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2 years ago

Task #3: Fuel for Thought-Student Activity Sheet Part 1

Mathematics

2 answers:

Ilia_Sergeevich [38]2 years ago

3 0

Answer:

Step-by-step explanation:

mrs_skeptik [129]2 years ago

3 0

Answer:

The method that would save the most fuel would be:

a. Replacing a compact car that gets 34 miles per gallon (mpg) with a hybrid that gets 54 mpg

Step-by-step explanation:

Hybrid cars are a very good way to save money on fuel and protect the environment by avoiding CO2 or CO emissions, this is because the hybrid vehicle uses both an internal combustion engine (which uses gasoline) and an electric motor (that uses electrical energy), in the example provided, the more miles per gallon (mpg) a car travels, it means that its fuel will last longer, as you can see, in case A the difference when making the change is 20 mpg, while in case B it is only 10 mpg, which is why option a is chosen.

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An airplane has its auto pilot set to fly in a direction of 40 degrees at a speed of 320 mph. The wind is blowing the airplane t

Effectus [21]

Answer:

distance: 320.624 miles

direction: 43.576°

Step-by-step explanation:

The speed and direction can be found by adding the given vectors.

... 320∠40° + 20∠130°

... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))

... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)

The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.

... = √(232.278² +221.013²)∠arctan(221.013/232.278)

... = 320.624∠43.576°

_____

A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.

_____

Comment on coordinate systems

Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.

Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.

_____

Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.

8 0

2 years ago

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for n = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for n = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

6 0

2 years ago

The formula for the area (A) of a circle is A = π • r2, where r is the radius of the circle. Ronisha wants to find the area of a

kobusy [5.1K]

Greetings from Brasil...

Here we will apply rule of 3...

This formula, A = πR², its for the whole circle, that is, 360° (2π)

We want the area of only a part, that is, a circular sector whose angle π/6

sector area

2π ----- πR²

π/6 ----- X

2πX = (π/6).πR²

2πX = π²R²/6

X = π²R²/12π

If Ronisha multiply the area by 1/12 she will get the area of sector with angle of π/6

6 0

2 years ago

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triang

luda_lava [24]

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

3 0

2 years ago

Read 2 more answers

A triangle has angles that measure 46 and 84 what is the third angle?

pentagon [3]

The measure of the third angle is 50 because a triangle has a sum of 180 degrees by angle.

so... 46+84=130 and to get to 180, the last angle has to be worth 50.

5 0

2 years ago