Two point particles are attached to each other via a light in-extensible string that passes over a ring hanging from the ceiling via a chain. Find an expres- sion for the tension in the string and the chain.​

We are asked to solve the integral:

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}}[/tex]

Re write as

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)\{1-\tan (x)\}}}[/tex]

Using (1/cos x) = sec(x), we have

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\sec^{2}(x)dx}{1-\tan (x)}}[/tex]

Now, substitute 1 - tan (x) = t, so that -dt = sec²(x) dx

[tex]{:\implies \quad \displaystyle \sf -\int \dfrac{1}{t}dt}[/tex]

[tex]{:\implies \quad \sf log|t|+C}[/tex]

[tex]{:\implies \quad \boxed{\displaystyle \bf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}=-log|1-\tan (x)|+C}}[/tex]

Where, C is any Arbitrary Constant

Answer:

A

Step-by-step explanation:

The quotation mark is missing at the very end of the last quote right after:

I was faking.

Answer:

i think A

Step-by-step explanation:

The quotation mark is missing at the very end

Answer:

A = 5 [tex]\frac{5}{6}[/tex] ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × 2 [tex]\frac{1}{3}[/tex] ← convert to improper fraction

   = [tex]\frac{5}{2}[/tex] × [tex]\frac{7}{3}[/tex]

   = [tex]\frac{5(7)}{2(3)}[/tex]

   = [tex]\frac{35}{6}[/tex]

   = 5 [tex]\frac{5}{6}[/tex] ft²

Answer:

216

Step-by-step explanation:

LxWxH fill it in 3x6x12=216

Answer:

Step-by-step explanation:

what does each block mean

Answer:

x = 2

y = 15

Step-by-step explanation:

As the triangle is split with a line that is parallel to the base:

[tex]\implies x:6=6:18[/tex]

[tex]\implies \dfrac{x}{6}=\dfrac{6}{18}[/tex]

[tex]\implies x=\dfrac{6\cdot 6}{18}[/tex]

[tex]\implies x=\dfrac{36}{18}[/tex]

[tex]\implies x=2[/tex]

Similarly:

[tex]\implies y:20=6 : (6+x)[/tex]

[tex]\implies y:20=6:8[/tex]

[tex]\implies \dfrac{y}{20}=\dfrac68[/tex]

[tex]\implies y=\dfrac{6 \cdot 20}{8}[/tex]

[tex]\implies y=\dfrac{120}{8}[/tex]

[tex]\implies y=15[/tex]

Answer:

x= 5.18

y= 16.97

Step-by-step explanation:

Solve Y first-

trigonometric theorems-

[tex]c^2 =a^2 + b^2\\\\b^2 =c^2 - a^2[/tex]

[tex]y^2 =18^2-6^2 \\y^2 =324 - 36\\y^2= 288\\\sqrt{2} = \sqrt{288} \\ y=16.97[/tex]

solve x-

20-16.97=3.03

x=5.18

(I'm not sure if the answers are correct. I tried my best. I was confused to solve x though. )

[tex]I=\displaystyle \int ^{\pi}_{\tfrac{\pi}3} \dfrac{ \sin x}{1 + \cos^2 x} dx\\ \\\\\text{let,}\\\\~~~~~u=\cos x\\\\\implies \dfrac{du}{dx} =-\sin x\\ \\\implies \sin x~~ dx = -du\\\\\text{When}~~ x = \pi , ~~ u = \cos \pi = -1\\\\\text{When}~~ x = \dfrac{\pi}3 , ~~u = \cos \dfrac{\pi}3 =\dfrac 12\\ \\\\I =- \displaystyle \int ^{-1}_{\tfrac 12} \dfrac{du}{1+u^2}\\\\\\[/tex]

  [tex]=\displaystyle \int ^{\tfrac 12}_{-1} \dfrac{du}{1+u^2}~~~~~~~~~~;\left[\displaystyle \int^{a}_b f(x) dx = - \displaystyle \int^{b}_a f(x) dx ,~ b < a\right]\\\\\\=\left[\tan^{-1} u \right]^{\tfrac 12}_{-1}~~~~~~~~;\left[ \ddisplaystyle \int \dfrac{dx}{ 1+ x^2} = \tan^{-1} x + C \right]\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \tan^{-1} 1\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \dfrac{\pi}4 \\\\\\=1.249[/tex]

Answer:

the answer to 2/5x+7=-11 is X=-45

Step-by-step explanation:

Multiply both sides by 5 to get rid of the division giving you 2x+35=-55

isolate the x Value by moving all non x numbers to one side giving you 2x=-90

divide by 2 to get X alone giving you x=-45

Answer:

9÷10

Step-by-step explanation:

9÷10=0.9

Answer: x > 64 and x < 68 is another way of rewriting inequality.

Step-by-step explanation:

To qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches.

⇒The inequality 64 < x < 68, where x represents height,gives the range of height.

⇒In other words range of height can be x > 64 and x < 68 , such that both conditions are applied to single actor.

[with the use of or it will appear to give priority by actor to follow any 1 conditon]

Answer:

$ 6.31

Step-by-step explanation:

The TOTAL amount in the account in 3 years will be

40 ( 1+.05)^3 = 46.31

  subtract the orignal 40 deposit to get the interest =6.31

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A=40\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A\approx 46.31~\hfill \underset{earned~interest}{\stackrel{46.31~~ - ~~46}{\approx 6.31}}[/tex]

D. 4032 cups

Step-by-step explanation:

336 x 12 = 4032

Hope this helps!

Answer:

4,032

Step-by-step explanation:

Just multiply 336 times 12. This is becuase they are not asking for adele's amount.

Answer:

$38

Step-by-step explanation:

[tex] \frac{40 + 30 + 32 + 45 + x}{5} = 37[/tex]

[tex] \frac{147 + x}{5} = 37[/tex]

[tex]147 + x = 185[/tex]

[tex]x = 38[/tex]

Answer:

66.9 ft

Step-by-step explanation:

Kite string forms a right triangle with the horizontal 3.5 feet off of the ground

sin 25  = opp / hyp  = height / 150

sin 25 = height / 150

150 sin25 = height      but it is 3.5 feet off of the ground...add that in

3.5  + 150 sin25 = true height = ~ 66.9 ft

Answer:

A) 50 households are randomly selected from the town; 14 own a dog

B) 98

Step-by-step explanation:

A) The first choice is the most logical because it doesn’t factor in the accommodations that the other two do.

B) There are 14 households that own dogs per 50 houses, so multiply by 7 to find how many dogs are in the whole town:

50 x 7 = 350 houses

14 x 7 = 98 households

Answer:

the answer should be 1,600,000

Step-by-step explanation:

hope this helps ya!!

Answer:

Step-by-step explanation:

1,5x0,000   x holds the place that you'll want to note if it's 5 or larger, to determine if you round up or down.   Because in the problem you've been given, it's an 8,   so round up

1,600,000  is the answer then.  

Answer:

  radius: 14.96 in

  length: 47 in

Step-by-step explanation:

The dimensions of the package with maximum volume can be found by differentiating the volume function, subject to the constraint on the dimensions.

__

The volume of the cylindrical package is ...

  V = πr²h

The constraint on the dimensions is ...

  circumference + length = 141 inches

  2πr +h = 141 . . . . . at maximum volume

Solving the second equation for h, we can write the volume function in terms of r alone:

  h = 141 -2πr

  V = πr²(141 -2πr) . . . . substitute for h

  V = 141πr² -2π²r³ . . . eliminate parentheses

__

Differentiating with respect to radius, we find the radius at maximum volume must satisfy ...

  V' = 282πr -6π²r² = 0

Dividing by 6πr, we can simplify this to ...

  47 -πr = 0

  r = 47/π ≈ 14.96 . . . . inches (radius)

  h = 141 -2πr = 47 . . . inches (length)

This is about optimization problems in mathematics.

Dimensions; Height = 48 inches; Radius =  48/π inches

We are told the combined length and girth is 144 inches.

Girth is same as perimeter which is circumference of the circular side.

Thus; Girth = 2πr

If length of cylinder is h, then we have;

2πr + h = 144

h = 144 - 2πr

Now, to find the dimensions at which the max volume can be sent;

Volume of cylinder; V = πr²h

Let us put 144 - 2πr for h to get;

V = πr²(144 - 2πr)

V = 144πr² - 2π²r³

Differentiating with respect to r gives;

dV/dr = 288πr - 6π²r²

Radius for max volume will be when dV/dr = 0

Thus; 288πr - 6π²r² = 0

Add 6π²r² to both sides to get;

288πr = 6π²r²

Rearranging gives;

288/6 = (π²r²)/πr

48 = πr

r = 48/π inches

Put 48/π for r in h = 144 - 2πr to get;

h = 144 - 2π(48/π)

h = 144 - 96

h = 48 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rate of change is defined as the derivative of the function, or also known as the slope. The derivative here would be 3. Another function which has the same rate of change would be any function with a slope of 3. A few example are:

f(x) = 3x + 1

f(x) = 3x + 2

Answer:

The answer is c

Step-by-step explanation:

Answer:

(x - 4)^2 + (y - 6)^2 = 100

Answer:

x=8

Step-by-step explanation:

If you combine like terms (5x and 4x) it would become:

x+9 = 17

subtract 9 on both sides

x=8

Answer:

8

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2+2-2+4÷2

we go through

P- parentheses

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

also note that we read it from left to right becaue × is not more important than ÷ and same goes to + and -

First step

2+2-2+(4÷2) --> 2+2-2+2

then

2+2-2+2 --> 4-2+2

then

4-2+2 --> 2+2

finally

2+2=4

Answer:

4

Step-by-step explanation:

Using compound interest, it is found that he must invest his money at a rate of 8.78% a year.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, the parameters are as follows:

t = 3, A(t) = 60000, P = 46150.3, n = 12.

Hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]60000 = 46150.3\left(1 + \frac{r}{12}\right)^{12 \times 3}[/tex]

[tex]\left(1 + \frac{r}{12}\right)^{36} = 1.3[/tex]

[tex]\sqrt[36]{\left(1 + \frac{r}{12}\right)^{36}} = \sqrt[36]{1.3}[/tex]

[tex]1 + \frac{r}{12} = (1.3)^{\frac{1}{36}}[/tex]

[tex]1 + \frac{r}{12} = 1.00731451758[/tex]

[tex]\frac{r}{12} = 0.00731451758[/tex]

r = 12 x 0.00731451758

r = 0.0878.

He must invest his money at a rate of 8.78% a year.

More can be learned about compound interest at https://brainly.com/question/25781328

Answer:

  D.  y = 1.5x +5

Step-by-step explanation:

The offered answer choices are equations in slope-intercept form. The constant in the equation is the y-intercept, the value of distance when time is zero.

   y = mx +b . . . . m is slope; b is y-intercept

__

The table tells you that the distance value is 5 when the time value is 0. In the equation, that means ...

  b = 5

Only one answer choice matches:

  y = 1.5x +5