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baherus [9]
3 years ago
7

Match each graph above with one of the corresponding sequences listed below:

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

Answer:

(a) geometric sequence; common ratio of 3

  • Graph 2

(b) geometric sequence; common ratio of 1/2

  • Graph 6

(c) geometric sequence; common ratio of -2

  • Graph 5

(d) arithmetic sequence; common difference of 3

  • Graph 4

(e) geometric sequence; common ratio of 2

  • Graph 1
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How do I do question 9? Please give answer thank you
kvasek [131]
<h3>Given</h3>
  • a cone of height 0.4 m and diameter 0.3 m
  • filling at the rate 0.004 m³/s
  • fill height of 0.2 m at the time of interest
<h3>Find</h3>
  • the rate of change of fill height at the time of interest
<h3>Solution</h3>

The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of

... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²

This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.

... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s

Dividing by the coefficient of dh/dt, we get

... dh/dt = 0.004·16/(0.09π) m/s

... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s

_____

You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)

Note that the cone dimensions mean the radius is 3/8 of the height.

V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³

dV/dt = 9π/64·h²·dh/dt

.004 = 9π/64·0.2²·dh/dt . . . substitute the given values

dh/dt = .004·64/(.04·9·π) = 32/(45π)

7 0
3 years ago
-20÷5(-3)+4(-2)(-1)-4²<br>step by step please and thank you!​
disa [49]

\huge \boxed{\mathbb{QUESTION} \downarrow}

\large \tt \: -20 \div  5(-3)+4(-2)(-1)-4  ^ { 2  }

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\tt \: -20 \div  5(-3)+4(-2)(-1)-4  ^ { 2  }

Divide -20 by 5 to get -4.

\tt \: -4\left(-3\right)+4\left(-2\right)\left(-1\right)-4^{2}

Multiply -4 and -3 to get 12.

\tt \: 12+4\left(-2\right)\left(-1\right)-4^{2}

Multiply 4 and -2 to get -8.

\tt \: 12-8\left(-1\right)-4^{2}

Multiply -8 and -1 to get 8.

\tt \: 12+8-4^{2}

Add 12 and 8 to get 20.

\tt \: 20-4^{2}

Calculate 4 to the power of 2 and get 16.

\tt \: 20-16

Subtract 16 from 20 to get 4.

=  \boxed{\boxed{ \bf 4}}

5 0
3 years ago
Heelllllllpi need help with A
olchik [2.2K]
A=29 theres 29 dots each dot is 1 student
4 0
3 years ago
Marjorie is building a dog run that is 25'8" long and 8'8" wide. How much fencing will she need if the opening is 3'6" wide and
antiseptic1488 [7]

Answer:

782 in

Step-by-step explanation:

To find the length of fence, we have to find the perimeter first.

Given

Length = l = 25 feet 8 in

Width = w = 8 feet 8 in

Opening = o =3 feet 6 in

So,

we have to convert the lengths into same unit first

So,

l = (25*12)+8 = 308 in

w = ( 8*12) +8 = 104 in

O = (12*3) + 6 = 42 in

Perimeter = 2(l+w)

= 2(308+104)

=2(412)

=824

As the opening does not need fencing

Total fence = P - o

= 824 - 42

=782 in

or

65 feet 2 in ..

3 0
3 years ago
You What mass of makes up 70 percent of all planetary mass in the solar system
MA_775_DIABLO [31]
My guess would be Jupiter But I'm not sure. Its certainly massive!!
7 0
4 years ago
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