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3 years ago

13

write an equation in point slope form of the line that passes through the point (3, -1) and has a slope of -2

1 answer:

Marysya12 [62]3 years ago

8 0

Answer:

m= -2

X1=3 Y1= -1

Y-Y1=m(X-X1)

Y-(-1)= -2(X-3)

Y+1= -2X+6

Y=-2X+6-1

Y=2X=5

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When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither nu

o-na [289]

The answer would be A. When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither numerator determinant is zero, then the system has infinite solutions. It would be hard finding this answer when we use the Cramer's Rule so instead we use the Gauss Elimination. Considering the equations:

x + y = 3 and <span>2x + 2y = 6
Determinant of the equations are </span>
<span>| 1 1 | </span>
<span>| 2 2 | = 0
</span>
the numerator determinants would be
<span>| 3 1 | . .| 1 3 | </span>
<span>| 6 2 | = | 2 6 | = 0.
Executing Gauss Elimination, any two numbers, whose sum is 3, would satisfy the given system. F</span>or instance (3, 0), <span>(2, 1) and (4, -1). Therefore, it would have infinitely many solutions. </span>

3 0

3 years ago

The volume of a cube is 512 cm3 . What is the area, in square centimetres, of each side of the cube?

lesantik [10]

Answer:

Step-by-step explanation:

V of a cube is s^3

V = 512

s = cube root of (V)

s = cube root of 512 cm^3

s = 8

The area of one face of the cube is s^2

s = 8

Area 1 face = 8^2

Area of 1 face = 64 cm^2

4 0

2 years ago

Kaya's family spends \$ 105$105 to rent a boat for 77 days. The total cost, cc, of the boat rental is proportional to the number

Anastaziya [24]

$c = 15d$

Step-by-step explanation:

find the value of the constant of proportionality k

$k = \frac{v}{d}$

c =total cost

d =days

8 0

2 years ago

MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

Please help please <br><br> -2x - x + 8 = ?

nataly862011 [7]

Answer:

-3x + 8

Step-by-step explanation:

Simplify. combine like terms (terms with the same amount of variables).

Subtract -2x and x: -2x - x = -3x

-3x + 8 is your answer.

~

7 0

3 years ago