Identify the set as integers, natural numbers, or whole numbers.<br> -1, 0, 1, 2, 3

Suppose that Y varies directly with X, and Y = 4 when X = 16

mylen [45]

Answer:

find k first

y=kx

4=k16

k=0.25

then find y

y=kx

y=0.25x3

y=0.75

6 0

3 years ago

One of the interior angles of a triangle is equal to 30°, and one of the exterior angles is equal to 40°. Find the remaining int

irina1246 [14]

Answer:

The remaining interior angles of this triangle are 140º and 10º

Step-by-step explanation:

The sum of the interior angles of a triangle is always 180º.

A triangle has 3 angles. In this problem, we have one of them, that i am going to call A1 = 30º.

The sum of a interior angle with it's respective exterior angle is also always 180º.

We have that one of the exterior angles is equal to 40°. So it's respective interior angle is

40º + A2 = 180º

A2 = 180º - 40º

A2 = 140º

Now we have two interior angles, and we know that the sum of the 3 interior angles is 180º. So:

A1 + A2 + A3 = 180º

A3 = 180º - A1 - A2

A3 = 180º - 30º - 140º

A3 = 180º - 170º

A3 = 10º

7 0

3 years ago

An airplane pilot wants to climb from an altitude of 6000 feet to 16,000 feet. If the plane climbs at an angle of 9 degrees, wit

puteri [66]

So, the pilot goes from 6,000 to 16,000 or distance up of 10,000 feet
the plane is going at a speed of 22,000 per minute, namely, dx/dt = 22,000

so. .if you look at the picture below... we can simply use tangent
keeping in mind that, as the plane moves up and up, the angle is "constant", is never changing, whilst "y" and "x" and even "r" are changing, but we're not using "r" in this case.... we know what dx/dt is, we know the angle is a constant, this matters because the derivative of a constant is just 0

so, we really just need to find dy/dt then, because whilst dx/dt is telling us how fast is moving horizontally, dy/dt is telling us how long it took to cover those 10,000 feet

thus $\bf tan(\theta)=\cfrac{y}{x}\implies tan(\theta)=yx^{-1}\implies tan(9^o)=yx^{-1}\\\\
-----------------------------\\\\
0=\left( \cfrac{dy}{dt}\cdot \cfrac{1}{x} \right)+\left( y\cdot -\cfrac{1}{x^2}\cdot \cfrac{dx}{dt} \right)\implies 0=\cfrac{\frac{dy}{dt}}{x}-\cfrac{y\frac{dx}{dt}}{x^2}
\\\\\\
$

$\bf \\\\\\
\cfrac{y\frac{dx}{dt}}{x^2}=\cfrac{\frac{dy}{dt}}{x}\implies \cfrac{y\frac{dx}{dt}}{x}=\cfrac{dy}{dt}
\\\\\\
\textit{so, what's "x" when y = 10000?}
\\\\\\
tan(9^o)=\cfrac{10000}{x}\implies x=\cfrac{10000}{tan(9^o)}\implies x\approx 63175.5$

once you find what dy/dt is... you can simply do a quick conversion for the 10,000 feet, to see how many minutes it took