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4 years ago

What is the minimum volume of hot air needed to lift a hot air balloon carrying 800kg

Mathematics

1 answer:

nevsk [136]4 years ago

3 0

Answer:

The minimum volume of hot air needed to lift a hot air balloon carrying 800kg

Is 653.1m³

Step-by-step explanation:

This problem bothers on the density of materials in this problem air

Given data

Volume of air V=?

Mass of air m= 800kg

From tables the density of air is

ρ =1.225 kg/m3

Now to solve for the volume we have

ρ=m/v

v=m/ρ

v=800/1.225

Volume v = 653.1m³

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Please help it’s due

vampirchik [111]

Answer:

x = 27.8, y = 35

Step-by-step explanation:

Angle D is equal to Angle A

Angle E is equal to Angle B

Angle F is equal to Angle C

So you can set those equal to each other:

2y - 5 = 65

2y = 70

y = 35

-------------------------

2x + y = 90.6

2x + 35 = 90.6

2x = 55.6

x = 27.8

6 0

4 years ago

What expression is equal to 7(3 - x) + 1?

Nesterboy [21]

7(3-x)+1 .. first you're going to distribute

21-7x+1 .. then combine like terms

22-7x .. subtract 22 from both sides to get the variable X alone.

-7x=-22

x=3.14

5 0

3 years ago

Help or I die,... HELP

irakobra [83]

Regarding the points on the given line, it is found that:

a) The midpoint is: (3,4.5).

b) The coordinates of C are: C(4,5).

c) The coordinates of the other end of the line are: (4,3).

<h3>Midpoint</h3>

The midpoint between two points is given by the mean of the coordinates of these points.

In this problem, the coordinates of points A and B are given as follows:

A(0,3) and B(6,6).

Hence the coordinates of the midpoint are given as follows:

x-coordinate: (0 + 6)/2 = 3.

y-coordinate: (3 + 6)/2 = 4.5.

As for point C, we have that C is closer to B then A, hence:

The x-coordinate is greater than 3.

The y-coordinate is greater than 4.5.

The coordinates are integers, hence it is given as follows:

C(4,5).

As for line AB, it is found that:

The other line is parallel, hence the slope is also of 0.5. (change in y divided by change in x is of 0.5).

For the x-coordinate, on line AB, they change by 6, hence in the new line they increase by 2/3 x 6 = 4.

For the y-coordinate, on line AB, they change by 3, hence in the new line they increase by 2/3 x 3 = 3.

Thus the other endpoint is:

(4,3).

More can be learned about the mid-point of a line at brainly.com/question/18315903

#SPJ1

4 0

1 year ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).