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Vadim26 [7]
2 years ago
6

Cos theta=8/17. Find tan thetaA. 15/8B. 15/17C. 17/15D. 8/15​

Mathematics
1 answer:
Natalija [7]2 years ago
8 0

Answer:

A) \frac{15}{8}

Step-by-step explanation:

remember Soh Cah Toa!!

sin=\frac{opposite}{hypotenuse}\\ cos=\frac{adjacent}{hypotenuse} \\tan=\frac{opposite}{adjacent} \\\\cos=\frac{8}{17}\\\\a^2+b^2=c^2\\8^2+b^2=17^2\\64+b^2=289\\b^2=225\\\sqrt{b^2} =\sqrt{225}\\b=15=opposite\\\\tan=\frac{15}{8}

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Step-by-step explanation:

7.50 x 8 = 60

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2 years ago
Which cube root function is always decreasing as x increases?
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The answer is O f(x) =-35x+5
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3 years ago
HELP PLEASE
nordsb [41]

Answer:

<h3>perpendicular line:    y = -¹/₆ x + 4¹/₃ </h3><h3>  parallel line:              y = 6x - 45 </h3>

Step-by-step explanation:

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y = 6x - 7   ⇒   m₁=6

6×m₂ = -1        ⇒    m₂ = -¹/₆

 

The line y=-¹/₆ x+b passes through point (8, 3) so the equation:

3 = -¹/₆ ×8 + b must be true

3 = -⁴/₃ + b

b = 4¹/₃

Therefore equation in  slope-intercept form:

                                                     y = -¹/₆ x + 4¹/₃

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 6x - 7   ⇒   m₁=6   ⇒   m₂=6

The line y=6x+b passes through point (8, 3) so the equation:

3 = 6×8 + b must be true

3 = 48 + b

b = -45

Therefore equation in  slope-intercept form:

                                                     y = 6x - 45

7 0
3 years ago
Round 1.983 to the nearest hundredth
svet-max [94.6K]

Answer:

1.98

Step-by-step explanation:

Find the number in the hundredth place 8 and look one place to the right for the rounding digit 3. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

4 0
3 years ago
The following parts refer to the letters: LAMEFIREALARM. Recall that "word" means distinguishable letter arrangements. (a) How m
larisa86 [58]

Answer:

Step-by-step explanation:

The word "LAMEFIREALARM" word consists of

2L , 2M, 2E , 2R , 3A , F and I

no of words with the above letters such that M's are not together

=Total No of words- M's are together

Total no of words=\frac{13!}{4\times 2!\times 3!}=64,864,800

When M's are together . considering 2 M's as one

therefore there are \frac{12!}{3\times 2!\times 3!}=9,979,200

No of ways=\frac{13!}{4\times 2!\times 3!}-\frac{12!}{3\times 2!\times 3!}=54,885,600

(b)No of ways such that M's are separated by at least 2 letters

at least  2 letter means 2 letter, 3 letter ......11 letters

So we have to subtract no of ways where there are 1 letter in between M's from total no of ways where 2 M's are not next to each other

No of ways in which there is 1 letter between 2 M's

This can be done by considering 11 cases

In first case Place first M in Starting Position and 2 M on third place

Second case place First M in 2 nd Position and second M on 4 th place

Similarly For 11th case

Place first M in 11th place and second M on 13th place

Total ways

=\frac{11\times 11!}{3!\times 2!\times 2!\times 2!}

So , the total number of arrangements of the letters of the word LAMEFIREALARM where the two M's are separated by atleast two letters is

=\frac{13!}{4\times 2!\times 3!}-\frac{12!}{3\times 2!\times 3!}-\frac{11\times 11!}{3!\times 2!\times 2!\times 2!}

=45738000

7 0
3 years ago
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