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Law Incorporation [45]

4 years ago

14

Consider each equation and solution. Is each solution correct? Select yes or no. 6 = − r 3 ; r = −2 a yes b no 1 − 2s = 3; s = 5

a yes b no 4 + 6t = −20; t = −4 a yes b no

1 answer:

Ahat [919]4 years ago

7 0

No − r 3 ; r = −2 a yes b no 1 − 2s = 3; s = 5 a

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Use slopes to determine if the triangle whose vertices are left parenthesis negative 3 comma 3 right parenthesis, left parenthe

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

vertices are A(-3,3),B(-2,4),C(4,0)

slope of AB=(4-3)/(-2+3)=1/1=1

slope of BC=(0-4)/(4+2)=-4/6=-2/3

slope of CA=(3-0)/(-3-4)=-3/7

two lines are perpendicular if product of slopes=-1

so it is not a right angled triangle .

4 0

4 years ago

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John has $1 in a savings account that earns 5% interest compounded annually

kiruha [24]

Answer:

16 cents

Step-by-step explanation:

A = P (1 + r)n

A = $1 (1 + 0.05)3

A = $1 x 1.16

A = $1.16

To find the compound interest only;

Compound Interest = Final Value - Initial Value

Compound Interest = $1.16 - $1

Compound Interest = $0.16

Hence the compound interest John will earn in his savings account will be 16 cents.

3 0

4 years ago

(a) The plane y + z = 13 intersects the cylinder x2 + y2 = 25 in an ellipse. Find parametric equations for the tangent line to t

klemol [59]

Answer:

Step-by-step explanation:

We have a curve (an ellipse) written as the system of equations

$\begin{cases} y+z &= 13\\ x^2+y^2 &= 25\end{cases}$ .

And we want to calculate the tangent at the point (3,4,9).

The idea in this problem is to consider two variables as functions of the third. Usually we consider $y$ and $z$ as functions of $x$ . Recall that a curve in the space can be written in parametric form in terms of only one variable. In this case we are considering the ‘‘natural’’ parametrization $(x, y(x), z(x))$ .

Recall that the parametric equation of a line has the form

$r(t)=\begin{cases} x(t) &= x_0 + v_1t \\ y(t) &= y_0 +v_2t\\ z(t) &= z_0 +v_3t \end{cases}$ ,

where $(x_0,y_0,z_0)$ is a point on the line (in this particular case is (3,4,9)) and $(v_1,v_2,v_3)$ is the direction vector of the line. In this case, the direction vector of the line is the tangent vector of the ellipse at the point (3,4,9).

Now, if we have the parametric equation of a curve $(x, y(x), z(x))$ its tangent line will have direction vector $(1, y'(x), z'(x))$ . So, as we need to calculate the equation of the tangent line at the point $(3,4,9) = (3, y(3), z(3))$ , we must obtain the tangent vector $(1, y'(3), z'(3))$ . This part can be done taking implicit derivatives in the systems that defines the ellipse.

So, let us write the system as

$\begin{cases} y(x)+z(x) &= 13\\ x^2+y^2(x) &= 25\end{cases}$ .

Then, taking implicit derivatives:

$\begin{cases} y'(x)+z'(x) &= 0 \\ 2x+2y(x)y'(x) &= 0\end{cases}$ .

Now we substitute the values $x=3$ and $y(3)=4$ , and we get the system of linear equations

$\begin{cases} y'(3)+z'(3) &= 0 \\ 2\cdot 3+2\cdot 4y'(x) &= 0\end{cases}$ ,

where the unknowns are $y'(3)$ and $z'(3)$ .

The system is

$\begin{cases} y'(3)+z'(3) &= 0 \\ 6+8y'(x) &= 0\end{cases}$ ,

and its solutions are

$y'(3) = -\frac{3}{4}$ and $z'(3) = \frac{3}{4}$ .

Then, the direction vector of the tangent is

$(1, -\frac{3}{4}, -\frac{3}{4})$ .

Finally, the tangent line has parametric equation

$r(t)=\begin{cases} x(t) &= 3 + t \\ y(t) &= 4 -\frac{3}{4}t\\ z(t) &= 9 +\frac{3}{4}t \end{cases}$

where $t\in\mathbb{R}$ .

7 0

4 years ago

The force, F, needed to break a board in a martial arts class varies inversely with the length, L, of the board. If it takes 24

9966 [12]

Answer:

it would take 40 pounds of pressure to break the board.

Step-by-step explanation:

$F = \frac{x}{L}$

Now we plug in the numbers of force and length

$24 =\frac{k}{2.5}$

Now we multiply both sides by 2.5 to get rid of the fraction.

$60=x$

Now we plug in our variation constant

$F=\frac{60}{L}$

So we convert the length of 2.5 feet into inches. This is 18 inches. Since there are 12 inches in one foot, we have that 18 inches is equal to 18 divided by 12.

18÷12=1.5

We get that 18 inches is equal to 1.5 feet

we plug L = 1.5 into our inverse variation equation and solve for F.

$F=\frac{60}{1.5}$

This simplifies to F = 40

If you have any questions feel free to ask in the comments - Mark

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4 years ago

Simplify -3/5 ÷ 7/6 what is the answer

Nesterboy [21]

-3/5 divided by 7/6 is -18/35

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3 years ago

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