4. The value of y varies directly with x. When y = 275, x = -22 What is y when x = 17.5?

Mumbi is approximately 845 kilometers away from Bangalore, and Mumbai is approximately 1160 km away from Delhi. The distances, m

Mazyrski [523]

Mumbi is approximately 845 kilometers away from Bangalore, and Mumbai is approximately 1160 km away from Delhi, then the ratio between these distances is

$\dfrac{845}{1160}=\dfrac{169}{232}.$

A. Bangalore to Mumbai: 116.5 cm;

Mumbai to Delhi: 174 cm

The ratio:

$\dfrac{116.5}{174}=\dfrac{233}{348}\neq \dfrac{169}{232}$

This option is false.

B. Bangalore to Mumbai: 42.25

Mumbai to Delhi: 58 cm

The ratio is

$\dfrac{42.25}{58}=\dfrac{845}{1160}=\dfrac{169}{232}$

This option is true.

C. Bangalore to Mumbai: 23.4 cm

Mumbai to Delhi: 29 cm

The ratio is

$\dfrac{23.4}{29}=\dfrac{117}{145}\neq \dfrac{169}{232}$

This option is false.

D. Bangalore to Mumbai: 16.9 cm

Mumbai to Delhi: 23.2 cm

The ratio is

$\dfrac{16.9}{23.2}=\dfrac{169}{232}$

This option is true.

E. Bangalore to Mumbai: 25.35 cm

Mumbai to Delhi: 34.8cm

The ratio is

$\dfrac{25.35}{34.8}=\dfrac{507}{696}=\dfrac{169}{232}$

This option is true.

Answer: correct options are B, D and E

8 0

3 years ago

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a dock is 5 feet above water. suppose you stand on the edge of the dock and pull a rope to a boat at a constant rate of 2 ft/s.

Firdavs [7]

Answer:

The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.

Step-by-step explanation:

The diagram of the situation described is shown in the attached image.

The distance of the boat to the dock along the water level at any time is x

The distance from the person on the dock to the boat at any time is y

The height of the dock is 5 ft.

These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.

According to Pythagoras' theorem

y² = x² + 5²

y² = x² + 25

(d/dt) y² = (d/dt) (x² + 5²)

2y (dy/dt) = 2x (dx/dt) + 0

2y (dy/dt) = 2x (dx/dt)

When the boat is 4 ft from dock, that is x = 4 ft,

The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s

The speed with which the boat is approaching the dock = (dx/dt)

Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock

When the boat is 4 ft from the dock, x = 4 ft.

And we can obtain y at that point.

y² = x² + 5²

y² = 4² + 5² = 16 + 25 = 41

y = 6.40 ft.

So, to the differential equation relation

2y (dy/dt) = 2x (dx/dt)

when x = 4 ft,

y = 6.40 ft

(dy/dt) = 2 ft/s

(dx/dt) = ?

2 × 6.40 × 2 = 2 × 4 × (dx/dt)

25.6 = 8 (dx/dt)

(dx/dt) = (25.6/8) = 3.20 ft/s.

Hope this Helps!!!

4 0

3 years ago

Express each ratio as a fraction in simplest form. A. 2/29 B. 29/10 C. 20/29 D. 10/29

Tresset [83]

<span>Express 10 pints to 29 pints in simplest form.
The answer is 10/29 since 10 and 29 don't have a common factor to divide them both with. As a result, they stay as is 10/29 in already the simplest form. A is also in simplest form. B is in improper fraction form, also in simple form, can be turned into mixed number form. C is also in simplest form. The best answer is D since 10 pints to 29 pints is the instructions.</span>

6 0

3 years ago

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(Easy 30 points) Solve the equation to find a positive value of c: 3^2 + 4^ = c^2

shusha [124]

Answer:

C= 5, -5

Step-by-step explanation:

8 0

3 years ago

Find the slope of the line that passes through the points (−2/3, 3/4) and (5/6, −1/2).

EastWind [94]