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Thepotemich [5.8K]
3 years ago
9

Please help!

Mathematics
1 answer:
dexar [7]3 years ago
3 0

Answer: 1/9

Step-by-step explanation:

You have 3 possible options. The probablility of the spinner landing on 3 is 1/3. The probability of it landing on 2 is also 1/3. For them to happen together, you multiply them. 1/3 * 1/3 = 1/9.

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A construction worker fills a mold with concrete. This solid figure represents the mold.
allochka39001 [22]

Answer:

6580cm

Step-by-step explanation:

The answer is 6580cm because....

  • Step one First let's figure out what the smaller shape's volume is. To do so we need to multiply ( LxWxH ) so 6x5x? it does not list what the height is so we know it has the same height as the larger shape and it's height is 14cm so we will use 14cm. 6x5x14=420cm
  • Step two Now lets find the Volume of the larger shape. So lets do LxWxH so Lx?x14 it does not give us the length so we need to add up all of the numbers along the line. We got 7cm then 5 from the bottom of the smaller shape and 10cm. all ads up to 22cm so 20x22x14=6160
  • Finally we add up the following shapes Volume which are 6160+420=6580cm
3 0
3 years ago
Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck
Nimfa-mama [501]
\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}
\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}

Now, isolate the variables, so you can integrate.
(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}
\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}
2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C


4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C
y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C
(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C
(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C


y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}
y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}

At x = 1, y = 0.
0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}
-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}

4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0
\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}


4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C
0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C
C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}
C = -\frac{\pi}{2}

\therefore y = 2 - \sqrt{4 + \frac{\pi}{2} - 2sin^{-1}\frac{x}{\sqrt{2}}}
6 0
3 years ago
After 3 days a sample of radon-222 has decayed to 58% of its original amount.(
iren2701 [21]
Half-life = [elapsed time * log (2)] / [log (begng amt / endg amt)]
half-life =  (3 days * 0.30102999566) / log (1 / .58)
<span>half-life =  0.903089987 / log </span> (<span> <span> <span> 1.724137931)
</span></span></span>half-life =  <span>0.903089987 / 0.23657200643</span>
half-life =  <span> <span> <span> 3.8174 days

Source:
http://www.1728.org/halflife.htm

</span></span></span>
3 0
3 years ago
Can u guys PLEASE answer this question ASAP. A fat cat that was initially 12 kg reduces its weight by 10% each month. How long d
Mkey [24]

Answer:

It takes at least 7 months for the cat to be at least 6 kg lighter than the original weight.

Step-by-step explanation:

Use exponential decay formula:

A = P (1-r)t

A = amount decreased to

P = original amount

r = rate of decrease

t = time

 

6 ≥ 12 (1-0.10)t      divide both sides by 12

0.5 ≥ (0.9)t            take log of both sides

log (0.5) ≥ log (0.9)t     power rule of logs lets the exponent t drop to front of log to become a factor

log (0.5) ≥ t log(0.9)     divide both sides by log(0.9) which is negative so reverse the inequality sign

log (0.5) / log (0.9) ≤ t     use calculator

6.57 ≤ t

 

It takes at least 7 months for the cat to be at least 6 kg lighter that original weight.

 

check:

12 (0.9)7≈ 5.73

12 (0.9)6 ≈ 6.37

5 0
3 years ago
Help me pls............​
rewona [7]

Answer:

1

Step-by-step explanation:

When n -->∞,

90/∞ ---> 0°.

cos(0° )= 1

1^(2n)=1, 1 in any power is 1.

\lim_{n \to \infty} 1 = 1

6 0
3 years ago
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