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3 years ago

Draw a model of 100oz of soda divided equally among 12 students. How many oz will each person have?

1 answer:

6 0

That's how many ounces of water you should drink per day. For instance, a person who is 200 pounds, should drink 100 oz. of water per day to be adequately hydrated. (That's 12.5 glasses of water!)

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The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.

Vladimir79 [104]

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

8 0

1 year ago

Lesson 10: Congruent Triangles ._.

spayn [35]

#1 is A
#2 IS c
#3 is B

3 0

3 years ago

Read 2 more answers

What is minimal completion time for the activities in the graph below? In a complete sentence, explain how you got your answer

kupik [55]

The minimal completion time for the activities is the shortest possible time for all the activities to be finished. In doing this, we look at the path that would require the greatest amount of time. At the START node, we choose the path that would take the longest which is 7 days leading to ACTIVITY D. Next, we choose the path leading to ACTIVITY B which takes 5 days. Then, we move to ACTIVITY C taking 5 days and finally, reach the END which would take 6 days. So, the minimal completion time is:
7 + 5 + 5 + 6 = 23 days

6 0

4 years ago

Simplify by using the distributive property and then combining like terms for the expression 7(2x+3)

max2010maxim [7]

Answer:

14x+21

Step-by-step explanation:

7*2x=14x

7*3=21

14x+21

hope this helps :9

6 0

3 years ago