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Vikki [24]
3 years ago
11

Jika garis 4x+ay = 8 dan ay=9x + 5 saling tegak lurus,maka nilai a

Mathematics
1 answer:
barxatty [35]3 years ago
4 0

We are given equations as

4x+ay=8

Firstly, we will write in slope intercept form of line

y=mx+b

4x+ay=8

Subtract both sides by 4x

4x+ay-4x=-4x+8

ay=-4x+8

now, we can divide both sides by a

y=-\frac{4}{a} x+\frac{8}{a}

we can find slope

so, we get

m_1=-\frac{4}{a}

we are given second equation as

ay=9x+5

Firstly, we will write in slope intercept form of line

y=mx+b

divide both sides by a

y=\frac{9}{a} +\frac{5}{a}

we can find slope

m_2=\frac{9}{a}

we are given both lines are perpendicular

so, the multiplication of their slopes must  be -1

m_1\times m_2=-1

we can plug values

-\frac{4}{a}\times \frac{9}{a}=-1

now, we can solve for a

\frac{36}{a^2}=-1

Multiply both sides by a

\frac{36}{a^2}\times a^2=1\times a^2

36= a^2

now, we can solve for a

we get

a=-6,a=6...............Answer

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4 0
3 years ago
A farmer plans to fence a rectangular pasture adjacent to a river the pasture must contain 405,000 square meters
jeyben [28]

The dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.

<h3>What is the area of the rectangle?</h3>

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let's suppose x and y are the sides of the rectangular garden and y is the parallel to the river.

Then according to the problem:

2x + y = P ..(1)

P is the perimeter of the rectangle.

xy = 405000  (area of the rectangle)

Plug the value of y in the equation (1) from the above equation.

P(x) = 2x + 405000/x

P'(x) = x—405000/x² = 0

x = 450 m

P''(x) > 0 hence at x = 450 the value of P(x) is minimum.

y = 405000/450

y = 900 m

P(min) = 1800 m

Thus, the dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.

Learn more about the rectangle here:

brainly.com/question/15019502

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7 0
2 years ago
What is 4 divided by 3/4?
musickatia [10]

Answer:

16/3 or 5.33

Step-by-step explanation:

Cross multiply

4/1 * 3/4

4 * 4 = 16

3 * 1 = 3

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2 years ago
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Answer:

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2 years ago
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Answer:

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Step-by-step explanation:

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8 0
3 years ago
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