Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)​

Answer: [tex]0.0003136\ J[/tex] or [tex]3.136*10^{-4}J[/tex]

Step-by-step explanation:

By definiition, when you multiply 1 Newton (N) by 1 meter (m), the unit obtained is an unit called "Joule", whose symbol is J.

Joule (J) is an unit of energy, work or heat.

Then to solve the exercise, you must multiply 0.0196 N by 0.016 m. Therefore, you obtain that the product is:

[tex](0.0196N)(0.016m)=0.0003136J[/tex] or [tex]3.136*10^{-4}J[/tex]

Answer:   0.000314mn

Step-by-step explanation:

(0.0196N)*(0.016M)

     0.000314mn

Answer:

line B.)

Step-by-step explanation:

2x+5y=10

5y=-2x+20

(5y/5) (2x+10/5)

y= (-2/5)x +2

The homogeneous ODE

[tex]36y''-y=0[/tex]

has characteristic equation

[tex]36r^2-1=0[/tex]

with roots at [tex]r=\pm\dfrac16[/tex], and admits two linearly independent solutions,

[tex]y_1=e^{x/6}[/tex]

[tex]y_2=e^{-x/6}[/tex]

as the Wronskian is

[tex]W(y_1,y_2)=\begin{vmatrix}e^{x/6}&e^{-x/6}\\\\\dfrac16e^{x/6}&-\dfrac16e^{-x/6}\end{vmatrix}=-\dfrac13\neq0[/tex]

Variation of parameters has us looking for solutions of the form

[tex]y_p=u_1y_1+u_2y_2[/tex]

such that

[tex]u_1=-\displaystyle\int\frac{y_2xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]

[tex]u_2=\displaystyle\int\frac{y_1xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]

We have

[tex]u_1=\displaystyle3\int x\,\mathrm dx=\dfrac{3x^2}2[/tex]

[tex]u_2=\displaystyle-3\int xe^{x/3}\,\mathrm dx=-9e^{x/3}(x-3)[/tex]

and we get

[tex]y_p=\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]

The general solution is

[tex]y=y_c+y_p[/tex]

[tex]y=C_1e^{x/6}+C_2e^{-x/6}+\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]

The initial conditions tell us

[tex]\begin{cases}1=C_1+C_2+27\\\\0=\dfrac{C_1}6-\dfrac{C_2}6-\dfrac92\end{cases}\implies C_1=\dfrac12,C_2=-\dfrac{53}2[/tex]

so that the particular solution is

[tex]y=\dfrac12e^{x/6}-\dfrac{53}2e^{-x/6}+\dfrac32x^2e^{x/6}-9e^{x/6}(x-3)[/tex]

No, it is not the same because in option 1, the interest is calculated based on two different principal amounts and then added together. The principal amounts will be different every year because of the varying interest rates. Since one of the interest rates in option 1 is 7%, the principal will grow at a faster rate because the interest rate is applied to a greater and greater principal amount over time. In option 2, the interest is being calculated only on one principal  

Answer:

Step-by-step explanation:

No, they are not always the same - the only time that they will be the same is after the first year:

$4000*1.05 + $4000*1.07 = $8480 = $8000*1.06

From there on, they will diverge. For example after the second year:

$4000*1.05^2 + $4000*1.07^2 = $8989.6

$8000*1.06^2 = $8988.8

After the third year:

$4000*1.05^3 + $4000*1.07^3 = $9530.672

$8000*1.06^3 = $9528.128

After the nth year:

The first option gives $4000*(1.05^n + 1.07^n)

The second option gives $8000*(1.06^n)

= $4000*(2)*(1.06^n)

= $4000*(1.06^n + 1.06^n)

Because 1.07^n - 1.06^n > 1.06^n - 1.05^n for n>1, the first option will be a better investment.

Buckets of Soil : Buckets of Peat Moss = 5 : 4

Since Mr Carver needs to use 324 buckets in all,

He needs to use 324 * 5/9 = 180 buckets of Soil and 324 * 4/9 = 144 buckets of Peat Moss.

Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed, based on the given ratio of 5 buckets of soil to 4 buckets of peat moss.

The problem at hand revolves around ratios and proportions where Mr. Carver is using a mix of soil and peat moss in a specific ratio to fill a planting bed. Given the ratio of 5 buckets of soil to 4 buckets of peat moss, we need to find the total number of buckets for each that will sum up to 324 buckets. First, we'll find the total number of parts in the ratio by adding 5 (for soil) and 4 (for peat moss), which gives us 9 parts. Since we have the total amount of 324 buckets, we can find the value of one part by dividing 324 by 9, which gives us 36.

Once we have the value of one part, we multiply it by the number of parts for soil and peat moss to find their respective quantities:

Therefore, Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed.

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D

Answer:

y = -3x + 20

Step-by-step explanation:

See attached photo for explanation

Answer: Option D.

Step-by-step explanation:

The expressions of boths sides of the equation must have the same value Or, in other words, if we call the expresion on the left side of the equation A, and the expression on the right side of the equation B, then:

[tex]A=B[/tex]

Keeping the above on mind, you can see that 5 and 11 are not equal, then:

5≠11

The correct value of s is:

[tex]s-3=11\\s=11+3\\s=14[/tex]

Substituting:

[tex]14-3=11\\11=11[/tex]

Answer:

No, because the last line of the work is not true. 5 and 11 are not equal.

Step-by-step explanation:

[tex]\boxed{A=43.54cm^2}[/tex]

To find this area we will use the law of cosine and the Heron's formula. First of all, let't find the unknown side using the law of cosine:

[tex]x^2=12^2+8^2-2(12)(8)cos(65^{\circ}) \\ \\ x^2=144+64-192(0.42) \\ \\ x^2=208-80.64 \\ \\ x^2=127.36 \\ \\ x=\sqrt{127.36} \\ \\ \therefore \boxed{x=11.28cm}[/tex]

Heron's formula (also called hero's formula) is used to find the area of a triangle using the triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] being [tex]a,\:b\:and\:c[/tex] the corresponding sides of the triangle.

So the semiperimeter is:

[tex]s=\frac{12+8+11.28}{2} \\ \\ s=15.64cm[/tex]

So the area is:

[tex]A=\sqrt{15.64(15.64-12)(15.64-8)(15.64-11.28)} \\ \\ \therefore \boxed{A=43.54cm^2}[/tex]

Answer:

92

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

140 = x+2 + 2x

Combine like terms

140 = 3x +2

Subtract 2 from each side

140-2 = 3x+2-2

138 = 3x

Divide by 3

138/3 = 3x/3

46=x

We want to find angle B

B = 2x

B = 2(46)

B = 92

Answer:

x = 13.9

Step-by-step explanation:

With respect to the angle shown, we have the hypotenuse (the side opposite the 90 degree angle) and we have the adjacent side (which is the side labeled x). thus we can use the ratio "cosine" to solve this.

The ratio of cosine is defined as:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]

Where adjacent and hypotenuse are the respective sides and [tex]\theta[/tex] is the angle

Thus, we can now write:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}\\Cos(35)=\frac{x}{17}\\Cos(35)*17=x\\x=13.9[/tex]

The first answer choice is right, x = 13.9

The value of X to the nearest tenth in the triangle is 13.9.  

We have the neighboring side, which is the side with the letter x, and the hypotenuse, which is the side across from the 90-degree angle, with regard to the angle displayed.

Therefore, the ratio "cosine" can be used to solve this.

The definition of the cosine ratio is:  [tex]Cos \theta[/tex] = Adjacent side / hypotenuse.

where the angle and the corresponding sides are called the hypotenuse and adjacent.

So that we may write now:

[tex]Cos(35)= \frac{x}{17}[/tex]

[tex]Cos(35) \times 17 = x[/tex]

Therefore 13.9 = x  .

For similar question on triangle.

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Answer:

60π

Step-by-step explanation:

If the circle has radius of 30 units, substitute r=30 into the formula C = 2πr.

C = 2π(30)

C = 60π

To find the circumference of the circle shown here, let's start with writing the formula down.

Circumference = 2[tex]\pi[/tex]r

We have to divide 60 by 2 because the radius is always half the diameter. Now, we can plug in 30 for r in the formula.

Now we have

circumference = 2[tex]\pi[/tex]30.

This equals 60[tex]\pi[/tex].

For this case we must express the number "423" in a radical way.

We have to, we can rewrite it as:

[tex]423 = 9 * 47 = 3 ^ 2 * 47[/tex]

So, we have to:

[tex]423 = \sqrt {3 ^ 2 * 47}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]423 = \sqrt {3 ^ 2 * 47} = 3 \sqrt {47}[/tex]

Answer:

[tex]3 \sqrt {47}[/tex]

Answer:

3^√4^2

Step-by-step explanation:

Answer:

Circumference

Step-by-step explanation:

The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr and C = πd.

Tom walks at a rate of 4/3 miles per hour, which means he will walk 1.333 miles in one hour at this rate.

To find out how many miles Tom will walk in 1 hour, we need to determine the distance he covers in 1/4 of an hour and then calculate how much he would walk in 1 hour at that rate.

Given Tom walks 1/3 of a mile in 1/4 of an hour, first find how much he walks in 1 hour:
1/3 mile ÷ (1/4 hour) = 1/3 mile * 4/1 hour = 4/3 miles in 1 hour

Therefore, Tom will walk 4/3 miles in 1 hour at that pace.

Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour given that he walks 1/3 of a mile in 1/4 of an hour based on the unit rate calculation.

The question deals with finding out how many miles Tom will walk in 1 hour if he walks 1/3 of a mile in 1/4 of an hour. To calculate this, we use the concept of a unit rate, which is finding how much of something is done in one unit of something else, in this case, miles per hour. Since Tom walks 1/3 of a mile in 1/4 of an hour, we can set up a proportion to find out how many miles he would walk in 1 full hour.

The proportion is: (1/3) miles / (1/4) hour = x miles / 1 hour. To solve for x, we multiply both sides of the equation by 1 hour so x would equal (1/3) miles \/ (1/4) hour. To simplify the right side, we invert the fraction in the denominator and multiply:
x = (1/3) miles \/ (1/4). When we multiply by the reciprocal of 1/4, which is 4, we get x = (1/3) \/ 1 \/ 4 = 4/3 miles.

Therefore, at this rate, Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour.

Answer:31.56

Step-by-step explanation:

take 37.50 and divide it by 100

then multiply that by 80

you should get 30,

30 is 80% of 37.50 which is 20% off of the original price

then you divide 30 by 100 and multiply it by 5.2

this will get you 1.56

add that to 30 and you get 31.56

This should help

3 * a - 2 = a + 10

Answer:

27 times

Step-by-step explanation:

Given that sphere A is  similar to sphere B

Let radius of sphere B be x. Then the radius of

sphere A be 3 times radius of sphere B = 3x

Volume of sphere A = [tex]V_A=\frac{4}{3} \pi (3x)^3\\V_A=36 \pi x^3[/tex]

Volume of sphere B = [tex]V_B = \frac{4}{3} \pi x^3[/tex]

Ratio would be

[tex]\frac{V_A}{V_B} =\frac{36 \pi x^3}{\frac{4}{3}\pi x^3 } \\=27[/tex]

i.e. volume of sphere is 27 times volume of sphere B.

Answer: 27

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

By using elimination to subtract the second equation from the first, we solve for x and then substitute x back into one of the original equations to solve for y, finding the solution as the ordered pair (1, -1).

To solve the system using elimination, we look at the given equations:

1) 5x + 4y = 1
2) -3x + 4y = -7

The goal is to eliminate one variable to solve for the other. In this case, we can subtract the second equation from the first one since they both have the same coefficient for y, which will eliminate the y variable.

Now that we have found x, we can substitute x into one of the original equations to find y:

5(1) + 4y = 1

The solution to the system is (1, -1), which is an ordered pair representing the x and y values that satisfy both equations.

the distance from the origin is 5, so

sqrt(x²+y²)=5

x²+y²=25

substitue y=x²

y+y²=25

y²+y-25=0

solve using calculator or the formula

to get

y =( -1+sqrt(1+4*25))/2

or y = (-1-sqrt(1+4*25))/2

the second solution is rejected because a square cannot be negative

the value of x is the positive or negative (sqrt... or -sqrt...) or y

Answer:

The exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

Step-by-step explanation:

We need to find the exact value of [tex]\tan(\frac{7\pi}{8})[/tex] using half angle identity.

Since, [tex]\frac{7\pi}{8}[/tex]  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

[tex]\frac{7\pi}{8}[/tex]  is not an exact angle.

First, rewrite the angle as the product of [tex]\frac{1}{2}[/tex] and an angle where the values of the six trigonometric functions are known. In this case,

[tex]\frac{7\pi}{8}[/tex] can be written as ;

[tex](\frac{1}{2})\frac{7\pi}{4}[/tex]

Use the half-angle identity for tangent to simplify the expression. The formula states that [tex] \tan \frac{\theta}{2}=\frac{\sin \theta}{1+ \cos \theta}[/tex]

[tex]=\frac{\sin(\frac{7\pi}{4})}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the numerator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the denominator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{\frac{2+\sqrt{2}}{2}}[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]\frac{-\sqrt{2}}{2}\times \frac{2}{2+\sqrt{2}}[/tex]

cancel the common factor of 2.

[tex]\frac{-\sqrt{2}}{1}\times \frac{1}{2+\sqrt{2}}[/tex]

Simplify,

[tex]\frac{-\sqrt{2}(2-\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-\sqrt{2}\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-2)}{2}[/tex]

simplify terms,

[tex]-\sqrt{2}+1[/tex]

Therefore, the exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

The exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] is [tex]\( \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

To find the exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] using the half-angle identity, we proceed as follows:

1. Identify the appropriate half-angle identity:

  The tangent half-angle identity is given by:

  [tex]\[ \tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos(\theta)}{\sin(\theta)} \][/tex]

2. Apply the identity for [tex]\( \theta = \frac{7\pi}{4} \)[/tex] :

  First, determine [tex]\( \theta = \frac{7\pi}{4} \)[/tex] , then find [tex]\( \frac{\theta}{2} \)[/tex].

3. Calculate [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex]:

  [tex]\[ \cos\left(\frac{7\pi}{4}\right) = \cos\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

  [tex]\[ \sin\left(\frac{7\pi}{4}\right) = \sin\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

4. Apply the half-angle identity:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{1 - \cos\left(\frac{7\pi}{4}\right)}{\sin\left(\frac{7\pi}{4}\right)} = \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \][/tex]

5. Simplify:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \][/tex]

Therefore, [tex]\( \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

Using the half-angle identity for tangent, we substituted [tex]\( \theta = \frac{7\pi}{4} \)[/tex] and calculated [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex] to find [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] in exact form.

1/4 = 1/8

times by 4 to find the whole song as 1/4 × 4 is 1

1 = 4/8

4/8 = 1/2 of a minute

Answer:

(F-G)(x) = -1

Step-by-step explanation:

The notation (F - G)(x) means to subtract each function when x = 6. According to the sets when x = 6 then F is (6,8) and G is (6,9). To subtract the functions, subtract their output values. (F-G)(x) = 8 - 9 = -1.

What sentence below

[tex]3 \times {( \frac{1}{8} )}^{2x} = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x} = 4 \\ \Leftrightarrow {( {2}^{ - 3}) }^{2x} = {2}^{2} \\ \Leftrightarrow {2}^{ - 6x} = {2}^{2} \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - \frac{1}{3} \\ \\ 2 {\sqrt[3]{5}}^{4x} = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^{4x} = 25 \\ \Leftrightarrow {5}^{ \frac{4x}{3} } = {5}^{2} \\ \Leftrightarrow \frac{4x}{3} = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = \frac{3}{2} [/tex]

Answer to Q1:

x= -1/3

Step-by-step explanation:

We have given the equations.

We have to solve these equations.

The first equation is :

[tex]3.(\frac{1}{8})^{2x}[/tex]

[tex](\frac{1}{8})^{2x}=4[/tex]

[tex](2^{-3x})^{2x}=4[/tex]

[tex]2^{-6x}=4[/tex]

[tex]2^{-6x}=2^{2}[/tex]

As we know that bases are same then exponents are equal.

-6x = 2

x = 2/-6

x=-1/3

Answer to Q2:

x = 3/2

Step-by-step explanation:

The given equation is :

[tex]2.\sqrt[3]{5}^{4x}=50[/tex]

We have to find the value of x.

First,we multiply both sides of equation by 1/2 we get,

[tex]5^{4x/3}=25[/tex]

[tex]5^{4x/3}=5^{2}[/tex]

4x/3=2

4x = 6

x = 3/2

Answer:

It is the answer C

Step-by-step explanation:

add payment history and total debt it gibes you 65%

The largest volume that the box can have is 2.25 ft^3, and it's obtained when x = 0.5 ft. This came from a mathematical analysis of the volume function V(x) = 4x^3 - 12x^2 + 9x.

Given that a square is cut from each corner of the cardboard to form an open box, we can come up with the following: The width of the base, represented by y, would be equal to the initial width of the cardboard (3 ft) minus two times the sides of the squares being cut out (2x), so y = 3 - 2x. Part c: will be the Volume of the box which is given by V = x * y^2, substituting for y from the relation obtained above we get. Part d: V = x * (3 - 2x)^2. Part e: is just the simplification of the equation obtained in part d: V(x) = 4x^3 - 12x^2 + 9x. Part f: To find the maximum volume, we need to find the critical points of the V(x) function, these are obtained by setting the derivative of the function equal to zero, solving for x will give x = 0.5 and x =1.5 but since x > 1.5 would give a negative y, the maximum volume is obtained at x = 0.5, substituting this x into the V(x) equation gives V = 2.25 ft^3.

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Answer:

128 ft / second.

Step-by-step explanation:

It's acceleration is due to gravity and is 32 ft s^-2.

To find the velocity when it hits the ground we use the equation of motion

v^2 = u^2 + 2gs    where  u = initial velocity, g = acceleration , s = distance.

v^2 = 0^2 + 2 * 32 * 256

v^2 = 16384

v =  128 ft s^-1.

The rock will strike the ground with a velocity of 128 ft/s and will experience an acceleration of 32 ft/s^2.

First, we need to calculate the time it takes for the rock to fall to the ground. We can use the equation h = (1/2)gt^2, where h is the height of the building (256 ft) and g is the acceleration due to gravity (32 ft/s^2). Solving for t, we find t = sqrt(2h/g) = sqrt(2(256)/32) = 4 seconds.

Next, we can calculate the velocity of the rock just before it hits the ground. We can use the equation v = gt, where g is the acceleration due to gravity and t is the time it takes to fall (4 seconds). Plugging in the values, we find v = (32 ft/s^2)(4s) = 128 ft/s.

Lastly, the acceleration of the rock is equal to the acceleration due to gravity, which is 32 ft/s^2.

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