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Arisa [49]
3 years ago
11

4. What is the equation of a line with a slope of 5 that passes through the point (4,2) ? Express this equation in all three for

ms: point-slope, slope-intercept, and standard.
Mathematics
2 answers:
Colt1911 [192]3 years ago
5 0
Incase you did not know, f(x) is a way of writing equations, for lines, if you do not know what the equation is.

2 = f(4)
f(x) = 5x-c
f(4) = 20-c
c = 20-2 = 18
f(x) = 5x-18

thus...
y = 5x-18

also...
the y intercept is -18
stiv31 [10]3 years ago
3 0
Slope = 5
y = mx + b
2 =5(4) + b
b = 2 - 20
b = -18


<span>point-slope equation
y - 2 = 5(x -4)

</span><span>slope-intercept equation
y = 5x - 18

standard form
5x - y = 18</span>
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A rectangular storage container with a lid is to have a volume of 2 m3. The length of its base is twice the width. Material for
Scilla [17]

Answer:

Dimensions are 2 m by 1 meter by 1 meter,

Minimum cost is $ 18.

Step-by-step explanation:

Let w be the width ( in meters ) of the container,

Since, the length is twice of the width,

So, length of the container = 2w,

Now, if h be the height of the container,

Volume = length × width × height

2 = 2w × w × h

1 = w² × h

\implies h=\frac{1}{w^2}

Since, the area of the base = l × w = 2w × w = 2w²,

Area of the lid = l × w = 2w²,

While the area of the sides = 2hw + 2hl

= 2h( w + l)

= 2\times \frac{1}{w^2}(w+2w)

=\frac{6w}{w^2}

=\frac{6}{w}  

Since, Material for the base costs $1 per m². Material for the sides and lid costs $2 per m²,

So, the total cost,

C(w) = 1\times 2w^2+2\times 2w^2 + 2\times \frac{6}{w}

=2w^2+4w^2+\frac{12}{w}

=6w^2+\frac{12}{w}

Differentiating with respect to w,

C'(w) = 12w -\frac{12}{w^2}

Again differentiating with respect to w,

C''(w) = 12 + \frac{24}{w^3}

For maxima or minima,

C'(w) = 0

\implies 12w -\frac{12}{w^2}=0

\implies 12w^3 - 12=0

w^3-1=0\implies w = 1

For w = 1, C''(w) = positive,

Hence, for width 1 m the cost is minimum,

Therefore, the minimum cost is C(1) = 6(1)²+12 = $ 18,

And, the dimension for which the cost is minimum is,

2 m by 1 meter by 1 meter.

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Step-by-step explanation:

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119 = 7x + 21

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