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olchik [2.2K]
3 years ago
15

Find an equation of the line perpendicular to the graph of 28x-7y=9 that passes through the point at (4,1)

Mathematics
1 answer:
kifflom [539]3 years ago
3 0

If it is perpendicular to the line 14x-7y=4, then we know our line has the opposite and inverse slope of that line. Solving for y of the first line, we get y=2x-(4/7). All we care about is the coefficient of the x term, because that will give us our slope. The slope of the first line is 2, so the slope of out line is the opposite and inverse of that slope, which -(1/2).

Plugging into our slope- point formula, where y1=(-9), x1=2, and m=(-1/2), then:

y-(-9)=(-1/2)(x-2)

y+9=(-1/2)x+1

y=(-1/2)x-8

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Step-by-step explanation:

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3 years ago
An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made
Lemur [1.5K]

Answer:

The dimension of box=2ft\times 2ft\times 1ft

Step-by-step explanation:

We are given that

Volume of box=4 cubic feet

Let x be the side of square base and h be the height of box

Volume of box=lbh=x^2h

4=x^2h

h=\frac{4}{x^2}

Now, surface area of box,A=x^2+4xh

A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}

\frac{dA}{dx}=2x-\frac{16}{x^2}

\frac{dA}{dx}=0

2x-\frac{16}{x^2}=0

2x=\frac{16}{x^2}

x^3=8

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Substitute x=2

\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0

Hence, the area of box is minimum at x=2

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Hence, the dimension of box=2ft\times 2ft\times 1ft

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2 years ago
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Answer:

Option B.

Step-by-step explanation:

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We need to express "next integer after the integer n" mathematically. So, we need to add 1 in n.

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