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LenKa [72]
3 years ago
13

PLEASE HELP

Mathematics
1 answer:
zmey [24]3 years ago
3 0

Law of cosines :

The law of cosines establishes:

c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.

general guidelines:

The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.


Law of the sines:


In ΔABC is an oblique triangle with sides a, b, and c, then:

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.

General guidelines:

To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).


The ambiguous case :


If two sides and an angle opposite one of them is given, three possibilities may occur.


(1) The triangle does not exist.


(2) Two different triangles exist.


(3) Exactly a triangle exists.


If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines

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bekas [8.4K]

Answer:             1/10 miles/hour

To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.

<h2>Unit Rate</h2>

The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.

<h2>Proportions</h2>

Proportions look like two fractions set equal to each other with a missing variable to solve.

<h3>State our variables</h3>

let <em>x</em> be the number of miles per hour

<h3>Write a proportion</h3>

The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}

<h2>Solve</h2>

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.

<h3>Find the scale factor</h3>

Start with the proportion.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}

To find the scale factor,

  1. Take the denominator from the fraction with a variable: 1\ hr
  2. Take the denominator from the fraction that has no variable:  \frac{1}{3}\ hr
  3. Divide step 1 by step 2 and solve:  1\ hr\ \div\ \frac{1}{3}\ hr = 3

Our scale factor is <u>3</u>.

<h3>Solve for x</h3>

We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}

Simplify 3/30 by dividing the fraction by 3.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}

x = 1/10

∴ a snail moves 1/10 miles per hour.

Learn another way to solve proportions here: brainly.com/question/18437927

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Kimberly is ordering bath towels and washcloths for the inn where she works. The total cost of the order is T=6b+2w, where T is
Arturiano [62]

Given:

The total cost of the order is

T=6b+2w

where, T is the total cost, b is the number of bath towels, and w is the number of wash cloths.

Her budget is $85.

To find:

The constraints, so that she can order a maximum of washcloths or bath towels.

Solution:

We have,

T=6b+2w

Her budget is $85. So, total cost is less than or equal to 85.

6b+2w\leq 85       ...(i)

For maximum number of bath towels, the number of wash cloths is 0.

6b+2(0)\leq 85

6b\leq 85

Divide both sides by 6.

b\leq \dfrac{85}{6}

b\leq 14.167

For maximum number of wash cloths, the number of bath towels is 0.

6(0)+2w\leq 85

2w\leq 85

Divide both sides by 2.

w\leq \dfrac{85}{2}

w\leq 42.5

Therefore, the required constraints for maximum of washcloths or bath towels are w\leq 42.5 and b\leq 14.167 respectively.

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ValentinkaMS [17]

Answer:

y=2x+6

Step-by-step explanation:

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