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2 years ago

Don't really understand this math question yet

Mathematics

1 answer:

olga_2 [115]2 years ago

7 0

Arranging the given distances from sea level on the number line, we have;

The error made by taking Egypt as being further from the sea level is assuming that the sea level is at the beginning (left) of the number line.

<h3>How can the number line be used to find the distance from the sea level?</h3>

The given elevation of the lowest points in the six countries are;

Country. Lowest point elevation (m)

China. →. -154

Egypt →. -133

Azerbaijan → -28

Serbia. →. 35

Israel. → -408

Laos. →. 70

Sorting the above countries from the country with the lowest point below sea level to the country with the highest point above sea level gives;

Israel → -408

China → -154

Egypt → -133

Azerbaijan → -28

Serbia. → 35

Laos. →. 70

On a number line, we have;

Israel < China < Egypt < Azerbaijan < Serbia < Laos

Relative to zero, which is the sea level, points -133 and -154 are located to the left of zero.

However, point -133 > -154, therefore, -154 < -133, the symbol < represents lesser (in this case 'lower') which indicates that China (point -154) is lower or further left from zero which is the sea level than Egypt (point -133).

The error is therefore mistaking the location of the sea level as being at the extreme left of the number line, rather than at the middle.

Learn more about the number line here:

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(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in

Sophie [7]

Answer:

Step-by-step explanation:

$\text{Show that a differentiable function f decreases most rapidly at x in the }$

$\text{direction opposite the gradient vector, that is, in the direction of}$ $-\bigtriangledown f(x)$ $\text{. Let}\ \theta \ \text{be the angle between} \bigtriangledown f(x) \ \text{and unit vector u. Then } D_u f = \mathbf{|\bigtriangledown f| \ cos \ \theta }}$

$\text{Since the minimum value of} \ \ \mathbf{cos \ \theta} \ \ is \mathbf{-1} \ \text{occuring \ for \ 0} \le \ \theta \ < 2x, \\ \\ when \ \theta = \mathbf{\pi} , \text{the mnimum value of} \ D_uf \ is} -|\bigtriangledown f|, \text{occuring when the direction of u is } \\ \\ \ \mathbf{the \ opposite \ of} \ \text{the direction of } \ \bigtriangledown f (assuming \ \bigtriangledown f\ is \ not \ zero)$

b) $\text{From part A:}$

$If \ f(x,y) = x^4y -x^2y^2 \ \ decreases \ fastest \ at \ the \point \ (2,-5)\\ \\ F(x,y) = x^4y -x^2y^3 \\ \\ f_x = \dfrac{df}{dx}= \dfrac{d}{dx}(x^4y-x^2y^3) \\ \\ f_x = \dfrac{df}{dx}= y4x^3 -2y^3x \\ \\ For(2,-5) \\ \\ f_x = (-5)4(2)^3 -2(-5)^3(2) \\ \\ \mathbf{ f_x = 340}$

$However; f_y = \dfrac{df}{dy} = \dfrac{d}{dy}(x^4y - x^2y^3) \\ \\ f_y = x^4 -3x^2y^2 \\ \\ Now, for (2, -5)\\ \\f_y = (2)^4 -3(2)^2(-5)^2 \\ \\ f_y = -284$

$So; \bigtriangledown = < 340,-284> \text{this is the direction of fastest decrease}$

6 0

3 years ago

0.125 in a fraction form

Yakvenalex [24]

$0.125=\frac{125}{1000}=\frac{1 \times 125}{8 \times 125}=\boxed{\frac{1}{8}}$

4 0

4 years ago

Read 2 more answers

Which of the following fractions have repeating decimal representations? Which have terminating decimal representations?

natali 33 [55]

Repeating decimal representation will be 3/13, 7/24. Terminating decimal representation will be 3/16, 4/125.

<h3>What is decimal?</h3>

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The base-10 number system, arguably the most widely used number system, is referred to as decimal. The decimal number system consists of ten single-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The number following nine is 10.

Here,

Repeating decimal representation,

=3/13, 7/24

Terminating decimal representation,

=3/16, 4/125

3/13 and 7/24 will be repeated in decimal form. The final two decimal places are 3/16 and 4/125.

To know more about decimal,

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7 0

2 years ago

I need help with this ASAP! Its about budgeting.

Umnica [9.8K]

Answer:

Step-by-step explanation:

I gave you all of the information to fill out the first page

i also answered some of the questions on the 2nd page. They are written sideways on the page. The other questions I didn’t answer yneed calculations after you add all of the expenses together.

put the amounts from each category I listed in the image and put them into the respective category and get the total for each category. Use those totals to fill out page two. If you get stuck I don’t mind helping but I thought this is the best way to get you started.