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3 years ago

9

Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?

1 answer:

12345 [234]3 years ago

5 0

Answer:

The equation of the parabola is,

x²+4y-12=0

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What are the domain and range of f(x)= (1/5)x

anyanavicka [17]

Answer:

domain and range is -∞,+∞

Step-by-step explanation:

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3 years ago

What is the equation of a line, in general form, that passes through the point (1, -2) and has a slope of 1/3.

slavikrds [6]

Y=1/3x+c as 1/3 is the gradient/slope
Plug in the coordinates into the equation
-2= 1/3*(1) +c
C=-2-1/3
C=-7/3
Y= 1/3x-7/3

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3 years ago

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Marcos is making three tile pictures.

Mazyrski [523]

Answer: 360

Step-by-step explanation:

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3 years ago

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A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

$H = \frac{64}{W^2}$

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

$Cost =18W^2 + \frac{768}{W^2}*3W$

$Cost =18W^2 + \frac{2304}{W}$

To minimize the cost, we differentiate

$C' =2*18W + -1 * 2304W^{-2}$

Then set to 0

$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

8 0

3 years ago

Jude types 1,170 characters in 6 minutes. What is her typing rate in characters per minute? A. 200 characters per minute B. 197

Kisachek [45]

Answer:

Option C) 195 characters per minute

Step-by-step explanation:

We are given the following in the question:

Jude types 1,170 characters in 6 minutes..

We have to find the typing rate in characters per minute.

Thus can be done in the following manner:

Typing rate =

$=\dfrac{1170\text{ characters}}{6\text{ minutes}}\\\\=195\text{ characters per minute}$

Thus, Jude speed in characters per minute is

Option C) 195 characters per minute

7 0

3 years ago