How many almonds in the cup? (1/4 cup) Help me

Paul [167]

Answer:

$\frac{dc}{dt}\approx13.8146\text{ km/min}$

Step-by-step explanation:

We know that the plane travels at a <em>constant</em> speed of 14 km/min.

It passes over a radar station at a altitude of 11 km and climbs at an angle of 25°.

We want to find the rate at which the distance from the plane to the radar station is increasing 4 minutes later. In other words, if you will please refer to the figure, we want to find dc/dt.

First, let's find c, the distance. We can use the law of cosines:

$c^2=a^2+b^2-2ab\cos(C)$

We know that the plane travels at a constant rate of 14 km/min. So, after 4 minutes, the plane would've traveled 14(4) or 56 km So, a is 56, b is a constant 11. C is 90+20 or 115°. Substitute:

$c^2=(56)^2+(11)^2-2(56)(11)\cos(115)$

Evaluate:

$c^2=3257-1232\cos(115)$

Take the square root of both sides:

$c=\sqrt{3257-1232\cos(115)}$

Now, let's return to our law of cosines. We have:

$c^2=a^2+b^2-2ab\cos(C)$

We want to find dc/dt. So, let's take the derivative of both sides with respect to t:

$\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2+b^2-2ab\cos(C)]$

Since our b is constant at 11 km, we can substitute this in:

$\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-(11)^2-2a(11)\cos(C)]$

Evaluate:

$\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-121-22a\cos(C)]$

Implicitly differentiate:

$2c\frac{dc}{dt}=2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}$

Divide both sides by 2c:

$\frac{dc}{dt}=\frac{2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}}{2c}$

Solve for dc/dt. We already know that da/dt is 14 km/min. a is 56. We also know c. Substitute in these values:

$\frac{dc}{dt}=\frac{2(56)(14)-22\cos(115)(14)}{2\sqrt{3257-1232\cos(115)}}$

Simplify:

$\frac{dc}{dt}=\frac{1568-308\cos(115)}{2\sqrt{3257-1232\cos(115)}}$

Use a calculator. So:

$\frac{dc}{dt}\approx13.8146\text{ km/min}$

And we're done!

6 0

3 years ago

Which sentence is true?

Sloan [31]

Answer:

Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…

Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…

All integers belong to the rational numbers. A rational number is a number

ab,b≠0

Where a and b are both integers.

Example

The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:

41

or

82

or even

−8−2

Whereas

15=0.2

is a rational number but not an integer.

A rational number written in a decimal form can either be terminating as in:

15=0.2

Or repeating as in

56=0.83333...

All rational numbers belong to the real numbers.

If you look at a numeral line

picture05

You notice that all integers, as well as all rational numbers, are at a specific distance from 0. This distance between a number x and 0 is called a number's absolute value. It is shown with the symbol

|x|

If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. Opposites have the same absolute value since they are both at the same distance from 0.

|10|=10=|−10|

Step-by-step explanation:

3 0

3 years ago

On January 15, the end of the first pay period of the year North company employees earned 26,000 of sales salaries.

cluponka [151]

Step-by-step explanation:

Is this meant to be a question?

5 0

2 years ago

The perimeter of a rectangle is 72 m. The width of the rectangle is 16 m. What is the area of the rectangle?

liq [111]

Answer:

320m

Step-by-step explanation

a rectangle has four sides, two pairs of identical sides. So two sides are 16. So that adds up to 32. Perimeter is all sides added together. so it has to add up to 72. 72 minus 32 is 40, so two of the sides have to be 40. Area is length times width, so 16 times 20, which is 320.

6 0

2 years ago

A girrafe runs at a rate of 32 miles per hour. Which equation models the situation?

Anastasy [175]

Answer:A girrafe runs at a rate of 32 miles per hour. Which equation models the situation?

Step-by-step explanation:

4 0

3 years ago

How many almonds in the cup? (1/4 cup) Help me​

How many almonds in the cup? (1/4 cup) Help me