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lawyer [7]
2 years ago
13

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the

length of the radius?
A(-7, -1), 36 units
B(7, 1), 36 units
C(7, 1), 6 units
D(-7, -1), 6 units
Mathematics
1 answer:
TiliK225 [7]2 years ago
7 0
Hello : 
<span>x² + y² + 14x + 2y + 14 = 0
</span>(x²  + 14x) + (y²+ 2y) + 14 = 0
(x²  + 14x+49-49) + (y²+ 2y+1-1) + 14 = 0
(x²  + 14x+49)-49 + (y²+ 2y+1)-1 + 14 = 0
(x+7)² + (y+1)² =6²...(answer : <span>D(-7, -1), 6 units )</span>

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21.6 ÷ 0.4 = 54 times for green
21.6 ÷ 0.6 = 36 times for purple

Together, 90 beads. Separately, 54 green and 36 purple.
3 0
1 year ago
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*Please Help* (Guaranteed brainliest for correct answer!)
FinnZ [79.3K]
Lets say that Williams current age is x, since it is currently unknown
From here we know that in 15 years (x+15) he will be 3 times his age 5 years prior (3x-5). Thus we can set these equations up as equal to one another
1) x + 15 = 3(x - 5)
2) x + 15 = 3x-15
3) 30= 2x
4) 15 = x
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The equation is x + 15 = 3(x - 5)

This should be correct now, sorry for the misconception. Good luck
 
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Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested fro
zalisa [80]

Answer:

a. The population does not become extinct in finite time.

Step-by-step explanation:

The model for the population of the fishery is

dP/dt = P(a-bP)-h, P(0) = P_0

If we rearrange and replace the constants we have:

\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}

Now we can calculate if the population become 0 in any finite time

\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\

To be a finite time, t>0

t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0

We can conclude that the only finite time in which P=0 is when the initial population is 0.

Because P0 is a positive constant, we can say that the population does not become extint in finite time.

5 0
1 year ago
Kara starts tying a baby quilt at the local community center. Each quilt takes 200 ties to complete. Ten minutes later Julie joi
Tju [1.3M]

Answer:

a) K(t)=6\frac{tie}{min}(t)

b)J(t)=11\frac{tie}{min}(t)

c)T_{f}(t)=K(t+10)+J(t) where T_{f}(t)= number ties finished per unit time

d) t≅8.24min

e) K=109tie

   J=91tie

f) K≅16.6min

  J≅9.09min

Step-by-step explanation:

Data

Kara_{(K)}=6\frac{tie}{min}\\Julie(J)=11\frac{tie}{min}

Kara begins ten minutes before julie, so when julie joins kara she has 60 ties

t=10 k=6\frac{tie}{min}*10min=60tie

a) K(t)=6\frac{tie}{min}(t)

b)J(t)=11\frac{tie}{min}(t)

c)T_{f}(t)=K(t+10)+J(t) where T_{f}(t)= number ties finished per unit time

d) if kara already has 60 ties and makes 6 per minute and Julie makes 11 per minute then per minute they makes 17 ties, so one minute per 17 ties for 200 ties ¿how long?. t=\frac{(200-60)tie*min}{17tie}≅8.24min

e) K=60tie+6tie/min*8.24min=109tie

   J=11tie/min*8.24min=91tie

f) K=100tie*min/6tie≅16.6min

  J=100tie*min/11tie≅9.09min

Note: the amount of ties were rounded to the nearest decimal

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The coordinate plane shows the floor plan for a swimming pool. What is the area of the pool’s border? A. 50 square meters B. 65
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Answer: Choice B

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