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2 years ago

Consider ∠A such that cos A = 12/13.

Mathematics

1 answer:

Georgia [21]2 years ago

5 0

Using the unit circle, for the cos function to be positive, angle A must lie in either quadrant I or quadrant IV

Using the unit circle, If the sine is negative, angle A must lie in either quadrant III or quadrant IV. Since we know that the cosine is positive, this only leaves quadrant IV

cos = adj/hyp

Using Pythagorean theorem,

$12^{2} +b^{2} = 13^{2}$

b = ±5 (we know its -5 since we know sinA is negative)

this means that the x coord is 12, and the y coord is -5

any proportion of these two numbers would work as an answer

e.g. (12, -5), (24,-10), (12/13, -5/13), are all valid answers

sinA = opp/hyp

sinA = -5/13

tanA = opp/adj

tanA = -5/12

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A model rocket is launched with an initial upward velocity of 60 m/s. The rocket's height h (in meters) after t seconds is given

Vedmedyk [2.9K]

Answer:

0.47 and 11.53

Step-by-step explanation:

h = 60t − 5t²

27 = 60t − 5t²

5t² − 60t + 27 = 0

Quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

t = [ -(-60) ± √((-60)² − 4(5)(27)) ] / 2(5)

t = (60 ± √3060) / 10

t = 0.47 or 11.53

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3 years ago

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liubo4ka [24]

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3 years ago

Read 2 more answers

Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall a

kherson [118]

Answer:

Yes, the background color appear to have an effect on the variation of word recall scores

Step-by-step explanation:

Given that results from scores on a test of word recall are given are as follows:

Two test scores have independent means and having normal distribution.

$H_0: Means are equal\\H_a: Means are not equal$

(Two tailed test at 5% significance level)

Group Group One Group Two

Mean 15.1400 12.4200

SD 5.9100 5.4200

SEM 0.9990 0.8910

N 35 37

The mean of Group One minus Group Two equals 2.7200

standard error of difference = 1.335

Hence t statistic = 2.0369

p value = 0.0454

Since p <0.05 we reject null hypothesis

Yes, the background color appear to have an effect on the variation of word recall scores

5 0

3 years ago

If the area of a square plot of land is 9 miles squared, what is the perimeter of this land?

tatyana61 [14]

Answer:

$\huge{ \fbox{ \sf{12 \: miles}}}$

Step-by-step explanation:

Given,

Area of a square plot = 9 miles

First, finding the length of the land

$\boxed{ \sf{Area \: of \: a \: square \: = \: {length}^{2} }}$

$\mapsto{ \sf{9 = {length}^{2} }}$

$\mapsto{ \sf{ {length}^{2} = 9}}$

$\mapsto{ \sf{ \sqrt{ {(length)}^{2} }} = \sqrt{9} }$

$\mapsto{ \sf{length = 3 \: miles}}$

Now , finding the perimeter of the land :

$\boxed{ \sf{perimeter \: of \: a \: square = 4 \: * length}}$

$\mapsto{ \sf{perimeter \: = \: 4 \: * \: 3}}$

$\mapsto{ \sf{perimeter \: = 12 \: miles}}$

The perimeter of the land = 12 miles

Hope I helped!

Best regards! :D

~ $\text{TheAnimeGirl}$

3 0

3 years ago

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

gavmur [86]

Answer:

Tobias did best on the aptitude test.

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Emilio

Emilio got a score of 76; this version has a mean of 70.6 and a standard deviation of 9.

z = (x-μ)/σ

z = 76 - 70.6/9

z = 0.6

For Alissa

Alissa got a score of 298.8; this version has a mean of 282 and a standard deviation of 24.

z = (x-μ)/σ

z = 298.8 - 282/24

z = 0.7

For Tobias

Tobias got a score of 8.04; this version has a mean of 7.2 and a standard deviation of 0.4.

z = (x-μ)/σ

z = 8.04 - 7.2/0.4

z = 2.1

Looking at the calculated z score above, we can see that Tobias did better on his aptitude test because he had a higher z score compared to Emilio and Alissa.

8 0

3 years ago