Answer: r ≈ 5.95
Step-by-step explanation:
Let S be the surface area , then
S = ![\pi](https://tex.z-dn.net/?f=%5Cpi)
+
r![\sqrt{r^{2}+h^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Br%5E%7B2%7D%2Bh%5E%7B2%7D%7D)
Differentiating S with respect to r , we have
dS =
dr +
dh
= (2
r +![\pi](https://tex.z-dn.net/?f=%5Cpi)
+
) dr +
dh
For the area to remain the same it means dS = 0
since r = 6cm , h = 8cm , dh = 0.28 then we have
0 = (12π + 10π +
)dr +
X 0.28.
Making dr the subject of formula , we have
(12π + 10π +
)dr = - (
X 0.28)
(
) dr = - ![\frac{6.72\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B6.72%5Cpi%20%7D%7B5%7D)
(640
)dr = - 33.6![\pi](https://tex.z-dn.net/?f=%5Cpi)
dr = - 33.6
/ 640![\pi](https://tex.z-dn.net/?f=%5Cpi)
dr = 0.05
This means that the radius should decrease by 0.05 for the area to remain the same. That means the radius = 6 - 0.05
r ≈ 5.95
The numbers in the sequence will be 40, 80, and 160.
<h3>How to get the values?</h3>
Let x be the first number in the sequence, so the first three numbers are {x, 0.5x, 0.5²x}.
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
0.5x - 10 = x/4 + 10 + c = x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c = x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are {160, 80, 40}
Learn more about sequence on:
brainly.com/question/6561461
#SPJ1
Answer:
X = 115 degrees
Y = 65 degrees
Z = 115 degrees
Step-by-step explanation:
X is supplementary to 65 degrees (180-65 = 115)
Y is complementary to 65 degrees (65 = 65)
X and Z are complementary so Z is also 115 degrees
Answer:
So, the probability is P=0.094.
Step-by-step explanation:
We know that in a recent survey, 73% of the community favored building a police substation in their neighborhood.
We get that p=0.73 and q=1-0.73=0.27.
We calculate the probability that exactly 8 of them favor the building of the police substation, if 14 citizens are chosen.
We get that n=14 and k=8.
We calculate the probability:
![P=C_k^n\cdot p^k\cdot q^{n-k}\\\\P=C_8^{14}\cdot 0.73^8\cdot 0.27^6\\\\P=3003\cdot 0.00003124\\\\P=0.094\\](https://tex.z-dn.net/?f=P%3DC_k%5En%5Ccdot%20p%5Ek%5Ccdot%20q%5E%7Bn-k%7D%5C%5C%5C%5CP%3DC_8%5E%7B14%7D%5Ccdot%200.73%5E8%5Ccdot%200.27%5E6%5C%5C%5C%5CP%3D3003%5Ccdot%200.00003124%5C%5C%5C%5CP%3D0.094%5C%5C)
So, the probability is P=0.094.
Answer:
284° F
Step-by-step explanation:
Formula:
<em><u>°Fahrenheit = 9/5 × °Celsius + 32</u></em>
9/5 × 140° +32
1.8 × 140 = 252
252 + 32 = 284