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4 years ago

The equation 2(4x + 1) = 4(2x + 5) has no solutions. Which of the following best explains why?

Mathematics

1 answer:

Vladimir79 [104]4 years ago

4 0

Answer:

See below

Step-by-step explanation:

$2(4x + 1) = 4(2x + 5)$

$8x + 2 =8x + 20$

$\nexists x \in \mathbb{R} \text{ That makes the equality true}$

The equation has no solution because no matter what the value we plug for $x$ in the equation, it will not be true and will lead to a contradiction. This is the meaning of not having a solution.

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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

Please help me graph!!!

jeka94

Step-by-step explanation:

go up 1 and across 3 crossing the y intercept on 5

is all i can do

but form a straight line

7 0

3 years ago

The points (-1, r) and (2, 3) lie on a line with slope -1.Find the missing coordinate r

Tomtit [17]

Answer:

r=0

Step-by-step explanation:

1) Place point (2, 3) on graph.

2) Use the slope of -1 to go left -1 and go down -1

3) Until you get to x value of -1

8 0

3 years ago

How does Rainsford end up on the island?

Pie

Answer:

he falls off the boat and swims ashore mainly because he's a rebel and junk and outta curiosity

Step-by-step explanation:

Hope it helps :) :p

7 0

3 years ago

Determine whether each function is even, odd, or neither. g(x) = |x-3| neither g(x) = x + x² neither

Lelechka [254]

Answer:

So, both the functions are neither even and nor odd.

Step-by-step explanation:

A function is even if g(x) = g(-x) and odd if g(x) = - g(x).

g(x) = |x-3|

g (-x ) = | -x -3 |

So, the function is neither even and nor odd.

g (x) = x + x²

g (- x) = (- x) + (- x) ² = - x + x²

So, the function is neither even and nor odd.

3 0

3 years ago