a diver has to dive a depth of 200.2 ft go study​

The solution to the trigonometric equation in the interval is given by:

[tex]x = \frac{\pi}{4}[/tex]

In this problem, the equation is given by:

[tex]\frac{1}{\sin{\theta}} = 2\cos{\theta}[/tex]

Applying cross multiplication, we have that:

[tex]2\sin{\theta}\cos{\theta} = 1[/tex]

Applying a trigonometric identity, we have that:

[tex]\sin{2x} = 1[/tex]

We have that on the interval [0, 2π), [tex]\sin{\left(\frac{\pi}{2}\right)} = 1[/tex]

Hence:

[tex]\sin{2x} = 1[/tex]

[tex]\sin{2x} = \sin{\left(\frac{\pi}{2}\right)}[/tex]

[tex]2x = \frac{\pi}{2}[/tex]

[tex]x = \frac{\pi}{4}[/tex]

For [tex]\frac{3\pi}{4}[/tex], we have that:

[tex]\sin{2x} = \sin{\left(\frac{3\pi}{2}\right)} = -1[/tex]

Hence only the first solution is correct.

More can be learned about trigonometric equations at https://brainly.com/question/24680641

Answer:

233.3

Step-by-step explanation:

7000 divided by 3 = 233.3

Answer:

Step-by-step explanation:

we want to set the per ... value to one

so for the dollars per pound we find how many dollars per one pound. we can set up a proportion to do so.

(6.79/16) = (x/1) so we can solve that by finding (6.79/16)(1) = x meaning x is 0.424 [3 sig figs] meaning its 0.424 dollars per pound

using the same process we find the other proportion which would be (16/6.79) = (x/1) -> (16/6.79)(1) = x -> 2.36 meaning 2.36 pound per dollar

Answer:28.16

Step-by-step explanation:

A markup of 220% would bring 11 to 35.20, and a mark down of 20% would bring 35.20 to 28.16.

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Answer:

there are 14 boys and 31 total students in chemistry class.

explanation:

total number of students: 100%

total number of students:

Boys in the class:

Boys total:

There are 14 boys and 31 total students in the chemistry class.

It is given that there are 17 female students which is also equal to 54.84 % of total students in chemistry class.

We have to find the total number of students and number of boys in chemistry class.

What will be the 50 % of 100 ?

The value will be 50.

Let's assume that total number of students be x.

∵ Number of female students ;

⇒  54.84 % of x  = 17

 ⇒ (54.84/100) × x = 17

⇒ x = 1700 ÷ 54.84

⇒ x = 31 (approximate)

So, the total number of students in chemistry class are 31.

&

Number of boys = 31 - 17 = 14

Thus , there are 14 boys and 31 total students in the chemistry class.

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the answer is just 50° for both

3/14 chance. There are 1 more red marble, and 4 more green marbles. The probability of a blue marble is low, but could still happen.

Answer:

x>-3

Step-by-step explanation:

4x>-12

x>-12/4

x>-3

Answer:

Option B

Step-by-step explanation:

Given the following question:

53 oz = c?
[tex]1c=8oz[/tex]
[tex]53\div8=6.625[/tex]
[tex]6.625=\frac{6625}{1000}\div125=\frac{53}{8}[/tex]
[tex]\frac{53}{8} =53\div8=6\frac{5}{8}[/tex]
[tex]=6\frac{5}{8}[/tex]

Your answer is option B or "6 5/8 cups."

Hope this helps

Answer:

10

Step-by-step explantion

Simplifying

2x + 3 + 25 = 3x + -17

Reorder the terms:

3 + 25 + 2x = 3x + -17

Combine like terms: 3 + 25 = 28

28 + 2x = 3x + -17

Reorder the terms:

28 + 2x = -17 + 3x

Solving

28 + 2x = -17 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

28 + 2x + -3x = -17 + 3x + -3x

Combine like terms: 2x + -3x = -1x

28 + -1x = -17 + 3x + -3x

Combine like terms: 3x + -3x = 0

28 + -1x = -17 + 0

28 + -1x = -17

Add '-28' to each side of the equation.

28 + -28 + -1x = -17 + -28

Combine like terms: 28 + -28 = 0

0 + -1x = -17 + -28

-1x = -17 + -28

Combine like terms: -17 + -28 = -45

-1x = -45

Divide each side by '-1'.

x = 45

Simplifying

x = 45

Answer:

Step-by-step explanation:

Exterior angle is same as sum of two remote interior angles:

Answer:

1[tex]\frac{4}{15}[/tex] of straw

Step-by-step explanation:

The total amount of straw and hay together is, [tex]4 \frac{2}{3}[/tex].

and the total amount of hay alone is, [tex]3\frac{2}{5}[/tex]

All you need to do is subtract the hay from the total, which gives you, the answer above.

answer:

y = 3x + 5

steps-explanation:

given sample equation:

comparing to the formula of slope intercept form: y = mx + b

                                              [ where m is the slope and b is the y-intercept ]

we can determine here that the slope is 3 and -1 is the y-intercept.

but here we need only the slope.

in parallel, the slope is same: 3

formula:                  

using the formula:                     [ here known that y1 is -1 and x1 is -2 ]

Answer:

Hong: 63

Alonzo: 21

Christine: 26

Step-by-step explanation:

110-5=105

105 divided by 5= 21

Answer:

I think its obtuse but I'm not sure

Answer:

it's obtuse because one of the angle is obtuse and other two are acute so it's obtuse angles triangle

Problem 1

If you need to convert to a mixed number, then follow these steps.

27.2 = 27 + 0.2

27.2 = 27 + 1/5

27.2 = 27 & 1/5

27.2 pizzas is the same as 27 & 1/5 pizzas. In other words, you have 27 whole pizzas plus 1/5 of an extra one.

===========================================

Problem 2

The decimal 1.75 converts to the mixed number 1 & 3/4 because of the steps below.

1.75 = 1 + 0.75

1.75 = 1 + 3/4

1.75 = 1 & 3/4

In my opinion, it is optional to convert to a mixed number for either problem 1 or problem 2. So you can stick with 1.75 as the answer if you want.

===========================================

Problem 3

16 & 3/4 = 16 + 3/4 = 16 + 0.75 = 16.75

To get the unit rate, which is the cost per unit, we divide the total cost over the amount.

cost/amount = (2.89)/(16.75) = 0.1725373

which is approximate.

Round to the nearest penny to get a unit cost of $0.17 per fluid ounce, i.e. a unit cost of 17 cents per fluid ounce.

===========================================

Problem 4

We follow the same idea as problem 3.

4 & 3/5 = 4 + 3/5 = 4 + 0.6 = 4.6

unit cost = (total cost)/(amount)

unit cost = (7.56)/(4.6)

unit cost = 1.643478 dollars approximately

unit cost = 1.64 dollars approximately

===========================================

Problem 5

6 & 1/2 = 6 + 1/2 = 6 + 0.5 = 6.5

Like before, we'll divide the total cost over the total amount.

unit cost = (total cost)/(amount)

unit cost = (8.22)/(6.5)

unit cost = 1.264615 dollars approximately

unit cost = 1.26 dollars approximately

===========================================

Here's another way to look at the unit cost or unit rate.

Notice in problem 5 it says "cost per yard". This is the same as "cost per 1 yard" or "cost for each yard".

We can express the given info as the ratio

6.5 yards:$8.22

Now we want the "6.5 yards" to become "1 yard" to achieve the unit rate.

So we'll divide both parts by 6.5

6.5 yards:$8.22

6.5/6.5 yards:$8.22/6.5

1 yard: $1.26 approximately

For each yard, we'll spend $1.26

Problems 3 and 4 follow similar ideas. So this is why we divided the total cost over the total amount.

Answer:

[tex]18=2^x[/tex]

Step-by-step explanation:

[tex]log_2(18)=x\\\\2^{log_2(18)}=2^x\\\\18=2^x[/tex]

Answer:

1st question answer is 3xy(x-3y+4xy)

2nd question answer is (2+y) (x+3)

hope it helps

Answer:

a) -6

b) -9

c) 27

Step-by-step explanation:

Since a=-3, plug in -3 for a and solve.

Answer:

3

Step-by-step explanation:

7x² is the first term,

14x is the second term and

2 is the third term.

Answer:

a. 25.2

Step-by-step explanation:

Step one: 560×4.5=2,520

Step two: 2,520÷100=25.2

Answer:

-10

Step-by-step explanation:

if negative meets a negative its gone come out as a positive

Answer:

b = 104°

Step-by-step explanation:

<DEA = <DAE (given)

Now,

<DEA + 142 = 180° (linear pairs)

<DEA = 180° - 142°

so, <DEA = 38°

Now,

<DEA + <DAE + b = 180° (sum of angles of triangle)

or, 38° + 38° + b = 180° (<DEA = <DAE)

or, b = 180° - 76°

so, b = 104°

Answer:

Step-by-step explanation:

im pretty sure its the 1st one

Answer:

[tex] \frac{ - 2 - 1}{4 - 0} \\ \\ \frac{ - 3}{4} \\ \\ \frac{3}{ - 4} [/tex]

Answer:

83in

Step-by-step explanation:

1 ft = 12 in

6 ft= 72 in + 11 in = 83

Answer:

x=4.285714286

Step-by-step explanation:

Let the number be x

Now we have,

→ [tex]32-7x=2\\\\[/tex]

→ [tex]32-2=7x\\\\[/tex]

→ [tex]30=7x\\[/tex]

→ [tex]x=\frac{30}{7} \\[/tex]

→ x=4.285714286