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Shtirlitz [24]
1 year ago
7

the depth of a rain puddle d(t) is given in inches, and t is given in minutes. if the depth is changing with respect to time, wh

ich expression gives the rate of change at which the depth is changing at 3 minutes?
Mathematics
1 answer:
garik1379 [7]1 year ago
7 0

The required expression gives the rate of change will be d'(3) at which the depth is changing at 3 minutes.

Let d(t) represent the depth of the rain puddle at any time t,

⇒ d(t)  ....(i)

The depth is changing with respect to time, which is given in the question

Differentiate equation (i) with respect to t and we get

⇒ δd(t)/δt = d'(t) ....(ii)

This is the rate of change in depth unit time

As per the question, the depth is changing at 3 minutes

Substitute the value of t = 3 in equation (ii), and we get

⇒ d'(3)

Therefore, the required expression gives the rate of change will be d'(3).

To learn more about the differentiation click here:

brainly.com/question/24898810

#SPJ1

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Geometry Question Help if you can please
docker41 [41]

Answer:

≈ 78.55 cm

Step-by-step explanation:

Using the ratio of arc (AB) to circumference (C) is equal to the ratio of angle subtended at centre by arc AB to 360°, that is

\frac{AB}{C} = \frac{110}{360} , that is

\frac{24}{C} = \frac{110}{360} ( cross- multiply )

110C = 8640 ( divide both sides by 110 )

C = \frac{8640}{110} ≈ 78.55 cm ( to 2 dec. places )

5 0
3 years ago
2, -2, 2, -2, common ratio
adelina 88 [10]
To get -2 from 2, you would multiple by -1.

To get 2 from -2, you also would multiple by -1.

Ad infinitum.

So the common ratio is -1.

Hope this helps.
8 0
3 years ago
Verizon has a special and is selling the new iPhone 7 for $299 to new customers. If the Apple Store is charging twice as much as
-Dominant- [34]

Answer:

$598

Step-by-step explanation:

2 x 299 = 598 so Apple is charging $598 for the new phone.

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2 years ago
Sharon drops a rubber ball from a height of 48 feet. Every bounce sends the
Reil [10]

Answer:

1.75 feet

Step-by-step explanation:

48 ÷ 2 = 14

14 ÷ 2 = 7

7 ÷ 2 = 3.5

3.5 ÷ 2 = 1.75

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2 years ago
I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP
aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

  • 0+1 = 1
  • 1+3 = 4
  • 3+6 = 9
  • 6+10 = 16
  • 10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

==========================================================

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

8 0
2 years ago
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