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dlinn [17]
3 years ago
5

I want help its urgent!!! (iv), (v), (vi) Questions​

Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0

Solution:

iv) Given equation: x^{2} - y^{2} - 4x - 2y + 3

Since we are given two variables, we need to split the original expression into two quadratic expressions as

x^{2} - 4x + 4 - y^{2} - 2y - 1

Factoring x first:

x^{2} - 4x + 4 = x^{2} - 2x - 2x + 4

= x (x - 2) - 2 (x-2)

= (x-2)(x-2)

= (x-2)^{2}

Factoring y now:

-y^{2} - 2y - 1 = -1(y^{2} + 2y + 1)

= -1(y^{2} + y + y + 1)

= -1[ y(y+1) + 1(y+1)]

= -1 [(y+1)(y+1)]

= (y+1)(-y-1)

Therefore, the original expression becomes

(x-2)^{2}+(y+1)(-y-1)\\or \\(x-2)(x-2) + (y+1)(-y-1)

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The new area of the given replica's base is; 6250 m²

<h3>What is the required area?</h3>

We are given;

Area of base of statue = 625 m²

Now, an artist wants to create a replica of the base of statue but in the ratio 1:10.

This means that the area will increase by a factor of 10 as 1 sq.unit of the old area will represent 10 sq. units in the new one.

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If 2 liters of sea water contain 70 grams of salt, how much salt is in 32 liters of seawater?
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