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Svetllana [295]
2 years ago
9

The base of a triangle is shrinking at a rate of 5 cm/s and the height of the triangle is increasing at a rate of 9 cm/s. Find t

he rate at which the area of the triangle changes when the height is 12 cm and the base is 4 cm.
Provide your answer below:
The rate of change of the area of the triangle is ___ cm²/s.
Mathematics
1 answer:
creativ13 [48]2 years ago
3 0

Answer:

Step-by-step explanation

Area of a triangle

      A = ½bh

dA/dt = ½(b(dh/dt) + h(db/dt)

dA/dt = ½(4(9) + 12(-5))

dA/dt = ½(36 - 60)

dA/dt = ½(-24)

dA/dt = -12 cm²/s

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Show that the sum of the first 2n natural numbers is n(2n+1)
Leokris [45]

Answer:

This sum is the sum of an arithmetic sequence.  There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.

A nice approach for this sequence is the following.  Notice  that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.

There are n of these pairs.  So the desired sum is n x (first number + last number).   But the first number is 1 and the last on is 2n.   Thus the desired sum is n(1 + 2n).

Hope this helps!!

Mark Brainleast!!!!!!!!!!!

7 0
2 years ago
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Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid 444 bones, Barry hid 555 bones, Larry hid 101010 bones, a
Nezavi [6.7K]

Answer:

58330.5 bones

Step-by-step explanation:

Essentially mean is taking the total and dividing that by the number of items.

Here, we need to add up all the bones and divide it by the number of dogs there are:

444 + 555 + 101010 + 131313 = 233322 bones

There are 4 dogs:

233322 / 4 = 58330.5 bones

4 0
3 years ago
Read 2 more answers
Convert the following fractions to decimals. go to the thousandths place 1/8
egoroff_w [7]

Answer: There answer is 0.125

Step-by-step explanation:

If you divide the fraction you will see

8 0
3 years ago
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At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while
aliya0001 [1]

Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

Let the height of the pole is x cm,

Also, let the angle of elevation of the sun to the pole at 3 pm is \theta

Thus, by the question,

tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}

\implies tan\theta = \frac{x}{x}    ( at 3pm the height of shadow = height of the pole)

\implies tan\theta = 1

\implies \theta = 45^{\circ}

Again, according to the question,

When the angle of elevation is   (\theta - 12^{\circ}),

The height of shadow = x + 95,

\implies tan(45-12)^{\circ}=\frac{x}{x+95}

\implies tan 33^{\circ}=\frac{x}{x+95}

\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x

\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}

\implies -0.3505924068 x = - 61.6937213538

x=175.969930202\approx 175.97\text{ cm}

4 0
3 years ago
Bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number
maw [93]

9/20 is the probability that Bob's password consists of an odd single-digit number followed by a letter and a positive single-digit number

It is given that bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number (which could be the same as the first one).

P (odd single digit number )  =  ( 5 odd single digits / 10 non-negative single digits)  = (5/10)  = 1/2

P (positive single digit number ) =  (9 positive single digits / 10 non-negative single digits)  = 9/10

The total probability is   (1/2) (9/10)  =  9/20

Learn more about word problems here: brainly.com/question/21405634

#SPJ4

5 0
2 years ago
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