Rearrange to make P the subject, :)..​

The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the

tunnel with a cross section that is the shape of half of a sine curve and the

height of the tunnel at the edge of the road, (approximately 7.07 ft.) are

found by applying the following steps

(a) The equation for the sine curve is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is approximately 7.07 feet

The reason for the above answers are presented as follows;

(a) From a similar question posted online, the missing part of the question

is, what is the height of the tunnel at the edge of the road

The known parameters;

The shape of the tunnel = One-half sine curve cycle

The height of the road at its highest point = 10 ft.

The opening of the tunnel at road level = 24 ft.

The unknown parameter;

The equation of the sine curve that fits the opening

Method;

Model the sine curve equation of the tunnel using the general equation of a sine curve;

The general equation of a sine curve is y = A·sin(B·(x - C) + D

Where;

y = The height at point x

A = The amplitude = The distance from the centerline of the sine wave to the top of a crest

Therefore;

The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.

D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)

The period is the distance between successive points where the curve passes through the center line while rising to a crest

Therefore

The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.

T = 48 ft.

We get;

48 = 2·π/B

B = 2·π/48 = π/24

By plugging in the values for A, B, C, and D, we get;

y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)

The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is given by substituting

the value of x at the edge of the road into the equation for the sine curve

as  follows;

The width of the shoulders = 6 feet

∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.

Therefore, we get;

y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2

y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2

The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.

Learn more about the sine curve here;

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Answer: [tex]9a+14[/tex]

Step-by-step explanation:

Simplify: [tex]4(a+1)+5(a+2)[/tex]

Step 1. Distribute 4 into a and 1. By distributing you would get 4a and 4.

[tex]4*a=4a. \\4*1=4[/tex]

Step 2. Plug 4a+4 back into the remaining equation, which can be viewed below:

[tex]4a+4+5(a+2)[/tex]

Step 3. Distribute, [tex]5(a+2)[/tex] again. Same principle as what you did previously. You should get 5a and 10.

[tex]5*a=5a.\\5*2=10.[/tex]

Step 4. Plug 5a+10 back into the leftover equation, which is as follows.

[tex]4a+4+5a+10[/tex]

Step 5. Combine like terms. Which is broken down below,

[tex]4a+5a=9a.\\4+10=14.[/tex]

Once you're done combining like terms, you'll get the simplified answer which is: [tex]9a+14[/tex]

Answer:

9a +14

Step-by-step explanation:

4(a + 1) + 5(a + 2)

Distribute

4a+4  +5a+10

Combine like terms

4a+5a  +4+10

9a +14

Answer:

B.

Step-by-step explanation:

Since C and A are parallel

and B is perpendicular to C

then B is also perpendicular to A

meaning they have the same angle so 90 Degrees.

All you do is first you ha

Answer:

17 days

Step-by-step explanation:

as you see, 4=2^2

and 8=2^3

so we have a number sequence:

2+2^2+2^3+...+2^n=260000 (1)

multiply (1) by 2 we have:

2^2+2^4 +...+2^(n+1)=520000 (2)

(2) minus (1) we have:

2^(n+1)-2=260000

2^n*2=260002

2^n=130001

and we have 2^17=131072 >130001

so it will take her at least 17 days to buy the car

It will take her about 17 days to buy the car worth 260000 cents

If a student decides she wants to save money to buy a used car that cost $2600 (260,000 cents)

If she saves 2 cents the first day and doubles the amount thereafter, the sequence of savings will be:

2, 4, 8...

This sequence is geometric in nature

In order to determine how long it will take her to save 260,000, we will use the sum of a GP formula expressed as:

[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]

Given the folowing

a = 2

r = 4/2 = 8/4 = 2

Sn = 260,000

Substitute into the formula the given parameters

[tex]260000= \frac{2(2^n-1)}{2-1}\\260000/2=2^n-1\\130000 = 2^n - 1\\2^n = 130000 + 1\\2^n = 130001\\nlog 2=log130001\\n = \frac{log130001}{log2} \\n \approx 17[/tex]

This shows that it will take her about 17 days to buy the car worth 260000 cents

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9514 1404 393

Answer:

  19 hours

Step-by-step explanation:

Add up the numbers:

  3×3.5 +2×2.0 +4.5 = 19

Jacob trains 19 hours per week.

Answer:

Sin43 = x/13

x= 13* sin43

x= 8.865

Answer:

8.9

Step-by-step explanation:

using sine rule

[tex] \frac{x}{sin \: 43} = \frac{13}{sin \: 90} [/tex]

cross multiply

x sin 90=13 sin 43

x=13 sin 43

x=8.9

Answer:

U={-2,-1,0,1,2,3,4,5,6,7,8}

Answer:

[tex] x = 8\sqrt{2} [/tex]

Step-by-step explanation:

Leg = x

Hypotenuse = 16

[tex] x\sqrt{2} = 16 [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]

[tex] x = 8\sqrt{2} [/tex]

If y = x + 6√(x + 4), then

y' = 1 + 3/√(x + 4)

Substituting y and y' into the DE gives

(y - x) y' = (x + 6√(x + 4) - x) (1 + 3/√(x + 4))

… = 6√(x + 4) (1 + 3/√(x + 4))

… = 6√(x + 4) + 18

on the left side, while on the right you get

y - x + 18 = x + 6√(x + 4) - x + 18

… = 6√(x + 4) + 18

so both sides match and the given function is indeed a solution to the DE.

Answer: 6 con ga

Step-by-step explanation:

So ga ca 2 ban mua la:

2+4=6 (con ga)

Answer:

The solution set is {-2, 3}.

Step-by-step explanation:

We can do this by elimination after manipulating the 2 equations so that the coefficients of  y  will disappear after addition:

5x - 2y = -16        Multiply this by -5:

-25x + 10y = 80 ...........(A)

4x - 5y = -23       Multiply this by 2:

8x - 10y = -46..............(B)

Now add A and B:

-17x = 34

x = 34/-17

x = -2.

Now substitute x = -2 into the first original equation:

5(-2) - 2y = -16

-2y = -16 +10 = -6

y = -6/-2

y = 3.

Confirm these results by substitution in the second original equation:

4(-2) - 5(3)

= - 8  - 15 = -23.

Checks OK.

Answer:

a) 3.19

b) 3.29

c) 96.81

Step-by-step explanation:

Question a:

Levere's: 10.63s

Ross: 10.98s

10.98 - 10.63 = 0.35s shorter than 10.98s, so:

0.35*100%/10.98 = 3.19% shorter.

Question b:

35s longer than 10.63s, so:

0.35*100%/10.63 = 3.29% longer.

Question c:

3.19% shorter, so 100 - 3.19 = 96.81% of Ross.

Answer:

[tex]P(G_1) = \frac{5}{13}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

Step-by-step explanation:

Given

[tex]G = 5[/tex]

[tex]R = 4[/tex]

[tex]B = 4[/tex]

[tex]n = 13[/tex]

Solving (a): [tex]P(G_1)[/tex]

This is calculated as:

[tex]P(G_1) = \frac{G}{n}[/tex]

[tex]P(G_1) = \frac{5}{13}[/tex]

Solving (b): [tex]P(G_2)[/tex]

This is calculated as:

[tex]P(G_2) = \frac{G - 1}{n - 1}[/tex] -- this is so because the selection is without replacement

[tex]P(G_2) = \frac{5 - 1}{13 - 1}[/tex]

[tex]P(G_2) = \frac{4}{12}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

Solving (c): [tex]P(X \ge 1)[/tex]

Using the complement rule, we have:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

To calculate [tex]P(X = 0)[/tex], we have:

[tex]G = 5[/tex] --- Green

[tex]G' = 8[/tex] ---- Not green

The probability that both selections are not green is:

[tex]P(X = 0) = P(G'_1) * P(G'_2)[/tex]

So, we have:

[tex]P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{7}{12}[/tex]

Simplify

[tex]P(X = 0) = \frac{2}{13} * \frac{7}{3}[/tex]

[tex]P(X = 0) = \frac{14}{39}[/tex]

Recall that:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

[tex]P(X \ge 1) = 1 - \frac{14}{39}[/tex]

Take LCM

[tex]P(X \ge 1) = \frac{39 -14}{39}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

Answer:

3h33j333jj3

Step-by-step explanation:b3n3n3nn3n33

Answer:

Answer:

Maaf saya tidak paham

jadikan jawaban tercerdas, terimakasih

Answer:

nợ tk 1381: 2 triệu / có tk 152: 2 triệu

Answer:

D

Step-by-step explanation:

if you draw any vertical line through a function it should have a max of one intersection point so if the graph, reading from left to right doubles back on itself, it is not a function

Answer:

B

Step-by-step explanation:

-2/3x<31/3

x>-31/2

x>-15 1/2

Answer:

x > - 15 1/2

Step-by-step explanation:

-2/3 x -10 < 1/3

Multiply each side by 3

3(-2/3 x -10 < 1/3)

-2x -30 < 1

Add 30 to each side

-2x-30+30 <1+30

-2x < 31

Divide by -2 remembering to flip the inequality

-2x/-2 > 31/-2

x > -31/2

x > - 15 1/2

Answer:

true

Step-by-step explanation:

the incenter of a triangle is the common intersection of the angle bisectors.hence always remains inside the triangle.

Answer:

breathing, jk buddy

Step-by-step explanation:

Answer:

85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1

Step-by-step explanation:

The range is the an interval on the y-axis where the function is defined.

You can see that your function is y-wise going all the way down to negative infinity but then stops and continues the path along 2 on the upper bound.

The inequality describing the interval is thusly B,

[tex]-\infty\lt y\lt2[/tex]

Hope this helps :)

Answer:

español :/

Step-by-step explanation:

Answer:

256/5 pi

Step-by-step explanation:

= angle/360 × pi×r^2

= 72/360 × pi × 16^2

= 51.2 pi

= 256/5 pi

Answer:

4

Step-by-step explanation:

The given data is :

8, 10, 12,14,16,18,20

We need to find the standard deviation. Here,

Count = 7

Sum, Σx: 98

Mean, μ: 14

The standard deviation is given by :

[tex]\sigma=\sqrt{\dfrac{1}{N}\Sigma(x_i-\mu)^2}[/tex]

or

[tex]\sigma^2=\dfrac{1}{N}\Sigma(x_i-\mu)^2\\\\=\dfrac{(8-14)^2+...+(20-14)^2}{7}\\\\=\dfrac{112}{7}\\\\\sigma^2=16\\\\\sigma=4[/tex]

So, the standard deviation of the given data is 4.

Answer:

If you multiply a decimal by 10, the decimal point will move one place to the right. If you divide a decimal by 10, the decimal point will move one place to the left.

Step-by-step explanation:

Multiplying a decimal by 10 increases the value of each digit by 10. Multiplying a decimal by a power of 10 increases the value of each digit by a number of times that is equivalent to that power of 10. When a digit's value is changed, that digit is moved to the appropriate place.

Answer:

2x^2 - 9x -1 = 0

Solution: x = 9 ±√89/4

2x^2 -9x +6 = 0

Solution: 9 ± √33/4

Step-by-step explanation:

Given the equation;2x^2 - 9x -1 = 0

From the quadratic formula;

-b ±√ b^2 -4ac/2a

We have;

x= -(-9) ± √(-9)^2 - -4(2)(-1)/2(2)

x = 9 ±√89/4

Also;

Given the equation: 2x^2 -9x +6 = 0

From the quadratic formula: -b ±√ b^2 -4ac/2a

We have;

x= -(-9) ± √(-9)^2 - 4(2)(6)/2(2)

x= 9 ± √33/4

1.) 2x^2-9x+6 2.)  2x^2-8x+5 3.) 2x^2-9x-1   4.) 2x^2-8x-3

Step-by-step explanation:

Answer:

[tex]-5, 18, \sqrt{13}[/tex]

Step-by-step explanation:

We can solve the first equation, f of -3. The value of the function f is [tex]\frac{1+x^2}{x+1}[/tex], and plugging in -3 gets us [tex]\frac{1+9}{1-3}[/tex], this results in 10 divided by negative 2, which is negative 5.

Now, we must solve g of negative one third. The function g is defined as [tex]|9x-15|[/tex]. Plugging in negative one third into the question gets us [tex]|9(-\frac{1}{3})-15|[/tex]

9 times negative one third is -3, and -3 minus 15 is -18. The absolute value of -18 is 18.

Now, we must solve h of negative 2, and h is defined as [tex]\sqrt{-3-8x}[/tex]. Plugging in negative 2, we have [tex]\sqrt{-3-8(-2)}[/tex]. Negative 8 times negative 2 is positive 16, and 16 minus 3 is 13. The answer is the square root of 13

These are variables on your graph