A grinding stone completes 175 revolutions before coming to a stop. How many radians did the stone complete

marta [7]

Answer:

11 units

Step-by-step explanation:

The height of a trapezoid is the distance between the parallel bases.

__

Here, one base lies on the horizontal line y=5, and the other lies on the horizontal line y = -6. The distance between them is ...

5 -(-6) = 5 +6 = 11

You can also find this distance by counting the grid squares between the two parallel lines.

The height of the trapezoid is 11 units.

_____

<em>Additional comment</em>

The base lengths are ...

AB = 2 -(-5) = 7

CD = 8 -(-7) = 15

The area is 1/2(b1 +b2)h = (1/2)(7 +15)(11) = 121 square units.

3 0

2 years ago

The rate of change in sales for Garmin from 2008 through 2013 can be modeled by

Zina [86]

Answer:

a) The model for the sales of Garmin is represented by $S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112$ .

b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Step-by-step explanation:

a) The model for the sales of Garmin is obtained by integration:

$S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt$

$S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C$ (1)

Where $C$ is the integration constant.

If we know that $t = 9$ and $S(t) = 2.9$ , then the model for the sales of Garmin is:

$-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9$

$C = 47.112$

The model for the sales of Garmin is represented by $S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112$ .

b) The average sales of the Garmin from 2008 through 2013 ( $\bar{S}$ ) is determined by the integral form of the definition of average, this is:

$\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt$ (2)

$\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112 \right]} \, dt$

$\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8) \right]$ $\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)$

$\bar{S} = 2.5$

The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

7 0

2 years ago

The amount y (in grams) of the radioactive isotope fermium-253 remaining after t hours is y=a(0.5)t/72, where a is the initial a

almond37 [142]

Answer:

Per hour decay of the isotope is 0.96%.

Step-by-step explanation:

Amount of radioactive element remaining after t hours is represented by

$y=a(0.5)^{\frac{t}{72}}$

where a = initial amount

t = duration of decay (in hours)

Amount remaining after 1 hour will be,

$y=a(0.5)^{\frac{1}{72} }$

y = 0.9904a

So amount of decay in one hour = a - 0.9904a

= 0.0096a gms

Percentage decay every hour = $\frac{\text{Amount of decay}}{\text{Initial amount}}\times 100$

= $\frac{0.0096a}{a}\times 100$

= 0.958 %

≈ 0.96 %

Therefore, per hour decay of the radioactive isotope is 0.96%.

7 0

3 years ago

Cali ran a 400-meter race in 65.49 seconds. Suppose that she ran the first half of the race in 31.73 seconds. How long did it t

zhenek [66]

Answer:

Step-by-step explanation:

time taken to complete the second half=65.49-31.73=33.76 seconds

3 0

3 years ago

Rob's family ate 3 5/8 pizzas at a local restaurant. Each pizza weighs 1 1/4 kg. Which expression can be used to determine how m

aleksklad [387]

Answer:

b

Step-by-step explanation:

g

4 0

2 years ago