I need help with this problem

Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.

Taking the derivative of the numerator:

d/dθ [1 - sin(θ)] = -cos(θ)

Taking the derivative of the denominator:

d/dθ [1 + cos(6θ)] = -6 sin(6θ)

Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))

When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:

= 0 / (-6)

= 0

Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.

Answer:

The parent function is y = x³.

After a vertical stretch by a factor of 3, obtain

y = 3x³

After a horizontal shift 4 unit to the right, obtain

y = 3(x - 4)³

After a vertical shift 3 units down, obtain

y = 3(x - 4)³ - 3

Answer:   y = 3(x - 4)³ - 3

y = 3(x - 4)³ - 3  is the equation of y=x³ with the given transformations

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The given equation is y=x³

A translation of a graph is its rigid movement, vertically or horizontally.

From given we have,

There is a vertical stretch of 3 units, hence the function is multiplied by 3.

There is a horizontal shift of 4 units to the right, hence x -> x - 4.

There is a vertical shift of 3 units down, hence 3 is subtracted from the function.

The required equation is given by y = 3(x - 4)³ - 3.

Hence  y = 3(x - 4)³ - 3  is the equation of y=x³ with the given transformations

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The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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The integral test can be applied to the series and it converges as the improper integral of ln(x)/x^7 from 1 to infinity convergent.

The integral test can be applied to the series because its terms are continuous, positive, and decreasing. To use the integral test, we consider the corresponding improper integral

\(\int\limits^1_\infty ln(x) / x^7 \, dx\)

Using integration by parts with u = ln(x) and dv = 1/x^7 dx, we obtain

\(\int\limits^1_\infty ln(x) / x^7 \, dx\) = [-ln(x) / 6x^6] [1,∞] + \(\int\limits^1_\infty1 / (x^2 6x^6) \, dx\)

The first term evaluates to zero because ln(∞) = ∞ and limx→0 ln(x) / x^6 = 0. The second term can be integrated as follows

\(\int\limits^1_\infty1 / (x^2 6x^6) \, dx\) = [-1 / 6x^5] [1,∞] = 1 / 30

Therefore, the integral test yields

\(\int\limits^1_\infty ln(x) / x^7 \, dx\) < ∞

Since the integral is convergent, the series is also convergent. Thus, the series [infinity] ln(n) n^7 n = 1 converges.

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Answer:

4, -3, -2, -1, 0, 1

Step-by-step explanation:

since there are 6 consecutive integers, we can say create an equation:

n + (n+1) + (n+2) + (n+3)+ (n+4) + (n+5) = -9

add like terms to get:

6n + 15 = -9

subtract 15 from both sides:

6n = -24

divide both sides by 6 and you get n:

n = -4

plug -4 into n + (n+1) + (n+2) + (n+3)+ (n+4) + (n+5) to find all six integers:

-4 + (-4 + 1) + (-4 + 2) + (-4 + 3)+ (-4 + 4) + (-4 + 5)

simplify the parenthesis:

-4, -3, -2, -1, 0, 1

the sum of all of these number are -9

Answer: a ≤ 2

Step-by-step explanation:

How to write an inequality statement:

Step 1: Write the two values being compared in the problem.

Step 2: Determine whether the first value is larger or smaller than the second value.

Step 3: Express the inequality with the right symbols:

≤ = less than or equal to

≥ = greater than or equal to

Therefore, the answer would be a≤2.

Hope this helped!

Answer:

6 and -2

Step-by-step explanation:

Answer:

the more pointy side is the way to go

Step-by-step explanation:

there will be a pointy side and a dull side the pointy side is the one

When a boat is traveling north, the compass needle will also point in that same direction.

The definition of direction includes the course that something follows, the route that must be taken to go to a particular location, the direction that something is beginning to travel, or the direction that you are facing.

When a boat is traveling north, the compass needle will also point in that same direction.

The compass needle will point North if it moves in the direction of North. Therefore, the boat can only be moving north if it is pointing in the same direction as the needle.

So, Where the point of red line in needle shows, it will be north direction.

And according to this direction remaining direction can be compared.

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Answer:

\(3x^2+4x+8\)

Step-by-step explanation:

To find the value of \(7x^2+6x+9-4x^2-2x-1\)

We need to combine like terms by grouping

\(7x^2-4x^2+6x-2x+9-1\)

= \(3x^2+4x+8\)

Hope this helps :)

Have a great day!

Answer:

19

Step-by-step explanation:

Substitute the value of x for 5 in the function.

f(x) = 3x + 4

f(5) = 3(5) + 4

f(5) = 19.

Answer:

Answer is 19

Step-by-step explanation:

\(f |x| = 3x + 4 \: \: \: \: \: f |5| = \\ f |5 | = 3 \times 5 + 4 \\ f |5| = 19\)

I hope this helps you

Cyber safety is the use of information and communication technologies in a responsible and safe manner. It involves protecting information and keeping it secure, but it also entails handling information responsibly, showing consideration for others online, and following proper internet etiquette.

The Essential Eight are a collection of eight mitigation techniques: application control, application patching, configuring Microsoft Office macro settings, user application hardening, limiting administrative rights, operating system patching, multi-factor authentication, and regular backups.

Best Cybersecurity Advice for 2023:

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Answer:

x=5

Step-by-step explanation:

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  4x - 8  =   4 • (x - 2)

Equation at the end of step

2

:

 (0 -  12 • (x - 2)) -  -36  = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  60 - 12x  =   -12 • (x - 5)

Equation at the end of step

4

:

 -12 • (x - 5)  = 0

STEP

5

:

Equations which are never true:

5.1      Solve :    -12   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-5 = 0

Add  5  to both sides of the equation :

                     x = 5

In linear equation, 103000  is the minimum acceptable settlement on a case on which the attorney spent 110 hours.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let x be the amount settlement.

  amount he earn from client = 175 * 110

                                         = 19250

     amount he earn from settlement = x * 25/100  = x/4

        according to given condition

                         19250 + x/4 ≥ 45000

                     x/4 ≥ 45000 - 19250

                    x/4 ≥ 25750

                    x ≥ 25750 * 4

                     x ≥ 103000

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Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

Answer:

Step-by-step explanation:

There are no statements here

The fixed asset turnover ratio for Gemology Inc. is 8.5.

The fixed asset turnover ratio measures how efficiently a company utilizes its fixed assets to generate sales.

It is calculated by dividing net sales by average net fixed assets.

To calculate the average net fixed assets, we sum the net fixed assets at the beginning and end of the period and divide by 2.

Given the information provided,

The net fixed assets at the beginning of the period are $125,000 and the net fixed assets at the end of the period are $75,000.

Therefore, the average net fixed assets would be

($125,000 + $75,000) / 2 = $100,000.

The net sales for Gemology Inc. are $850,000.

Now, we can calculate the fixed asset turnover ratio by dividing net sales ($850,000) by the average net fixed assets

($100,000): $850,000 / $100,000 = 8.5.

Therefore, the fixed asset turnover ratio for Gemology Inc. is 8.5, indicating that the company generates $8.50 of sales for every dollar invested in fixed assets.

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Answer:

£12000

Step-by-step:

x*1.005³=12180.9

12180.9/1.005³ = 11999.998

=£12000

The amount of money Simon invested in the savings account is £12000.06

The formula for calculating the compound interest is expressed as:

A = P(1+r)^t where;

A is the amount after 3 years = £12180.90

P is the amount invested (principal)

r is the rate = 0.5% = 0.005

t is the time (in years) = 3years

Substitute the given values into the formula as shown:

12180.90 = P(1+0.005)^3

12180.90 = P(1.005)^3

12180.90 = 1.01508P

P = 12180.90/1.01508

P = 12,000.06

This shows that the amount of money Simon invested in the savings account is £12000.06

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Answer:

Step-by-step explanation:

Total number of days

The number of days she bought a banana or orange

The probability of buying a banana or an orange is

Answer:

\(\sf \dfrac{7}{10}=0.7=70\%\)

Step-by-step explanation:

Given information:

Total number of days = 30

Probability Formula

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

Probability of buying a banana:

\(\implies \sf P(Banana)=\dfrac{12}{30}\)

Probability of buying an orange:

\(\implies \sf P(Orange)=\dfrac{9}{30}\)

Therefore,

\(\implies \sf P(Banana) \: or \: P(Orange)=\sf \dfrac{12}{30}+\dfrac{9}{30}=\dfrac{21}{30}=\dfrac{7}{10}\)

So the probability of buying either a banana or an orange is:

  \(\sf \dfrac{7}{10}=0.7=70\%\)

The value of Z is -66.7

What is an inverse function?

An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.

Here, we have

Given: Suppose x varies directly as y, and x varies inversely as z.

Find z when x= 10 and y= −7, if z= 20 when x= 6 and y= 14.

X = K(Y/Z) if x =10, y=-7, Z=20

substituting in the equation 10 = K(-7/20)

solving for K = -28.6

When x = 6, Y = 14, and K(constant) = -28.6

6 = -28.6(14/Z)

solving for Z by cross multiplication, we get

Z = -66.7

Hence, the value of Z is -66.7

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Answer:

31/3÷43/4

=31×4/43×3

=124/129

Answer:

40/57

Step-by-step explanation:

keep change flip.

change the mixed fractions to improper by multiplying the integer by the denominator and then add the numerator.

should give you an answer of 10/3 and 19/4

which when put into the fraction-division rule equals 40/57

A) The probability of selecting a tomato soup can on the first draw = 4/10

The probability of selecting another tomato soup can on the second draw (without replacement) = 3/9

The probability of selecting a pumpkin soup can on the first draw = 6/10

The probability of selecting another pumpkin soup can on the second draw (without replacement) = 5/9

B) Probability of selecting one tomato soup can and one pumpkin soup can = probability of (i) + probability of (ii)

= 2/15 + 1/3

= 1/3

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Using the theories of Application of derivative,we got that  59.11221inches³/sec  is rate of volume changing when the radius is 2.3 inches.

We are given rate of change of radius (dr/dt)=0.6inches

We know very well that volume of sphere is given by (4/3)πr³

where r is the radius of the sphere.

Now, differentiating the volume with respect to radius, we get

=>dV/dr=4πr²

=>dV/dt=(dv/dr)·(dr/dt)

=>dV/dt=4πr².(dr/dt)

We are given that dr/dt=0.6inches/sec

So, dV/dt=4πr²·(0.6)

Now, putting values of r=2.3

 dV/dt=4π(2.3)²×(0.6)

=>dV/dt=4×3.14×2.3×2.3×0.6

=>dV/dt=59.11221inches³/sec

Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.

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Answer:

x=3 and y= 4 / 3 (Fraction)

Step-by-step explanation:

Substitute x for 6y-5.

2(6y−5)−3y=2

Add 6y and 3y, and multiply 5 by 2/Simplify the equation.

9y−10=2

Add  10 to both sides, and then divide each side by 9.

9y−10+10=2+10

9y / 9 = 12 / 9

y = 4/3.

Repeat the process but replace y with 4/3!

Answer:

x=3

y= 4/3

Step-by-step explanation:

2(6y-5)-3y=2

y= 4/3

x=6x 4/3-5

x=3

Complete question :

Abdul's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Abdul $4.25 per pound, and type B coffee costs $5.90 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $337.05 . How many pounds of type A coffee were used?

Answer:

21 pounds

Step-by-step explanation:

Pounds of coffee A used = x

Pounds of coffee B = 2x

Cost per pound of A = $4.25

Cost per pound of B = $5.90

Total cost of coffee = $337.05

4.25x + 2x(5.90) = 337.05

4.25x + 11.8x = 337.05

16.05x = 337.05

x = 337.05 / 16.05

x = 21

Hence, 21 pounds of coffee A was used

Answer:

(4,3)

Step-by-step explanation:

f(x) = a(x-h)^2 +k is the vertex form of a parabola

where (h,k) is the vertex

f(x) = (x-4)^2 +3

    yields a  vertex of (4,3)

Answer: The answer is A 4,3

Step-by-step explanation:

Step-by-step explanation:

1)

Prime factorization of 36 is: 2 x 2 x 3 x 3.

Prime factorization of 196 is: 2 x 2 x 7 x 7.

Prime factorization of 361 is: 19 x 19.

2)

Greatest Common Factor of 126 and 144 is: 18.

Least Common Multiple of 28, 42, and 63 is: 252.

3)

2/3+3/4=17/12.

2/3-3/4= -1/12.

3 2/3 x 1 3/4 = 6 5/12.

The given problem states that x and y vary inversely, and by using the given values, an equation is formed (x * y = 9) which can be used to find y when x = 3 (y = 3).

Since x and y vary inversely, we can write the equation as x * y = k, where k is a constant.

Using the given values x = 1 and y = 9, we can substitute them into the equation to find the value of k:

1 * 9 = k

k = 9

Therefore, the equation relating x and y is x * y = 9.

To find y when x = 3, we substitute x = 3 into the equation:

3 * y = 9

y = 9 / 3

y = 3

So, when x = 3, y = 3.

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