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3 years ago

Solve using substitution y=x y=-2x+9

Mathematics

1 answer:

balu736 [363]3 years ago

8 0

Answer: x= (-1/7) and y= 8/5/7

Step-by-step explanation:

I don't know if I got it wrong or not but if I did please tell me.

HOPE I HELPED!!

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Solve the inequality<br> 3n + 2 > 17

Sergio039 [100]

Answer:

n > 5

Step-by-step explanation:

6 0

3 years ago

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A rectangular storage container with an open top is to have a volume of 10 m3 . then length of its base is twice the width. mate

katrin [286]

Answer:

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

$\text{Volume} =\text{Length} \times \text{Width} \times \text{Height}$

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

$10 =2w\times w\times h$

$10=2w^2h$

The height in terms of width is represented as,

$h=\frac{10}{2w^2}$

$h=\frac{5}{w^2}$

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

$C=10(L\times W)+6(2\times L\times H+2\times W\times H)$

$C=10(2w\times w)+6(2\times 2w\times \frac{5}{w^2}+2\times w\times \frac{5}{w^2})$

$C=20w^2+\frac{120}{w}+\frac{60}{w}$

$C(w)=20w^2+\frac{180}{w}$

To get the minimum value,

Differentiate the cost w.r.t 'w',

$C'(w)=20\frac{d(w^2)}{dw}+180\frac{d(w^{-1})}{dw}$

$C'(w)=20\times 2w-180 w^{-2}$

$C'(w)=40w-\frac{180}{w^2}$

To find critical points put derivate =0,

$40w-\frac{180}{w^2}=0$

$40w=\frac{180}{w^2}$

$w^3=\frac{180}{40}$

$w=\sqrt[3]{4.5}$

$w=1.65$

We find the second derivative to minimize,

$C''(w)=40\frac{d(w)}{dw}-180\frac{d(w^{-2})}{dw}$

$C''(w)=40+360(w^{-3})$

$C''(w)>0$

As $C''(w)>0$ it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

$C(1.65)=20(1.65)^2+\frac{180}{1.65}$

$C(1.65)=54.45+109.09$

$C(1.65)=163.54$

Therefore, the cost of materials for the cheapest such container is $163.54.

7 0

4 years ago

14.............................

exis [7]

Answer:

A. 3

Step-by-step explanation:

6 0

3 years ago

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90 POINTSSSSSSS:

denis23 [38]

Answer:

Part A: 12 plus x, the x being how much money he made on Sunday.

Part B: 2 plus x times 2

Step-by-step explanation:

3 0

3 years ago

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Which statement best compares the spread of the data sets?

MrRa [10]

Answer:

Choice B is correct

Step-by-step explanation:

The Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.

The spread of a data set is a measure of the dispersion or variability of the data set. The spread can be measured by various statistical quantities depending on the nature of the data (skewed or symmetric);

The IQR

Variance

Standard Deviation

Range

A box plot is a graphical representation of the five number summary;

The minimum, first quartile, median, third quartile, and the maximum value in that order.

The IQR is defined as;

third quartile - first quartile

With this definition, the Interquartile Range (IQR) for Florida is;

28 - 17 = 11

while the Interquartile Range (IQR) for Australia is;

14 - 10 = 4

Therefore, the Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.

5 0

3 years ago