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3 years ago

4.(06.05 MC)

Mathematics

1 answer:

neonofarm [45]3 years ago

3 0

Answer:

where is the question can u atach a picture

Step-by-step explanation:

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

slava [35]

Step-by-step explanation:

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

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

Therefore,

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

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

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

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

Can someone help with art plz...

belka [17]

What art? May you add additional words so that i may assist you?

7 0

3 years ago

Estimate unit rate four $74.75 glass white paint 5 gallons

alekssr [168]

74.75 for 5 gallon unit rate

74.75 / 5 = 14/95

Answer: $14.95 per gallon of paint

Therefore, about 15 dollars per gallon of paint since we need to estimate.

3 0

3 years ago

Solve for x. Express the answer in simplest form.

svlad2 [7]

$\dfrac{1}{7}=\dfrac{3}{4x-1}\\
4x-1=21\\
4x=22\\
x=\dfrac{22}{4}=\dfrac{11}{2}
$

5 0

3 years ago

Answer Please first = brainliest only if correct.

Kisachek [45]

Answer:

3x + 2y = 315 -----(1)

2x + 4y = 450 -----(2)

from (1) 3x + 2y = 315

2y = 315-3x

y = 157.5 - 3/2x ---- (3)

substitute (3) into (2)

2x + 4y = 450

2x + 4(157.5 - 3/2x ) = 450

2x + 630 - 6x = 450

-4x = -180

x = 45 ---- (4)

substitute (4) into (3)

y = 157.5 - 3/2x

y = 157.5 - 3/2(45)

y = 90

a haircut,x = 45 minutes

dye hair,y = 90 minutes

3 0

3 years ago