Solve for x.
75°
11x-2

Answer:

\(transformation: (y,-x)\)

----------------------------

hope it helps...

have a great day!!

The derivative of \(r\) with respect to \(\theta\) can be found using the chain rule. Let's proceed with the differentiation:

\frac{dr}{d\theta} = \frac{d}{d\theta}\left(\cos\left(\frac{\theta}{3}\right)\right)

To differentiate \(\cos\left(\frac{\theta}{3}\right)\), we treat \(\frac{\theta}{3}\) as the inner function and differentiate it using the chain rule. The derivative of \(\cos(u)\) with respect to \(u\) is \(-\sin(u)\), and the derivative of \(\frac{\theta}{3}\) with respect to \(\theta\) is \(\frac{1}{3}\). Applying the chain rule, we have:

\frac{dr}{d\theta} = -\sin\left(\frac{\theta}{3}\right) \cdot \frac{1}{3}

Now, let's evaluate this derivative at \(\theta = \pi\):

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\sin\left(\frac{\pi}{3}\right) \cdot \frac{1}{3}

The value of \(\sin\left(\frac{\pi}{3}\right)\) is \(\frac{\sqrt{3}}{2}\), so substituting this value, we have:

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\frac{\sqrt{3}}{2} \cdot \frac{1}{3} = -\frac{\sqrt{3}}{6}

Therefore, the slope of the tangent line to the polar curve \(r = \cos(\theta / 3)\) at the point specified by \(\theta = \pi\) is \(-\frac{\sqrt{3}}{6}.

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Answer:

12 dimes, 10 nickels

Step-by-step explanation:

12x10=120 or in this case $1.20

10x5=50 or $0.50

50+120=170 or $1.70

Sorry if any of it is wrong, I am doing this in the car and in my head

the expression 7^-3 can be rewritten as 1/(7^3), and the calculated values of both expressions are equivalent.

Using a calculator to verify the equivalence, we can calculate:

7^-3 = 1/(7^3) = 1/343 ≈ 0.0029154518950437

Now, let's calculate the original expression 7^-3 using the calculator:

7^-3 ≈ 0.0029154518950437

As we can see, the calculated value for both expressions is approximately the same, verifying the equivalence.

Therefore, the expression 7^-3 can be rewritten as 1/(7^3), and the calculated values of both expressions are equivalent.

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The correct option is B. $35,713. f someone saves $950.00 of their take home pay at the end of every six months for 15 years and invests in an account earning 3% compounded monthly, they will have accumulated $35,713.

To calculate how much money will be accumulated in 15 years, we need to apply the formula;A=P(1+r/n)^(n*t)where;A = the accumulated amount

P = principal (the initial amount) r = annual interest raten = number of times the interest is compounded in a year t = number of years.

In this case, the principal amount is $950, the annual interest rate is 3%, compounded monthly. We need to find out how much will be accumulated in 15 years.

Therefore;A = 950(1+0.03/12)ᵃ  (a=12*15)A = 35,713

Thus, the total accumulated amount in 15 years would be 35,713. Therefore, the correct option is B. 35,713.

In conclusion, if someone saves $950.00 of their take home pay at the end of every six months for 15 years and invests in an account earning 3% compounded monthly, they will have accumulated $35,713.

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After solving, the factors of equation 4x²+16=34x are:

So,

Given equation: 4x²+16=34x

Then,

Factors are: (x-8) and (4x-2)

Therefore, after solving, the factors of equation 4x²+16=34x are:

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The correct question is given below:
Solve each equation.

4x²+16=34x

If the log odds of raining is a negative value, it indicates that the probability of not raining is higher than the probability of raining.

However, to determine which statements are correct, we need to further analyze the relationship between log odds, probabilities, and odds. Understand the relationship: Log odds represent the logarithm of the ratio between the probability of an event occurring (e.g., raining) and the probability of it not occurring (e.g., not raining). Odds, on the other hand, are the ratio of the probability of the event occurring to the probability of it not occurring.

Determine the effect of negative log odds: Negative log odds indicate that the odds of the event (raining) are less than 1. This implies that the probability of not raining is greater than the probability of raining.

Analyze the statements:

A. The probability of raining is greater than the probability of not raining: This statement is incorrect. Negative log odds imply the opposite; the probability of raining is lower than the probability of not raining.

B. The odds of raining is greater than 1: This statement is incorrect. Negative log odds suggest that the odds of raining are less than 1.

C. The odds of raining is less than 1: This statement is correct. Negative log odds indicate that the odds of raining are indeed less than 1.

D. The probability of raining is less than the probability of not raining: This statement is correct. Negative log odds imply that the probability of raining is lower than the probability of not raining.

Therefore, the correct statements are C and D.

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The Laplacian of the function r = xi + yj + zk is zero. This implies that the function r is harmonic, meaning it satisfies Laplace's equation.

The Taylor series expansion of a function f(t, x) to first order in At is given by:

f(t + At, x + Atf(t, x)) = f(t, x) + At ∂t f(t, x) + O(At^2)

where ∂t f(t, x) represents the partial derivative of f with respect to t evaluated at (t, x), and O(At^2) denotes higher-order terms.

Now, let's consider the function r = xi + yj + zk, where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

The Laplacian of a scalar function ϕ(r) is defined as the divergence of the gradient of ϕ. In Cartesian coordinates, it is given by:

∇²ϕ = ∂²ϕ/∂x² + ∂²ϕ/∂y² + ∂²ϕ/∂z²

Applying the Laplacian operator to the function r, we have:

∇²r = ∂²(xi + yj + zk)/∂x² + ∂²(xi + yj + zk)/∂y² + ∂²(xi + yj + zk)/∂z²

Since the unit vectors i, j, and k are constant with respect to x, y, and z, respectively, their second derivatives are zero. Therefore, we are left with:

∇²r = 0 + 0 + 0 = 0

So, the Laplacian of r is equal to zero.

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Answer:

the last one

Step-by-step explanation:

Answer:

352 students

Step-by-step explanation:

Given

See attachment for table

\(n = 400\)

Required

Attendance of students in this year's show

First, we calculate the mean of the table

\(Mean= \frac{\sum x}{n}\)

So, we have:

\(Mean= \frac{85\% + 91\% + 92\% + 87\% +84\% + 89\%}{6}\)

\(Mean= \frac{528\%}{6}\)

\(Mean= 88\%}\)

Multiply the mean by the total students

\(Expected = Mean * n\)

\(Expected = 88\% * 400\)

\(Expected = 352\)

Answer:352

Step-by-step explanation:

You basically just find the mean

Answer:

Step-by-step explanation: oop

Answer:

1. 5/2 2. -1/4 3. 0 4. 2 and 5. -1

Step-by-step explanation:

The photo above show you how I solved each problem out.

Hope this helped

Answer:

x - 3 > 10

There were more than

13

board games in Anne's cabinet to start.

Step-by-step explanation:

The variable x represents how many board games were in Anne's cabinet to start. Since she has already picked out 3 board games to bring, the expression x–3 represents how many board games are still in the cabinet.

And, since Anne has more than 10 board games still in her cabinet, x–3 must be greater than 10.

This inequality shows the relationship.

x–3>10

Now, solve for x.

x–3

> 10

x–3+3

> 10+3 Add 3 to both sides

x

> 13 Simplify

So, there were more than 13 board games in Anne's cabinet to start.

Step-by-step explanation:

a. parameter = (3x)+(3x)+(4x+3)+(4x+3) = 14x+6

b. area = (3x)(4x+3) = 12x²+9x

c. parameter = 14(2)+6 = 34

d. area = 12(2²)+9(2) = 66

e. parameter = (3x+1)+(3x+1)+(4x+3)+(4x+3) = 14x+8

Answer:

Range: 40

Median: 55

Mode: 72

Mean: 54.6

Step-by-step explanation:

First, let's put all of the numbers down.

32, 34, 35, 40, 41, 54, 54, 56, 63, 69, 70, 72, 72, 72

Now, to find the range, subtract 72 - 32 = 40

To find the median, find the number in the middle

32, 34, 35, 40, 41, 54, 54, 56, 63, 69, 70, 72, 72, 72

Because there are an even amount of numbers we will find the mean of those two numbers which would be 55.

To find the mode, look for the number that appears the most.

32, 34, 35, 40, 41, 54, 54, 56, 63, 69, 70, 72, 72, 72

To find the mean, add everything up.

32, + 34, + 35, + 40, + 41, + 54, + 54, + 56, + 63, + 69, + 70, + 72, + 72, + 72 = 764

Then, divide. 764 ÷ 14 = 54.6 when rounded to the nearest tenth.

I hope that this helps, and you have a great day! :)

Answer:

y=-1/2x+4

Step-by-step explanation:

the slope is -1/2x and y intercept is 4

Answer:

604

Step-by-step explanation:

Answer:

604

Step-by-step explanation:

6x10^2+4

6x100+4

600+4

= 604

Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".

The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.

The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:

(0.5x) + (0.1 * 80) = (0.4 * (x + 80))

Expanding and solving for x, we get:

0.5x + 8 = 0.4x + 32

0.1x = 24

x = 240

Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.

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Answer:

Your answer is: \(6+3i\)

Simplify by combining the real and imaginary parts of each expression.

Step-by-step explanation:

Hope this helped : )

Answer:

Monday

Step-by-step explanation:

Sophie tells truth on Monday, Tuesday, Wednesday, and Thursday. Mary tells truth on Monday, Friday, Saturday, and Sunday. Yesterday is the Sunday so Monday is the answer.

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Answer:

3x10 15x2 5x6

Step-by-step explanation:

Answer:

30 degrees

Step-by-step explanation:

if the hand goes from 3 to 5 it has rotated 30 degrees

If the first number is not allowed to be "0", we will have that the aviable numbers will be:

So, we will have 9 posibilites, now:

First, we will have that the biggest number of 7 digits that we will be able to write will be 9 999 999 and the smallest is 1 000 000.

Now, we will have that the total number of aviable values is:

Then, the total number of possible is:

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

-110

Step-by-step explanation:

Use PEMDAS

5[3(2) - 4(7)]

5(6 - 28)

5(-22)

-110

Step-by-step explanation:

5(3z-4r)

5(3*2-4*7)

5(6-28)

5(-22)=-110

The evaluated integral is (7/4) (π - (3√3)/6) (rounded to an appropriate decimal approximation based on the given values of π and √3).

To evaluate the integral ∫∫(7/2 cos(x)) dV, where the region of integration is given by V: 1 ≤ c ≤ 2 and 0 ≤ x ≤ cos⁻¹(2c-1), we can reverse the order of integration.

Step 1: Write the integral with reversed order of integration:

∫∫(7/2 cos(x)) dc dx

Step 2: Determine the limits of integration for the reversed order. The variable c now varies from 1 to 2, and x varies from 0 to cos⁻¹(2c-1). Therefore, the integral becomes:

∫[1,2] ∫[0,cos⁻¹(2c-1)] (7/2 cos(x)) dx dc

Step 3: Integrate with respect to x first. The integral with respect to x is straightforward:

∫[1,2] [sin(x)] [0,cos⁻¹(2c-1)] (7/2) dc

Step 4: Evaluate the inner integral:

∫[1,2] [sin(cos⁻¹(2c-1))] (7/2) dc

Step 5: Simplify the inner integral using the trigonometric identity sin(cos⁻¹(u)) = √(1 - u²):

∫[1,2] [√(1 - (2c-1)²)] (7/2) dc

Step 6: Integrate with respect to c:

(7/2) ∫[1,2] [√(1 - (2c-1)²)] dc

Step 7: Evaluate the integral:

Using the trigonometric substitution u = sin(t), du = cos(t) dt, and the limits change to t: π/6 ≤ t ≤ π/2.

(7/4) ∫[π/6, π/2] [√(1 - sin²(t))] cos(t) dt

Step 8: Simplify the integrand:

(7/4) ∫[π/6, π/2] [cos²(t)] dt

Step 9: Apply the double-angle formula for cosine:

(7/4) ∫[π/6, π/2] [(1 + cos(2t))/2] dt

Step 10: Split the integral into two separate integrals:

(7/4) [∫[π/6, π/2] (1/2) dt + ∫[π/6, π/2] (cos(2t)/2) dt]

Step 11: Integrate each term separately:

(7/4) [(t/2) + (sin(2t)/4)] evaluated from π/6 to π/2

Step 12: Substitute the limits and simplify:

(7/4) [((π/2)/2 + (sin(2(π/2))/4) - ((π/6)/2) - (sin(2(π/6))/4)]

Step 13: Simplify further:

(7/4) [(π/4 + 0 - π/12 - (1/4)(√3/2))]

Step 14: Simplify and calculate the final value:

(7/4) [(π/4 - π/12 - (√3/8))]

= (7/4) [(3π - π - 3√3)/12]

= (7/4) [(2π - 3√3)/12]

= (7/4) (π - (3√3)/6)

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We would need 168 square inches of Teflon to completely cover the triangular prism machinery.

To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.

The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.

The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.

Therefore, the total surface area of the triangular prism is

bh + 3lh

To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.

Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is

bh + 3lh

= (4 in. x 6 in.) + 3(8 in. x 6 in.)

= 24 in² + 144 in²

= 168 in²

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