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3 years ago

6

Another middle schooler (Swimmer 2) swims 24 laps in 20 minutes, what is the unit rate?

1 answer:

prohojiy [21]3 years ago

6 0

Answer:

1.2 laps per minute

Step-by-step explanation:

divide laps/minutes.

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Please answer the question from the attachment.

Serhud [2]

5/3 means (5 over 3 since I can't do fractions on this) 5/3-3/3=___ 5-3=2 first you do the numerators You keep the denominator the same since both denominators are 3 Then you put it together and get 2/3 and since 2/3 can't be reduced, 2/3 is the answer

4 0

4 years ago

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

Artemon [7]

Answer:

a) The height decreases at a rate of $\frac{7}{12}$ ft/sec.

b) The area increases at a rate of $\frac{527}{24}$ ft^2/sec

c) The angle is increasing at a rate of $\frac{1}{12}$ rad/sec

Step-by-step explanation:

Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.

a) Using pythagorean theorem, we have that $25^2 = h^2+b^2$ . From here, we have that

$h^2 = 25^2-b^2$

if we differentiate with respecto to t (t is time), by implicit differentiation we get

$2h \frac{dh}{dt} = -2b\frac{db}{dt}$

Then,

$\frac{dh}{dt} = -\frac{b}{h}\frac{db}{dt}$ .

We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,

$\frac{dh}{dt} = -\frac{2\cdot 7}{24}= \frac{-7}{12}$

b) The area of the triangle is given by

$A = \frac{1}{2}bh$

By differentiating with respect to t, using the product formula we get

$\frac{dA}{dt} = \frac{1}{2} (\frac{db}{dt}h+b\frac{dh}{dt})$

when b=7, we know that h=24 and dh/dt = -1/12. Then

$\frac{dA}{dt} = \frac{1}{2}(2\cdot 24- 7\frac{7}{12}) = \frac{527}{24}$

c) Based on the drawing, we have that

$\sin(\theta)= \frac{b}{25}$

If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get

$\cos(\theta)\frac{d\theta}{dt}=\frac{1}{25}\frac{db}{dt}$ or, by replacing the value of db/dt

$\frac{d\theta}{dt}=\frac{2}{25\cos(\theta)}$

when b = 7, we have that h = 24, then $\cos(\theta) = \frac{24}{25}$ , then

$\frac{d\theta}{dt} = \frac{2}{25\frac{24}{25}} = \frac{2}{24} = \frac{1}{12}$

7 0

3 years ago

Can someone please help me with 8,040 divied 12?with example

mylen [45]

Answer:

670

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Three bells ring at an interval of 10,20,and 30 minutes respectively. If they all ring together at 10:30 p.m.,at what time will

Ahat [919]

Answer:

11:30 PM

Step-by-step explanation:

This question is essentially asking for the lowest common multiple of 10, 20, and 30. If we write out all the multiples of each, we get:

10: 10, 20, 30, 40, 50, 60, 70, ...

20: 20, 40, 60, 80, ...

30: 30, 60, 90, ...

As you can see, the lowest common multiple is 60, and 60 minutes after 10:30 PM is 11:30 PM.

7 0

3 years ago

Read 2 more answers

Find the standard form of the equation of the circle with endpoints of a diameter at the points (5,6) and (-1,8)

netineya [11]

Very interesting problem

3 0

2 years ago