A) The velocity function is v(t)=t2−6t+8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,5].
.................................................................................................................................................................
B) Given that 7<=f(x)<=10 for −4<=x<=4, use property 8 of Section 5.2 of the Stewart Essential Calculus textbook to estimate the value of ∫-4 to 4 f(x)dx
(-----------------) <= ∫-4 to 4f(x)dx <= (--------------)

Answer: 39. x= 37, 41. x=7, 43. x = 29

Step-by-step explanation:

39. 2x + 4 + 2x - 9 + x = 180

5x - 5 = 180

5x=185

185/5

x=37

41. 90 + 8x - 1 + 4x+7 =180

8x-1+4x+7=90

12x+6=90

12x=84

84/12

x=7

36+x=2x+7

36=x+7

29=x

Hope this helps.

Answer:

Hope this helps

Answer: pink

Step-by-step explanation:

The content of your cover letter should be brief and structured. Avoid lengthy repetition of information covered in your CV. Unlike a CV, it is acceptable to write a cover letter in the first person. Your letter should address the relevant contact, whose name often appears in the job advertisement

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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The actual width of the plane = 6.5 feet and the actual length of the plane = 8.5 feet.

Provided that the die-cast plane toy is scaled at an inch to 1 foot, we can determine the dimensions of the actual plane by converting the measurements from inches to feet.

The width of the toy plane is 6.5 inches.

To obtain the actual width, we divide this measurement by the scale of 1 inch to 1 foot:

Actual width = 6.5 inches / 1 inch/1 foot = 6.5 feet.

Therefore, the actual width of the plane is 6.5 feet.

Similarly, the length of the toy plane is 8.5 inches.

Converting this measurement to feet, we have:

Actual length = 8.5 inches / 1 inch/1 foot = 8.5 feet.

Therefore, the actual length of the plane is 8.5 feet.

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Answer:

Step-by-step explanation:

Sum of interior adjacent angle is 180 degrees.

Given  

m∠BNR=12w-19,

m∠RNA= ¼(w+199)

m∠BNA=2(12w-19).

Substitute

m∠BNR+m∠RNA=

¼(w+199)+12w-19, = 2(12w-19).

W+796+48W-76 = 96W-152

49W-96W = -152+76-796

-47W = 872

W = 872/47

W = 18.55

Answer: 28

Step-by-step explanation:

28 is thhe missing number

Answer: I think that the answer is all of the above.

I am not 100% sure if that is completely correct so just pick some answers and see if they are correct.

Step-by-step explanation:

Answer:

The recipe originally required 50 grams of cheese.

Step-by-step explanation:

1.6x=80

x=50

Answer:

-4.3, -3.4, -0.43, -0.34, -0.043

Answer:

Step-by-step explanation:

(x+2)²+5=0

\(x^{2} +4+5 = 0\)

\(x^{2} +9 = 0\)

\(x^{2} = -9\)

x= no solution

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We know that the square of any number is greater or equal to zero Thus ;

\( ({x + 2})^{2} \geqslant 0\)

And ;

\(5 > 0\)

Sum of the two positive numbers never equal zero Thus there isn't any value for x

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Check the picture below.

Answer: Linear.

Step-by-step explanation:

      A linear function forms a straight line when it is graphed.

      A nonlinear function will be curved in some way when graphed.

      We can graph the given points to find the answer to this question. See attached for this graph. These points create the function y = 3x + 2, which is a linear function.

Answer:

yes angle measures 84°as they are alternate angles

C). cosθ. is the correct option. The given expression is equivalent to cscθ(1+cosθ)(1−cosθ). We know that cscθ is defined when sinθ ≠ 0, which means θ cannot be equal to 0°, 180°, 360°, etc.

Expanding the expression (1+cosθ)(1−cosθ), we get:

(1+cosθ)(1−cosθ) = 1 − cos^2θ

We can use the identity sin^2θ + cos^2θ = 1 to write:

1 − cos^2θ = sin^2θ

Substituting this in the original expression, we get:

cscθ(1+cosθ)(1−cosθ) = cscθ sin^2θ

Using the identity cscθ = 1/sinθ, we get:

cscθ sin^2θ = 1/sinθ * sin^2θ = sinθ

Therefore, the given expression is equivalent to sinθ.

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Answer:

What subject is this?. May you please take apicture clear so i can see perfectly

thank you by Tracy Stewart

Step-by-step explanation:

If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be  984N.

As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.

We are required to calculate the force required to compress this spring by 1.2 cms

To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as

[F = (k * x)]

Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and

(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.

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Answer:

  15

Step-by-step explanation:

You want the sum of the numbers in the diagram that belong to exactly 3 circles.

We find it easier to eliminate numbers that do not belong to 3 circles. In the attachment, the red lines strike through numbers belonging to 1 circle, the blue lines strike numbers belonging to 2 circles, and the green line strikes the number belonging to 4 circles. (The numbers inside the smallest circle are also in the larger circle surrounding it.)

The numbers that are in 3 circles only are 1, 3, 11. Their sum is 15.

0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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Using Euler's method with two steps of equal size, we approximate h(1) ≈ 1.3125.

What is Euler's method?

To use Euler's method to approximate h(1) with two steps of equal size, we first need to find the step size, h. Since we're taking two steps, the step size will be 1/2 (since we're starting at x = 0 and ending at x = 1).

Next, we need to use the initial condition h(0) = 2 to find the initial approximation. Since we're starting at x = 0, the initial approximation will simply be h(0) = 2.

Now, we can use Euler's method to find the next approximation:

h(1/2) ≈ h(0) + f(0, 2)h

where f(x,y) = x² - 1/2 y is the right-hand side of the differential equation. Plugging in x = 0 and y = 2, we get:

f(0, 2) = 0² - 1/2(2) = -1

So, we have:

h(1/2) ≈ 2 + (-1)(1/2) = 1.5

Now, we can use Euler's method again to find the final approximation:

h(1) ≈ h(1/2) + f(1/2, 1.5)h

where we use the previous approximation h(1/2) as our starting value. To find f(1/2, 1.5), we plug in x = 1/2 and y = 1.5 into the right-hand side of the differential equation:

f(1/2, 1.5) = (1/2)² - 1/2(1.5) = -0.375

So, we have:

h(1) ≈ 1.5 + (-0.375)(1/2) = 1.3125

Therefore, using Euler's method with two steps of equal size, we approximate h(1) ≈ 1.3125.

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Answer: x=7

Step-by-step explanation: 6x-15=27

6x=42

x=7

The difference between the two calendars is very small, and in a human life they are not noticeable, but on the long run there some differences.

The Julian calendar has one year as 365.25 days, but the problem is that it is 11 minutes less, and it also has a leap year on every year that is dividable with 100.

The Gregorian calendar, on the other hand, has one year as 365 days, and it has a leap year on every year that is dividable with the number four, so it is slightly more accurate.

Most of the countries nowadays are having the Gregorian calendar in usage.

The difference in the average length of the year between Julian (365.25 days) and Gregorian (365.2425 days) is 0.002%, making the Julian 10.8 minutes longer.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

A probability distribution has a mean and a standard deviation.

The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. The standard normal distribution is centered around zero, and the standard deviation indicates how much a particular measurement differs from the mean.

The normal (or Gaussian) distribution is the most common continuous probability distribution. This function gives the probability that an event will fall between any two real boundaries when the curve approaches zero on either side of the mean. The area under the normal curve is always 1.

The variance of a probability distribution is the mean squared distance from the mean of the distribution. If you take multiple samples of a probability distribution, the expected value, also called the mean, is the value you get by averaging them.

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Answer:

The answer 5.83

Step-by-step explanation:

Answer:

0.06 or 6%

Step-by-step explanation:

35000+25000=60000

3600/60000=0.06

Answer:

x=250

Step-by-step explanation:

Answer:

if you're trying to find out how long paul's car is, do 1/8 * 13

1/8 * 13 = 1.625 ft long

Step-by-step explanation:

\(1.25\)

\(3 \times \frac{5}{8} - 2 \times \frac{3}{8} = \frac{29}{8} - \frac{19}{8} = \frac{10}{8} = 1.25\)

The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers  .

Let us understand the Division with the help of example ;

let the number be 10 ;

first we divide the number 10 by 0.5 ;

this can be written mathematically as ⇒ \(\frac{10}{0.5}\)  ;

⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;

So , on dividing 10 by 0.5 , we get the answer as 20 .

Second , the number 10 is divided by 2 ;

this can be written mathematically as ⇒ \(\frac{10}{2}\) ;

⇒ \(\frac{10}{2 }\)  = 5  ;

So , on dividing 10 by 2 , we get the answer as 5  .

Therefore , dividing by 0.5 is not same as dividing by 2 .

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