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2 years ago

Each scarf requires. Meters of yarn, and each beanie requires meters

Mathematics

1 answer:

stiv31 [10]2 years ago

8 0

1 scarf = 6m of yarn

1 beanie = 2m of yarn

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0

3 years ago

A sign language club made $627.50 from selling popcorn at a festival. The popcorn cost the club $95.00. Which expression represe

liq [111]

Answer:

option 3

Step-by-step explanation:

7 0

2 years ago

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What are vertically opposite angles

NeTakaya

When two lines cross, there are four angles at the place where they cross.
Two angles that do NOT share a side are vertical angles. There are two pairs
of vertical angles where the lines cross.

Also, by the way, vertical angles are always equal to each other. It's often
very helpful to know that.

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3 years ago

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A 20-ounce bag of popcorn costs $2.80. If the unit price stays the same, how much does a 35-ounce bag of popcorn cost?

Wittaler [7]

Answer:

I think the answer is C

4 0

2 years ago

Given the exponential equation 4x = 64, what is the logarithmic form of the equation in base 10?

zysi [14]

$4^{x} = 64$

By taking logarithmic of base 10

∴ $log 4^{x} = log 64$

∴ x log 4 = log 64

∴ $x = \frac{log \ 64}{log \ 4}$
note: we don't need to write the base in case of the base =10

∴ The correct choice is
x = log base 10 of 64, all over log base 10 of 4

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3 years ago

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