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3 years ago

Solve 2/3 divided by 4/5 a.6/15 b.6/8 c.8/15 d.5/6

Mathematics

2 answers:

Bumek [7]3 years ago

6 0

Answer:

d.5/6

Step-by-step explanation:

2/3÷4/5

2/3×5/4

5/6

vladimir1956 [14]3 years ago

6 0

Answer:

2/3÷ 4/5 is 5/6

Step-by-step explanation:

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Given the position of the particle, what the position(s) of the particle when it’s at rest

choli [55]

The position function of a particle is given by:

$X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t$

The velocity function is the derivative of the position:

$\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}$

The particle will be at rest when the velocity is 0, thus we solve the equation:

$2t^2-9t-18=0$

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

$t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Substituting:

$\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}$

We have two possible answers:

$\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}$

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

$undefined$

6 0

1 year ago

Select the two values of x that are roots of this equation.<br> 2x^2+ 1 = 5x

iren [92.7K]

Answer:

$\frac{5+\sqrt{17}}{4}$ , $\frac{5-\sqrt{17}}{4}$

Step-by-step explanation:

One is asked to find the root of the following equation:

$2x^2+1=5x$

Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:

$ax^2+bx+c=0$

Change the given equation using inverse operations,

$2x^2+1=5x$

$2x^2-5x+1=0$

The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:

$\frac{-b(+-)\sqrt{b^2-4ac}}{2a}$

Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,

$\frac{-b(+-)\sqrt{b^2-4ac}}{2a}$

$\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}$