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3 years ago

Rewrite the hyperbolic equation 4y^2 -9x^2 +54x-8y-113=0

Mathematics

1 answer:

maksim [4K]3 years ago

6 0

Answer:

Standard form:

(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1

Step-by-step explanation:

4y^2 -9x^2 +54x-8y-113=0

-9(x^2 - 6x) + 4(y^2 - 2y) - 113 = 0

Completing the square:-

-9 [(x - 3)^2 - 9] + 4 [ y - 1)^2 - 1] = 113

-9(x - 3)^2 + 81 + 4(y - 1)^2 - 4 = 113

-9(x - 3)^2 + 4(y - 1)^2 = 113 - 77

-9(x - 3)^2 + 4(y - 1)^2 = 36.

Divide through by 36:-

(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1.

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The coordinate pairs could represent the the vertices of a triangles congruent to KLM?

Pavlova-9 [17]

Answer:

Step-by-step explanation:

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3 years ago

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Find ten solutions to the linear equation to the linear equation 1/2x+y=5

yuradex [85]

Answer:

(0,5), (2,4), (4,3), (6,2), (8,1), (10,0), (12,-1), (14,-2), (16,-3), (18,-4), and (20,-5)

Step-by-step explanation:

The given linear equation is :

$\frac{1}{2} x + y = 5$

$y = - \frac{1}{2} x + 5$

Any ordered pair that satisfies this equation is a solution.

When x=0,

$y = - \frac{1}{2} \times 0 + 5 = 5$

(0,5) is a solution

When x=2,

$y = - \frac{1}{2} \times 2+ 5 = 4$

(2,4) is a solution.

When x=4,

$y = - \frac{1}{2} \times 4+ 5 = 3$

(4,3) is a solution;

When x=6:

$y = - \frac{1}{2} \times 6+ 5 = 2$

(6,2).

When x=8,

$y = - \frac{1}{2} \times 8 + 5 = 1$

Another solution is (8,1)

When x=10,

$y = - \frac{1}{2} \times 10 + 5 = 0$

(5,0) is a solution

When x=12,

$y = - \frac{1}{2} \times 12+ 5 = - 1$

(12,-1) is a solution.

When x=14,

$y = - \frac{1}{2} \times 14+ 5 = - 2$

When x=16, we get:

$y = - \frac{1}{2} \times 16 + 5 = - 3$

When x=18, we get:

$y = - \frac{1}{2} \times 18+ 5 = - 4$

7 0

4 years ago

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the

shepuryov [24]

The area of a shape is the amount of space it can occupy.

The surface area of the larger prism is 4 times the surface area of the smaller prism.

Let the dimension of one side of the smaller prism be: l and w

Let the dimension of one side of the bigger prism be: L and W

So, we have:

$L = 2l$

$W =2w$

The area of these corresponding sides are:

$A_1 =l \times w$ ---- the first

$A_1 = lw$

While, the area of the second is:

$A_2 =2l\times 2w\\$

$A_2 =4lw$

The ratio of these two sides are:

$Ratio = A_1 : A_4$

This gives

$Ratio = lw : 4lw$

Cancel out common terms

$Ratio = 1 : 4$

Express as fractions

$Ratio = \frac 14$

Also, we have:

$Ratio = \frac{Small}{Large}$

This gives

$\frac{Small}{Large} = \frac 14$

Cross multiply

$Large = 4 \tiimes Small$

$Large = 4\4Small$

Hence, option (c) is true