1 cm = 5km scale ratio

Answer:

See Below.

Step-by-step explanation:

We are given the function:

[tex]\displaystyle y=\sqrt{\sin x}[/tex]

And we want to show that:

[tex]\displaystyle 4y^3\frac{d^2y}{dx^2}+y^4+1=0[/tex]

Find the first derivative of y using the chain rule:

[tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{\sin x}}\cdot \cos x = \frac{\cos x}{2\sqrt{\sin x}}[/tex]

And find the second derivative using the quotient and chain rules:

[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{1}{2}\left(\frac{(\cos x)'(\sqrt{\sin x})-(\cos x)(\sqrt{\sin x})'}{(\sqrt{\sin x})^2}\right) \\ \\ &=\frac{1}{2}\left(\frac{-\sin x\sqrt{\sin x} - \left(\cos x\right) \left (\dfrac{\cos x}{2\sqrt{\sin x}}\right)}{\sin x}\right) \\ \\ & = \frac{1}{2}\left(\frac{ -\sin x(2\sin x) -\cos x(\cos x) }{\sin x \left(2\sqrt{\sin x}\right) }\right) \\ \\ &= -\frac{1}{2} \left(\frac{2\sin^2 x + \cos^2 x}{2\sin^{{}^{3}\!/\! {}_{2}}x}\right)\end{aligned}[/tex]

Find y³:

[tex]\displaystyle y^3 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right) ^3= \sin^{{}^{3}\! / \! {}_{2} }x[/tex]

And find y⁴:

[tex]\displaystyle y^4 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right)^4 = \sin^2 x[/tex]

Substitute:

[tex]\displaystyle 4\left( \sin^{{}^{3}\! / \! {}_{2} }x\right)\left(-\frac{1}{2}\left(\frac{2\sin ^2x + \cos ^2 x}{2\sin^{{}^{3}\!/ \! {}_{2}}x}\right)\right)+\left(\sin ^2 x\right) + 1= 0[/tex]

Simplify:

[tex]-\left(2\sin^2 x + \cos^2 x\right) + \sin ^2 x + 1=0[/tex]

Distribute:

[tex]-2\sin ^2 x - \cos^2 x + \sin ^2 x + 1=0[/tex]

Simplify:

[tex]-\sin ^2 x - \cos^2 x + 1= 0[/tex]

Factor:

[tex]-(\sin ^2 x + \cos^2 x ) + 1=0[/tex]

Pythagorean Identity:

[tex]-(1)+1=0\stackrel{\checkmark}{=}0[/tex]

Q.E.D.

Answer:

c. y=2x−48

Explanation:

It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept

It also says he earns $2 per hot dog, so that will be our slope (rate of change)

Hope it helps! :]

y = 2x - 48 equation represents the profit earned by the x hot dog sold.

A linear equation is an algebraic expression in which highest power of the given variable is equals to one.

Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.

It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.

We need to establish an equation that represents the total profit,

According to the question,

x represents the number of hot dogs sold

y represents the total profit earned

Cost required for supply = $48

Profit on each hot dog sold = $2

As per the condition given, the required linear equation is =

y = 2x - 48

Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.

Learn more about linear equation here :

brainly.com/question/11897796

#SPJ7

Answer:

200

Step-by-step explanation:

4 is in the ones place so 4 just 4

7 is in the tens place so it is 70

2 is the hundreds place so 200

9 is in the thousands place so 9.000

The sum of the interior angles is 1260°

Answer:

The missing side length is of 5.

Step-by-step explanation:

The sides are proportional, which means that the missing side can be found using a rule of three.

x - 10

3 - 6

Applying cross multiplication:

[tex]6x = 30[/tex]

[tex]x = \frac{30}{6} = 5[/tex]

The missing side length is of 5.

Answer:

−2x^2+6x

Explanation:

You just have to distribute meaning you have to multiply -2x to the equation.

Answer:

Hello,

Answer 26.9

Step-by-step explanation:

[tex]z=\dfrac{x-m}{\sigma} \\m=20.8\\\sigma=5.2\\\\p(z>?)\geq 0.12\ \longrightarrow 1-p(z\leq ?)=(1-0.12))\\\\Using\ table\ of\ normal\ reduce\ with\ 4 \decimals : ?=1.175\\\\x=1.175*5.2+20.8=26.91\approx{26.9}[/tex]

9514 1404 393

Answer:

  $11,715.65

Step-by-step explanation:

The applicable formula is ...

  FV = P(1 +r/n)^(nt)

where principal P earns interest at rate r compounded n times per year for t years.

  FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65

The account will hold $11,715.65 after 5 years.

Answer:

0.01

Step-by-step explanation:

6/7% = 6÷7÷100 = 0.0085714286 round to the nearest hundredth = 0.01

Answer:

A) Exponential growth

Step-by-step explanation:

Answer:

i think 3

Step-by-step explanation:

Answer: [A] 2

Step-by-step explanation:

100% on edge 2023

Answer:

the last two answers are the only correct ones

9514 1404 393

Answer:

  x = 45°

Step-by-step explanation:

The triangle interior angle at I will be the supplement of the angle marked 2x. The triangle interior angle at G will be equal to x, the alternate interior angle with respect to transversal GI crossing the parallel lines.

The angle marked 3x is the sum of these "remote" interior angles:

  3x = 180 -2x +x

  4x = 180 . . . . . . . . . add x; next, divide by 4

  x = 180/4 = 45 . . . . . degrees

  x = 45°

Answer:

AC+ CD = ACD

X+1 + 2X + 2 = 30

3X+3 =30

3X=30–3

3X=27

X= 27/ 3

X= 9

I'm not sure of the solution, but I solved it according to a straight line (Line segment) .

I hope I helped you^_^

[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]

Answer:

Let r = amount of the 7% solution

y represent the amount of the 15 percent solution

r =7.5 L

y = 12.5 L

Step-by-step explanation:

Let r = amount of the 7% solution

y represent the amount of the 15 percent solution

.07r + .15 y = (r+y) .12

r+y = 20

y = 20-r

.07r + .15 (20-r) = (20) .12

0.07r+0.15(20-r)=2.4

.07r+ 3 - .15r = 2.4

-.08r = 2.4-3

-.08r = -.6

Divide by-.08

r =7.5

y = 20-7.5

y = 12.5

Step-by-step explanation:

there must be something wrong with your text.

what we can see is

3.8 × 105

and

1.9 × 1022

the true answer for these values has nothing to do with the 4 answer options.

maybe you meant

1.9 × 10.5 ?

because that answer would be 20.

but first working with the presented numbers :

3.8 × 105 = 399

1.9 × 1022 = 1941.8

so, the second number is actually much bigger than the first number.

but if it is

1.9 × 10.5 = 19.95

that works.

and we can either use the calculator to calculate

399 / 19.95 = 20

or we can simply look at the factor changes of the multiplication terms.

3.8 = 1.9 × 2

105 = 10.5 × 10

so, the multiplication product of the two larger numbers is then 2×10=20 times larger than the product of the 2 smaller numbers.

Answer:

8.75

Step-by-step explanation:

211/8 = 26.375

141/8 = 17.625

now,

211/8-141/8

26.375-17.625

8.75

I

2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound

Step-by-step explanation:

Which is the first sincetist of world

Option 1 - StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.

Step-by-step explanation:

Given : Expression "six less than the quotient of a number and two, increased by ten".

To find : What is the expression and value of expression when n = 8?

Solution :

Let the number be 'n'.

The quotient of a number and two i.e. \frac{n}{2}2n

Six less than the quotient of a number and two i.e. \frac{n}{2}-62n−6

Six less than the quotient of a number and two, increased by ten i.e. \frac{n}{2}-6+102n−6+10

The required expression is \frac{n}{2}-6+102n−6+10 .

Now, when n=8,

\frac{n}{2}-6+10=\frac{8}{2}-6+102n−6+10=28−6+10

\frac{n}{2}-6+10=4-6+102n−6+10=4−6+10

\frac{n}{2}-6+10=82n−6+10=8

The value of the expression is 8.

Therefore, option 1 is correct.

StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.

Answer:

37

Step-by-step explanation:

Tan(B) = 6/8

B= arctan(3/4)=37

Answer:

a)  [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

b)  [tex]n=24[/tex]

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]

Differentiating

[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]

Equating equ 1 to zero

[tex]0=\frac{20n^2+11556}{n}[/tex]

[tex]n=24[/tex]

Therefore

Substituting n

For Equ 1

[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]

F(n)>0  

For Equ 2

[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]

F(n)'<0

Answer:

1/144

Step-by-step explanation:

(-1/12)^2

(-1/12)*(-1/12)

1/144

Answer:

77/306 or around 25.2%

Step-by-step explanation:

[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement

just solve and you get 77/306

Answer:

Step-by-step explanation:

Use ^2 to indicate ²

y = (x-3)² + 8

This is an up-opening parabola.

Vertex (3,8)

Axis of symmetry: x = 3

Domain: ℝ

Range: [8,+∞)

Answer:

12 feet

BRAINLIEST, PLEASE!

Step-by-step explanation:

Area = base x height

60 = base x 5

base = 60/5

base = 12

Answer:

Paul is 2 and Kennedy is 6

Step-by-step explanation:

6 × 1/3 = 2

2 + 4 =6