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2 years ago

If you were to plot y versus m using the equation y = (g/k) m yo, how would you calculate the value for k?

Mathematics

1 answer:

Zanzabum2 years ago

3 0

Equation is given as;

y = (g/k) yo

To find the value of “k”, divide both sides of the equation with yo;

y/yo = (g/k)yo/yo

it implies that;

y/yo = (g/k)

Now following steps will obtain the value of “k” as;

ky/yo = g

ky = gyo

k = gy0/y

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Identify the rule of inference that is used to derive the conclusion "You do not eat tofu" from the statements "For all x, if x

Arturiano [62]

Answer:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )

Step-by-step explanation:

1) Tofu is healthy

2) Tofu is healthy to eat

3) Tofu eats what taste good

1a) For all x, if x is healthy to eat

2a) For all x, if x is not healthy to eat, then x does not taste good.

3a) For all x, if x is healthy to eat, then x is healthy to eat what tastes good

For all x in order to symbolize the statement

1(a) 2(a) 3(a)

If we use:

A(x): Tofu is healthy

B(x): Tofu is healthy to eat

C(x): Tofu eats what taste good

E(x): Tofu only eat what tastes good

If we symbolize "For all x" by the symbol ∀ then then the propositions 1(a), 2(a) and 3(a) can be written as:

1(b) ∀ (A(x) ⇒ B(x) )

2(b) ∀ (B(x) ⇒ C(x) )

3(b) ∀ (B(x) ⇒ E(x) )

6 0

2 years ago

On a science test, 2 points are deducted from a total of 100 points for each question answered incorrectly. Trevor scored an 84

valentinak56 [21]

Trevor answered seven questions incorrectly.

6 0

1 year ago

Order from least to greatest 2.8%, 7/40, 1/50, 0.044

lord [1]

Answer:

1/50 < 2.8% < 0.044 < 7/40

Step-by-step explanation:

2.8%, 7/40, 1/50, 0.044

2.8% = 0.028 = 28/1000
7/40 = 0.175 = 175/1000
1/50 = 0.020 = 20/1000
0.044 = 44/1000

Ordering in ascending order

20/1000 < 28/1000 < 44/1000 < 175/1000

Same order in original numbers

1/50 < 2.8% < 0.044 < 7/40

3 0

2 years ago

Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .