All categories

2 years ago

Which of the following is a key element in the proof of the law of cosines?

2 answers:

4 0

The best and most correct answer among the choices provided by the question is the fourth choice "d=square root of (x^2+x^1)+(y^2-y^1)^2"
The law of cosines<span> for calculating one side of a triangle when the angle opposite and the other two sides are known. Can be used in conjunction with the </span>law<span> of sines to find all sides and angles. </span>

I hope my answer has come to your help. God bless and have a nice day ahead!

Vikentia [17]2 years ago

4 0

The <em><u>correct answer</u></em> is:

D) d=√((x+x¹)+(y²-y¹)² )

Explanation:

The distance formula is a key component to the proof of the law of cosines.

First we define sin θ = y/b and cos θ = x/b, using the standard law of cosines diagram.

We then use the distance formula, replacing the second y coordinate with 0 and the second x coordinate with a.

We then substitute our values for sin θ and cos θ, square them and simplify.

You might be interested in

A collector has 120 movie posters and 100 band posters. She wants to sell 24 movie posters but still have her poster collection

Serga [27]

Answer:

She must sell 20 band posters

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Find the product of 12 and 8. Find the greatest common factor of 12 and 8. Find the least common multiple of 12 and 8. Find the

Fudgin [204]

Answer:

12x8=96, GCF is 4, LCM is 24

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

In a restaurant, the proportion of people who order coffee with their dinner is p. A simple random sample of 144 patrons of the

mote1985 [20]

<h2>Answer with explanation:</h2>

Given : In a restaurant, the proportion of people who order coffee with their dinner is p.

Sample size : n= 144

x= 120

$\hat{p}=\dfrac{x}{n}=\dfrac{120}{144}=0.83333333\approx0.8333$

The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-

Null hypothesis : $H_0: p\geq0.85$ [ it takes equality (=, ≤, ≥) ]

Alternative hypothesis : $H_1: p$ [its exactly opposite of null hypothesis]

∵Alternative hypothesis is left tailed, so the test is a left tailed test.

Test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$z=\dfrac{0.83-0.85}{\sqrt{\dfrac{0.85(1-0.85)}{144}}}\\\\=-0.561232257678\approx-0.56$

Using z-vale table ,

Critical value for 0.05 significance ( left-tailed test)=-1.645

Since the calculated value of test statistic is greater than the critical value , so we failed to reject the null hypothesis.

Conclusion : We have enough evidence to support the claim that p is greater than or equal to 0.85.

8 0

2 years ago

A particle moves along the x-axis so that its velocity in feet per second at time x, in seconds, is modeled by the quadratic fun

Katyanochek1 [597]

For this case we have the following equation:

$y = 2x ^ 2 - 10x + 12$

Where, we have the following variables:

x: time in seconds

y: speed in feet per seconds

For the initial velocity, we evaluate x = 0 in the given equation:

$y = 2 (0) ^ 2 - 10 (0) + 12\\y = 12$

Therefore, the initial speed is 12 feet per second.

Answer:

The particle's initially velocity is 12.

6 0

3 years ago

If h(x) = (f o g)(x) and h(x) = sqrt(x+5), find g(x) if f(x) = sqrt(x+2)

agasfer [191]

Answer:

g(x) = x + 3

Step-by-step explanation:

<h3>Given</h3>

h(x) = (f ο g)(x)
h(x) = $\sqrt{x+5}$
f(x) = $\sqrt{x+2}$

g(x)

<h3>Solution</h3>

(f ο g)(x) = f(g(x))

<u>Substitute x with g(x) and solve for g(x):</u>

$\sqrt{x+5}$ = $\sqrt{g(x)+2}$
x + 5 = g(x) + 2
x + 3 = g(x)
g(x) = x + 3

7 0

2 years ago