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3 years ago

True Or False?

Mathematics

1 answer:

MariettaO [177]3 years ago

4 0

False, would mess up your whole geometric figure including the equation.

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A car breaks from a speed of 108km/h to 72km/h during a displacement of 100m, what is its aceleration ?

sergejj [24]

First, note that 100 m = 0.100 km.

Recall that

v² - u² = 2 a ∆x

where u and v are initial and final velocities; a is acceleration; and ∆x is displacement. Solve for a :

(72 km/h)² - (108 km/h)² = 2 a (0.100 km)

a = ((72 km/h)² - (108 km/h)²) / (0.200 km)

a = -32,400 km/h²

If you want to convert this to m/s², we have

(-32,400 km/h²) = (-32,400 km/h²) (1000 m/km) (1/3600 h/s)²

(-32,400 km/h²) = -2.50 m/s²

4 0

3 years ago

Calculus Application

Fiesta28 [93]

<h3>Answer:</h3>

-8/3 ft/s

<h3>Step-by-step explanation:</h3>

We are given:

distance of the top of the ladder from the ground (h) = 12 ft

height of the ladder = 20 ft

rate of change of the distance of the base of ladder from the wall (dx/dt):

2 ft/s

Finding the distance of the base of the ladder from the wall:

From the Pythagoras's Theorem, we know that:

hypotenuse² = height² + base²

replacing the given values

20² = 12² + x²

400 = 144 + x²

x² = 256 [subtracting 144 from both sides]

x = 16 ft [taking the square root of both sides]

The rate of change of the height of the Ladder from the ground:

We know that:

h = 12 ft

( $\frac{dh}{dt}$ ) = ?

x = 16 ft

( $\frac{dx}{dt}$ ) = 2 ft/s

According to the Pythagoras's Theorem:

20² = x² + h²

differentiating both sides with respect to time

$\frac{d(400)}{dt} = \frac{d(x^{2} + h^{2})}{dt}$

$0 = \frac{d(x^{2})}{dt} + \frac{d(h^{2})}{dt}$

$0 = \frac{d(x^{2})}{dx}(\frac{dx}{dt}) + \frac{d(h^{2})}{dh}(\frac{dh}{dt})$

$0 = 2x(\frac{dx}{dt}) + 2h(\frac{dh}{dt})$

replacing the variables

$0 = 2(16)(2) + 2(12)(\frac{dh}{dt})$

$0 = 64 + 32(\frac{dh}{dt})$

$-64 =32(\frac{dh}{dt})$ [subtracting 64 from both sides]

$\frac{-64}{32} =(\frac{dh}{dt})$ [dividing both sides by 32]

$\frac{dh}{dt} = \frac{-8}{3} ft/s$

Hence, the ladder will slide down at a speed of 8/3 feet per second

7 0

3 years ago

One to one relationships describe situations where people are matched with with unique identities, such as their Emirates ID num

GuDViN [60]

A one to one function is a function which matches exactly one x value with exactly one y value. The fancy term for this is an injective function.

4 0

3 years ago

What are the features of the function f(x) = –2 (2)x + 4 graphed below?

julia-pushkina [17]

Answer:

Plot each graph on the same coordinate system.

f(x)=−2

(2)x+4

Step-by-step explanation:

5 0

3 years ago

Leon tried to solve an equation step by step.

In-s [12.5K]

Step-by-step explanation:

in step 2 leon made mistake

8 0

3 years ago

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