - x = - 10[/tex]

[tex]0 - ( - 3) = = 3[/tex]

[tex]0 - 10 = 10[/tex]

So we would represent that's as

[tex]x - 3[/tex]

and

[tex]x + 10[/tex]

Multiply the two binomial together.

[tex](x - 3)(x + 10) = {x}^{2} + 7x - 30[/tex]

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

[tex] \frac{5}{ {x}^{2} + 7x - 30 } [/tex]

Which graph best represents y = -x2 + 6x - 1?

Answers

The answer choice would be D

⛔️NO LINK JUST WANT ANSWER NONE OF THAT BIT.L STUFF⛔️The biggest frog on record
is the goliath frog. These
frogs can be up to 3.3
kilograms and can jump a
distance of 3 meters. If the
goliath frog was found i
km from the nearest water,
about how many jumps
would he have to take to
get a drink?, JUST TYPE THE ANSWER NO FILES

Answers

Answer:

The answer would be 333.334 jumps.

Step-by-step explanation:

So remember, there are 1000 meters in 1 kilometer. The frog can jump 3 meters. The nearest water is 1 kilometer. So, lets divide 1 km(1000m) by 3m:

1000/3

=

333.34

This is the answer.

Hope this helps!

A book contains 27 pages with print and 8 pages with print and pictures and 3 blank pages with is the theoretical probability of not opening the book to a printed page only

Answers

Answer: 11/38

Step-by-step explanation: x - y v q r 2÷x029 2%.091 57rq x2 = 11/38

me pueden ayudar por favor si no saben no respondan (:

Answers

Answer:

Step-by-step explanation:

A system of two linear equations has no solution if the graphs of both equations have
y-intercept and
slope.

Answers

Answer:

A system has no solutions if two equations are parallel. Let's take a look at an example. When two equations have the same slope but different y-axis, they are parallel. Since there are no intersection points, the system has no solutions.

Step-by-step explanation:

is it possible to form a triangle with the given side lengths? 15 yd,16yd,30yd

Answers

Answer:

Yes

Explanation:

15 < 16+30

16 < 15+30

30 < 16+15

Yes it is possible to form a trial for

Help!

An airplane takes off at an angle of 15 degrees with the ground. To the nearest 10 feet, how far has the airplane flown when it has covered a horizontal distance of 1800 feet?

Answers

Answer:

1863.5 feets

Step-by-step explanation:

Using Trigonometry :

The distance, d in the attached diagram can be obtained using the trigonometric relation :

Cosθ = adjacent / hypotenus

Cos 15° = 1800 / d

0.9659258 = 1800 / d

0.9659258 * d = 1800

d = 1800 / 0.9659258

d = 1863.4971 feets

The distance covered to the nearest 10 feet = 1863.5 feets

What type of function is this equation?
h(x) = 3x - 1
O Exponential
O Linear
O Quadratic

Answers

Answer:

Linear

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form: f(x) - mx +b

Hope this helps! :)

The dimensions of a right rectangular prism are shown below.





How many cubes with side lengths of 1 over 6 inch are needed to fill the prism without gaps or overlaps?

Answers

Answer:

91 cubes

Step-by-step explanation:

518 cubes are needed to fill the right rectangular prism without gaps or overlaps.

What is right rectangular prism?

"It is a prism whose all faces are rectangles."

What is the volume of rectangular prism?

The volume of a rectangular prism with length l, width w and height h is,

V = l × w × h

What is the volume of cube?

The volume of a cube having side length 'a' is given by,

[tex]V=a^3[/tex]

For given example,

The dimensions of a right rectangular prism are:

length : [tex]l=2\frac{1}{6}[/tex]

⇒ [tex]l=2.17[/tex] in.

width: [tex]w=1\frac{1}{6}[/tex]

⇒ [tex]w= 1.17[/tex] in.

height : h = 1 in.

So, the volume of a right rectangular prism would be,

⇒ V = l × w × h

⇒ V = 2.17 × 1.17 × 1

⇒ V = 2.5389 cu. in .

Now, the side lengths of a cube : [tex]a=\frac{1}{6}[/tex]

⇒ [tex]a=0.17[/tex]

So, the volume of a cube would be,

⇒ [tex]V=a^3[/tex]

⇒ V = (0.17)^3

⇒ V = 0.0049

Let, 'n' cubes are needed to fill the right rectangular prism without gaps or overlaps.

volume of a right rectangular prism = n × volume of a cube

⇒ 2.5389 = n × 0.0049

⇒ 2.5389/0.0049 = n

⇒ n = 518.14

⇒ n ≈ 518

Therefore, 518 cubes are needed to fill the right rectangular prism without gaps or overlaps

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