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2 years ago

Find the unit rate. Round to the nearest hundredth, if necessary. $5.99 for 19 lb

Mathematics

1 answer:

sveta [45]2 years ago

5 0

Answer:

0.315 per lb

Step-by-step explanation:

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5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:

Damm [24]

The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.

$(a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}$

(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.

Reasons:

(a) The distance from the cart to the pulley, r is given by Pythagoras's

theorem as follows;

r = √((3 - 0.6)² + x²) = √(2.4² + x²)

The speed of the wagon = $\mathbf{\dfrac{dx}{dt}}$

The speed of the rope, q = $\mathbf{\dfrac{dr}{dt}}$

By chain rule, we have;

$\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}$

$\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}$

Therefore;

$\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}$

$\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}$

(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;

$\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243$

The speed of the wagon when x = 0.6 and q = 0.5 m/s, $\dfrac{dx}{dt}$ ≈ 0.243 m/s

Learn more here:

brainly.com/question/17081984

4 0

2 years ago

F(x) = –2x2 + 17 Find f(10)

nikdorinn [45]

Answer:

If its -2x^2+17 the answer would be -183.

Step-by-step explanation:

-2(100)+17

-200+17

= -183

4 0

3 years ago

Read 2 more answers

A young oak tree is planted when it is 5 cm tall. It grows 3 cm every month. Write an equation to describe its growth

Naily [24]

Answer:

y=3x+5

Since it's already 5 cm we have +5

every month it would go up by 3 cm so we have 3 and x is to represent the # of months.

8 0

3 years ago

A glass contains 250.55 mL of water the actual amount of water in a glass was 279.45 ml to the nearest tenth of percent what is

dezoksy [38]

%= (exact-appropriate)/exact
so 279.45-250.55 divided by 279.45
basically .103417 nearest tenth is 10.3%
i believe

5 0

2 years ago

Jug

lesantik [10]

Answer:

1050 ml ÷1000 = 1.05 liters of water

6 0

3 years ago