9514 1404 393
Answer:
√629 ≈ 25.08
Step-by-step explanation:
The distance formula is useful for this.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-12 -13)² +(6 -8)²) = √(625 +4) = √629 ≈ 25.08
The distance between the points is about 25.08 units.
Answer:
c. 500
Step-by-step explanation:
125+125=250
250+125=375
375+125=500
Answer:
Step-by-step explanation:
Consider the graphs of the
and
.
By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.
then
o
. Therefore the integration limits are:
and 
The inverse functions are given by:
and
. Then
The volume of the solid of revolution is given by:
![\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2} dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\ dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B2%5Csqrt%7By%7D%20-%20%5Cfrac%7By%7D%7B4%7D%5D%5E%7B2%7D%20%20dy%20%3D%20%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B4y%20-%20y%5E%7B3%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B2%7D%7D%7B16%7D%20%5D%5C%20%20dy%20%3D%20%5B2y%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7B5%7Dy%5E%7B5%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B3%7D%7D%7B48%7D%20%5D%5Climits%5E%7B64%7D_%20%7B0%7D%20%3D%20546.133%20u%5E%7B2%7D)
Answer:
21.68 minutes ≈ 21.7 minutes
Step-by-step explanation:
Given:

Initial temperature
T = 100°C
Final temperature = 60°C
Temperature after (t = 3 minutes) = 90°C
Now,
using the given equation

at T = 90°C and t = 3 minutes


or

taking the natural log both sides, we get
3k = 
or
3k = -0.2876
or
k = -0.09589
Therefore,
substituting k in 1 for time at temperature, T = 65°C

or

or

or

taking the natural log both the sides, we get
( -0.09589)t = ln(0.125)
or
( -0.09589)t = -2.0794
or
t = 21.68 minutes ≈ 21.7 minutes