Solve for x: −1 < x + 3 < 5

Mathematics

1 answer:

Inessa05 [86]3 years ago

3 0

Answer:

-4<x<2

Step-by-step explanation:

the picture is the steps

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Jack ran at 880 ft./min. For the first 10 min. Of the 3 mi. Race before slowing his pace to finish the race with a total time of

Nina [5.8K]

Answer:

Jack ran 704 ft/min during the second half of the race.

Step-by-step explanation:

Here the distance traveled was 3 miles, and the total elapsed time was 20 minutes. Recall that distance = rate * time, or rate = distance / time.

Find the pace (speed, rate) for the second part of the race.

Here, the total distance was 3 miles and the elapsed time 20 minutes. Jack's average speed was thus 3/20 miles/minute. Converting this to feet per minute, we get:

3 mi 5280 ft

------------ * ------------- = 792 ft/min (Jack's average speed)

20 min 1 mi

Recall that the formula for finding the average of x and y is (x + y) / 2.

(1/2)(880 ft/min + p) = 792 ft/min; find p, which represents Jack's pace for the second part of the race.

If (1/2)(880 ft/min + p) = 792 ft/min, and we mult. both sides by 2, we get:

880 ft/min + p = 1584 ft/min.

To solve this for p, subtract 880 ft/min from both sides, obtaining:

p = 704 ft/min

Jack ran 704 ft/min during the second half of the race.

3 0

2 years ago

The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$