Ask question

Ask question

All categories

2 years ago

12

A commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude o

f 41,000 feet. Model the most fuel-efficient altitudes using a compound inequality.
x ≥ 29,000 and x ≤ 41,000
x ≤ 29,000 and x ≥ 41,000
x ≥ 41,000 and x ≥ 29,000
x ≤ 41,000 and x ≤ 29,000

1 answer:

Cloud [144]2 years ago

7 0

Answer:

$x\geq 29,000$ and $x\leq 41,000$

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

$x\geq 29,000$

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

$x\leq 41,000$

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

$x\geq 29,000$ and $x\leq 41,000$

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

You might be interested in

Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. T

Blizzard [7]

Answer:

The area of the square base is 114 in. 2

The area of each triangular face is 66 in. 2

Gabriel will need 408 in. 2 of paint

8 0

2 years ago

Read 2 more answers

he temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the

PIT_PIT [208]

We have that
<span>K = C + 273.15
solve for C
subtract 273.15 both sides
K-273.15=C
C=K-273.15

the answer is
</span>C=K-273.15<span>

</span>

5 0

2 years ago

Read 2 more answers

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

Jocelyn is considering taking out one of the two following loans. Loan H is a three-year loan with a principal of $5,650 and an

Alexus [3.1K]

<span>c.<span>Loan I's monthly payment will be $11.88 smaller than Loan H's.</span></span>

7 0

2 years ago

Read 2 more answers

The correlation coefficient for the ages of drivers in a driver safety class and the number of traffic violations they have rece

Doss [256]

A correlation coefficient is always a value in between -1 and 1
The closest a coefficient to -1, the correlation is a strong negative correlation
The closest a coefficient to 1, the correlation is a strong positive correlation
The closest a coefficient to 0, there is no correlation at all

The coefficient -0.61 shows a strong negative correlation
This means that the relationship between the age and the violation is an inverse relationship; as age increases, violation decreases

Answer: option C

7 0

2 years ago