A bicyclist travels 1 miles in 5 minutes .If m represents minutes , what does the expression m/5 represents

1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β

slava [35]

Step-by-step explanation:

1.

$\tan \beta = \frac{1}{ \cot \beta } = - \frac{3}{2 \sqrt{10} } = - \frac{3 \sqrt{10} }{20}$

$\csc \beta \tan \beta = \frac{1}{ \cos \beta } = \sec \beta$

Therefore,

$\sec \beta = ( \frac{7}{3} )( - \frac{3 \sqrt{10} }{20} ) = - \frac{7 \sqrt{10} }{20}$

2.

$\csc y = \frac{1}{ \sin y} = - \frac{ \sqrt{6} }{2}$

$= > \sin y = - \frac{ \sqrt{6} }{3}$

Use the identity

$\cos y = \sqrt{1 - \sin ^{2} y} \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{1 - {( - \frac{ \sqrt{6} }{3}) }^{2} } = - \frac{ \sqrt{3} }{3}$

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

$\tan \beta = \frac{ \sin y}{ \cos y} =( - \frac{ \sqrt{6} }{3} )( - \frac{3}{ \sqrt{3} } ) = \sqrt{2}$

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

$\sin x = \sqrt{1 - \cos ^{2} x} = \sqrt{ \frac{11}{6} }$

Solving for tan x:

$\tan x = \frac{ \sin x}{ \cos x} = (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) = \frac{ \sqrt{66} }{5}$

5 0

3 years ago

Bridget went fishing with her dad. Bridget Bridget caught the first fish of the day, another was 2 more than 3 times the weight

Arturiano [62]

Answer:

Bridget's first fish =f = 5 ounces

Bridget's dad first fish weighs 17 ounces

Step-by-step explanation:

Solution:

Bridget's fishes:

f ounces

2f ounces

3f+2 ounces

1/2f ounces

3/5f ounces

Total= f +2f + (3f+2) + 1/2f +3/5f

=3f + 3f + 2 + 5f+6f/10

=6f + 2 + 11f/10

=60f+11f/10 +2

=71/10f +2

Bridget's dad fishes

3f+2

4/5f

2f+4

1/2f

Total =(3f+2) + (2f+4) + 4/5f +1/2f

=3f+2+2f+4 + 8f+5f/10

=5f + 6 + 13/10f

= 50f+13f/10 + 6

=63/10f +6

Equate the total weight

71/10f +2=63/10f +6

Collect like terms

71/10f - 63/10f =6-2

71f-63f/10 = 4

8f/10=4

Cross product

8f=40

Divide both sides by 8

f=5

Bridget's first fish =f = 5 ounces

Bridget's dad first fish = 3f +2

=3(5)+2

=15+2

=17 ounces

Bridget's dad first fish weighs 17 ounces

8 0

3 years ago

Use Euclid’s Ladder (or a factor tree) to write the prime factorization.

Veseljchak [2.6K]

Answer:

64

Step-by-step explanation:

the answer is 64 hope this helps

5 0

3 years ago

Read 2 more answers

Please answer 9-12!!!

Ivan

Answer: (2,9) and (5,3)

Step-by-step explanation:

7 0

3 years ago

To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times. The

zhannawk [14.2K]

Answer:

(0.9464,1.034)

Step-by-step explanation:

First find the mean μ of all values as;

(0.95+1.02+ 1.01+ 0.98 ) /4 =0.99

μ=0.99

Find the standard deviation as;

-For each value subtract the mean and square the results

0.95-0.99 = -0.04 , -0.04² = 0.0016

1.02-0.99= 0.03, 0.03²=0.0009

1.01-0.99= 0.02, 0.02²= 0.0004

0.98-0.99 = -0.01, -0.01²=0.0001

Find mean of squared deviations as;

(0.0016+0.0009+0.0004+0.0001)/4 =0.00075 ----variance

Standard deviation = √0.00075 = 0.0274

δ = 0.0274

n=4

Thus n< 30 , confidence interval for μ = x ± t*δ/√n ---------(i)

Degree of freedom (df) = n-1 =4-1 =3

The t value for 95% confidence with df= 3 is t=3.182

Substituting the values in equation (i)

0.99 ± 3.182 * 0.0274/√4

0.99 ± 3.182 * 0.0274/2

0.99 ± 3.182 * 0.0137

0.99 ± 0.0436

(0.9464,1.034)

8 0

3 years ago