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Anton [14]
2 years ago
11

Which of the following is a function?

Mathematics
1 answer:
seropon [69]2 years ago
7 0

Answer:

C

Step-by-step explanation:

For any of the functions described above, the only way any of those could be functions is that there has to be a difference value for each x, unless it is the same x-value. If the x is mentioned twice, that is fine, as long as the y point is also the same. If it is different, it is not a function.

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A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the cha
Galina-37 [17]

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

  • The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
  • the radius r=5cm
  • Punch is being poured into the bowl
  • The height at which the punch is increasing in the bowl is \frac{dh}{dt} = 1.5
  • the exposed area is a circle, (since the bowl is a hemisphere)
  • the radius of this circle can be written as 'a'
  • what is being asked is the rate of change of the exposed area when the height h = 2 cm
  • the rate of change of exposed area can be written as \frac{dA}{dt}.
  • since the exposed area is changing with respect to the height of punch. We can use the chain rule: \frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}
  • and since A = \pi a^2 the chain rule above can simplified to \frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt} -- we can call this Eq(1)

Solution:

the area of the exposed circle is

A =\pi a^2

the rate of change of this area can be, (using chain rule)

\frac{dA}{dt} = 2 \pi a \frac{da}{dt} we can call this Eq(2)

what we are really concerned about is how a changes as the punch is being poured into the bowl i.e \frac{da}{dh}

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

r = \frac{a^2 + h^2}{2h}

and rearrage the formula so that a is the subject:

a^2 = 2rh - h^2

now we can derivate a with respect to h to get \frac{da}{dh}

2a \frac{da}{dh} = 2r - 2h

simplify

\frac{da}{dh} = \frac{r-h}{a}

we can put this in Eq(1) in place of \frac{da}{dh}

\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}

and since we know \frac{dh}{dt} = 1.5

\frac{da}{dt} = \frac{(r-h)(1.5)}{a}

and now we use substitute this \frac{da}{dt}. in Eq(2)

\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}

simplify,

\frac{dA}{dt} = 3 \pi (r-h)

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

r = 5cm

h = 2cm from the question

\frac{dA}{dt} = 3 \pi (5-2)

\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s

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2 years ago
A. x= 2 0
Elanso [62]

Answer:

Step-by-step explanation:

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3 years ago
When Shanaje baby-sits her nephews, she charges $8 plus $4 per hour. If
Vlad1618 [11]
4h +8=20
Hours worked times rate paid plus 8 must equal 20
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In his bank account, Jean-Paul has a balance of $0.00
GenaCL600 [577]
Well JP has $0.00 in his bank account which means his has more debt

Albert has $11.10 which means he has greater absolute value.

5 0
3 years ago
Read 2 more answers
The sales tax on a surfboard is $12. What is the percent of sales tax if it is $240
Mazyrski [523]

Answer: Percentage of sales tax will be 5%.

Step-by-step explanation:

Since we have given that

Original amount of a surfboard = $240

Sales tax on a surfboard = $12

So, Percentage of sales tax will be

\frac{Sales\ tax}{Original\ price}\times 100\\\\=\frac{12}{24}\times 100\\\\=\frac{1}{2}\times 100\\\\=\frac{100}{2}\\\\=5\%

Hence, Percentage of sales tax will be 5%.

3 0
2 years ago
Read 2 more answers
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