The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.

What is the position of the scuba diver now relative to the water surface?

Enter your answer as a mixed number, in simplified form, in the box.

Answer:

pi/3, 5pi/3

Step-by-step explanation:

We can see that when cosine is at 1/2, the angle measures are pi/3 degrees and 5pi/3 degrees. You can use a unit circle to find this. You can also find arccos(1/2), but that will only give you the value pi/3, not 5pi/3.

We can plug these in to find that they are indeed equal to 1/2.

The x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.

Here, we have,

To find the x-value that corresponds to a y-value of 1/2 between π and 2π for the equation y = cos(x), we can use the inverse cosine function (also known as arccosine or cos⁻¹).

The inverse cosine function will give us the angle whose cosine is a specific value.

In this case, we want to find the angle whose cosine is 1/2.

Using the inverse cosine function, we can write the equation as:

x = arccos(1/2)

To solve this equation, we need to evaluate the inverse cosine of 1/2. In general, the inverse cosine of a value returns an angle between 0 and π (180 degrees). In this case, we are interested in finding an angle between π and 2π.

The value of arccos(1/2) is π/3.

Therefore, the x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.

It's important to mention that the cosine function is periodic, so there are multiple x-values that can correspond to a y-value of 1/2. In this case, we have chosen the x-value that lies between π and 2π.

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no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

Step-by-step explanation:

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

6ft

Step-by-step explanation:

The Dolphin is 8 feet apart from starting point along the water surface.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Equation: x²- 8x + 4y = 0

Now, solving for variable 'y' we get

y= (8x - x²) /4

y= 2x - x²/4

So, the Dolphin is 8 feet apart from starting point along the water surface.

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Answer:

e = 2

Step-by-step explanation:

7(2e - 1) - 3 = 6 + 6e

14e - 7 - 3 = 6 + 6e

14e - 10 = 6 + 6e

14e - 6e - 10 = 6

8e - 10 = 6

8e = 6 + 10

8e = 16

8e/8 = 16/8

e = 2

Recheck:

7(2e - 1) - 3 = 6 + 6e

7(2(2) - 1) - 3 = 6 + 6(2)

7(4 - 1) - 3 = 6 + 12

7(3) - 3 = 18

21 - 3 = 18

18 = 18 ✅

Answer:A. y=1.5x

Step-by-step explanation:

x represents the number of twizzlers

1.5 represents the the price that you have to pay for each Twizzlers

And y represents the total cost

Answer:

The perimeter of the rectangle is 3.5 m or 350 cm.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer: 12 men would be needed to repair the same road in 3 1/3 hrs. Inverse proportion because usually in work,food and time its inversly proportional.

8 hours --> 5 men

1 hour --> 5*8 = 40 men

3 1/3 hours --> 40/ (3 1/3) men

                  --> 12 men

Answer:

42x - 54 I think

Step-by-step explanation:

Just simplify it  

Answer:

m∠DEB = _70_°

m∠BCD= _110_°

m∠EAB= _73_°​

Step-by-step explanation:

To find ∠DEB:

Take the angle of ∠EDC, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.

To find ∠BCD:

Because EBCD is an isosceles trapezoid, this means that ∠D and ∠C both have the congruent angles. Since we know ∠EDC is 110°, this means that ∠C is also 110°.

To find ∠EAB:

We know that m∠ABC is 133° and ∠DEA is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠DEB is 70°. We'll take the angle of ∠DEA and subtract the angle of ∠DEB from it, which gets us 44°. To figure out the angle of ∠B, we take the angle of ∠ABC and subtract 70° or the angle of ∠DEB, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.

- 2021 Edmentum

Answer: 7 weeks

Step-by-step explanation:

Let x represent number of weeks

Let y represent the total amount

Amount = Paycheck deposited * number of weeks + Initial amount

y = 125x + 475

Number of weeks until she has $1350

1350 = 125x + 475

125x+475-475=1350-475

125x=875

x=7

Therefore, the student will have $1350 in her bank account after 7 weeks

Answer:

first one: x<9 second: x<3.5 or 7/2

Step-by-step explanation:

first: substract 3 from both sides

second: substract 5 and then divide by 2

Answer:

87/103

Step-by-step explanation:

Answer:

answer below

Step-by-step explanation:

f(x) = a* bˣ

if a>0 and b>1 : growth

if a>0 and 0<b<1 : decay

5) 7) 9) : growth

6) 8) 10) : decay

When analyzing whether an equation represents growth or decay, we examine the relationship between the variables involved. If an equation shows a positive relationship, it represents growth, while a negative relationship indicates decay.

When determining whether an equation represents growth or decay, we need to examine the relationship between the variables involved. 1. If the equation represents a positive relationship, where as one variable increases, the other variable also increases, then it represents growth. 2. On the other hand, if the equation represents a negative relationship, where as one variable increases, the other variable decreases, then it represents decay.

Let's look at some examples to illustrate this: Example 1: y = 2x In this equation, as x increases, y also increases. Therefore, it represents growth. Example 2: y = -3x In this equation, as x increases, y decreases. Therefore, it represents decay. Example 3: y = -0.5x + 3 Here, as x increases, y decreases. So, this equation represents decay. Example 4: y = 4.5x + 2 As x increases, y also increases. Hence, this equation represents growth. In summary, when analyzing whether an equation represents growth or decay, we examine the relationship between the variables involved. If an equation shows a positive relationship, it represents growth, while a negative relationship indicates decay.

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Answer:

0.73

Took the quiz

The probability that a randomly chosen college student does not use a ride sharing app is 0.73.

Probability is a stastistical measure that is used to determine who likely it is that event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a randomly chosen college student does not use a ride sharing app = 1 - 0.27 = 0.73

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Answer:

$2421.95

Step-by-step explanation:

To calculate the final value from compound interest, we can use the formula

A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.

Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get

2000(1+0.012/2)^(2*16) = 2421.95

Answer:

solution here

length

c=170

a=162

b=177

perimeter=?

now,

perimeter of triangle = a+b+c

=170+162+177

=511

perimeter=511 cm

perimeter = length of fence

therefore,the fence should be 511 cm long.

The length of the fence needed would be 509 meters.

Given is that a city park is in the shape of a triangle where the sides have lengths 170 m, 162 m, and 177 m.

The length of the fence needed would be the perimeter of the triangle. We can write the perimeter of the triangle as -

P = sum of the side lengths

P = 170 + 162 + 177

P = 509 meters

Therefore, the length of the fence needed would be 509 meters.

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

Explanation:

The ratio we want is in the format green:red:total which means we list the number of green first, then the number of red next, then the number total last. The order is very important. This is because we'll simply list the numbers without saying the color name or "total". So the reader will imply what the numbers refer to, based on this order mentioned.

We have:

The ratio of green to red to total is 70:50:162

To reduce the ratio, we divide all three parts of that ratio by the GCF 2

The ratio 70:50:162 fully reduces to 35:25:81 which is the final answer.

This says that for every 35 green marbles, we have 25 red marbles and 81 total marbles.

Answer:

A

Step-by-step explanation:

20% of 60 is 12

Hope that helps

Answer:

  x = 50

  y = 65

Step-by-step explanation:

The marked sides show you that the triangle is isosceles. That means the base angles, y° and 65°, are congruent.

  y = 65

__

The sum of the angles in a triangle is 180°.

  65° +65° +x° = 180°

  x° = 180° -130° = 50° . . . . . . subtract 130°

  x = 50

Answer:

6.93

Step-by-step explanation:

hope this helps

Given that:

f(x) = 5(3)x-4

f(6) = 5(3)(6) - 4 ⇛15(6) - 4 ⇛90-4 ⇛86Ans.

Answer:

n is 0.5

Step-by-step explanation:

Answer:

1:0.5

Step-by-step explanation:

Answer:

1581.62810745 square km

Step-by-step explanation:

P = Initial Area = 2500 square km.

r = rate of decreasing = 8.75%

n = number of years = 5 years

A = 2500 ( 1 - 8.75/100)^5

A = 2500 {(100–8.75)/100}^5

A = 2500 (91.25/100)^5

A = 2500 (0.9125)^5

A = 2500 * 0.63265124298

A = 1581.62810745

Answer:

what's thequestion?

Step-by-step explanation:

Answer:

-5 less than or equal to x less than or equal to -8

Step-by-step explanation:

You have to isolate x.

Start with removing +2.

Take 2 away from both sides

15 less than or equal to -3x less than or equal to 24

Then, the only thing you have to isolate after that is -3, you have to remove it from x.

Since -3x is multiplying, you have to divide by -3 on the other sides.

15 divided by -3 is -5

24 divided by -3 is -8

Therefore,

The answer is...

-5 less than or equal to x less than or equal to -8

Answer:

length (l) = 14 feet

breadth (b) = 7 feet

height (h) = 7 feet

so, volume of the

rectangular moving

van = l*b*h

=14feet * 7feet *7feet

= 686 cubic feet

Answer:

16

Step-by-step explanation:

261 - 256 - 251

-5 by step

to 50th term there is 49 -5's from 261.

261 + 49.(-5) = 261 - 245 = 16

Answer:

16

Step-by-step explanation:

The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.

General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]

where An = nth term, a1 = first term , n = number of terms and d = common difference.

The first term is 261 so a1 = 261

The common difference appears to be -5

( 256 - 261 = -5 ) and ( 251 - 256 = -5 )

so d = -5

We want to find the 50th term so n = 50

We then plug all of this in to get the 50th terms

Formula : [tex]a_n=a_1+(n-1)d[/tex]

a1 = 261 , n = 50 and d = -5

[tex]a_n=261 + (50-1)-5[/tex]

subtract 1 from 50

[tex]a_n=261+(49)(-5)[/tex]

multiply 49 and -5

[tex]a_n=261-245[/tex]

subtract 245 from 261

[tex]a_n=16[/tex]

The 50th term is 16

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

Where, the constant term, c = 0

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

(c) The given function for R is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function R is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c,  we have;

[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]

Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]

The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

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Answer:

-2 gallons per minute

Step-by-step explanation:

As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.

So, the rate of change is -30 gallons per 15 minutes

However, we can simplify this ratio by dividing both sides by 15, so we get

-2 gallons per minute