find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (3π, 0)

Answer:

[tex]0.15*x \leq 4.5\\x \leq 30\\Where\ x \ represents\ the\ amount\ of\ candy[/tex]

Step-by-step explanation:

Divide the amount we have by the price of the sweets, and write it into an inequality.

The inequality symbol represents that the total price of all the sweets we want to buy cannot be larger than our budget.

The value of the the angle tanPQS is 24.65⁰

You should understand that a cuboid is a polygon with six faces, the four opposite sides form a quadrilateral and diagonals make right triangles.

The image is a cuboid that has similar sides

From the cuboid, the length of PS=QR=5cm

Also, the length PQ = 12 cm

Using Pythagoras rule,

12²-5²=SQ

This means that 144-25 = SQ

Then SQ=√19 = 10.9

Also, from trigonometric ratio,

TanPQS= opposite/adjacent

Tan PQS= 5/10.5

Tan PQS= 0.4587

PQS = tan⁻¹0.4587

In conclusion <PQS=24.65⁰

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About 13 gallons. Paid $2.76 per gallon rounded

12.762 rounded up is about 13. After tge decimal look at the 7, then 6 next to it. Anything 5 or higher round up. 4 or lower, round down.

Same rules with the amount per gallon.

The equation of the circle with a radius of 12 and a center at (11, -9) is

x² + y² - 22x + 18y + 58 = 0

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is given as πr²

We have,

Equation of a circle:

(x - h)² + (y - k)² = r²

Where (h. k) is the center of the circle and r is the radius of the circle.

Now,

The radius of the circle = 12

Center of the circle = (11, -9) = (h, k)

Now,

(x - h)² + (y - k)² = r²

(x - 11)² + (y + 9)² = 12²

(x - 11)² + (y + 9)² = 144

x² - 22x + 121 + y² + 18y + 81 = 144

x² + y² - 22x + 18y = 144 - 121 - 81

x² + y² - 22x + 18y + 58 = 0

Thus,

x² + y² - 22x + 18y + 58 = 0 is the equation of the circle.

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Option(C) represents the function.

What is a function?

A function is a relation between a set of inputs (also called the domain) and a set of outputs (also called the range) such that for each input, there is exactly one output. A graph of a function is a visual representation of the relationship between the inputs and outputs, with the inputs represented on the x-axis and the outputs represented on the y-axis.

A curve can be a function if it meets the definition of a function, which states that for each input (x value), there is exactly one output (y value). In other words, no two points on the curve have the same x-coordinate but different y-coordinates.

Hence, Option(C) represents the function.

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Using Pythagoras theorem, the hypothenuse is equal 4 units

Pythagoras theorem states that in a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as a²+ b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

The length of the third side is the hypothenuse and we can use Pythagoras theorem to find that.

a²+ b² = c²

3² + (√7)² = c²

9 + 7 = c²

c² = 16

Taking the square root of both sides;

c = √16

c = 4

The third side is 4 units

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The third side which is a hypotenuse of the right angle triangle have the length equal to 4.

We shall represent the length of the third side with x, so that by Pythagoras rule we evaluate for the hypotenuse as follows:

x² = 3² + (√7)² {note that: (√7)² = √7 × √7 = 7}

x² = 9 + 7

x² = 16 {square root of both sides}

x = √16

x = 4.

Hence the length of the hypotenuse is equal to 4 by proper application of the Pythagoras rule.

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Answer:

x = -4

y = -3

Step-by-step explanation:

-4x + 4y = 4          Eq.  1

y = 3x + 9             Eq. 2

Replacing Eq. 2 in Eq. 1:

-4x + 4(3x+9) = 4

-4x + (4*3x + 4*9) = 4

-4x + (12x+ 36) = 4

8x + 36 = 4

8x = 4 - 36

8x = -32

x = -32/8

x = -4

From Eq. 2

y = 3*-4 + 9

y = -12 + 9

y = -3

Check:

From Eq. 1

-4x + 4y = 4

-4*-4 + 4*-3 = 4

16 - 12 = 4

The area of the enclosed region is 83.4 square units.

To calculate the integral, first determine the limits, which will be the points where both curves meet.

The area will be integrated with respect to y.

In respect to y:

[tex]2x + y^{2}[/tex] = 24

[tex]2x[/tex] = 24 - [tex]y^{2}[/tex]

[tex]x[/tex] = 12 - [tex]\frac{y^{2} }{2}[/tex]

Finding limits:

y = 12 - [tex]\frac{y^{2} }{2}[/tex]

12 - [tex]\frac{y^{2} }{2}[/tex] - y = 0

Multiply by 2 to facilitate calculations:

24 - [tex]y^{2}[/tex] - 2y = 0

Resolving quadratic equation:

- [tex]y^{2}[/tex] -2y + 24 = 0

- ([tex]y^{2}[/tex] + 2y - 24 ) = 0

Divide both sides the same factor,

[tex]y^{2}[/tex] + 2y - 24  = 0

Use Quadratic formula,

y = (-b ± [tex]\sqrt (b^{2} -4ac)[/tex] ) / 2a

y = (-2 ± [tex]\sqrt{2^{2}-4*1*(-24) }[/tex] ) / 2*1

y = (-2 ± [tex]\sqrt{4+96}[/tex] ) / 2

y = (-2 ± [tex]\sqrt{100}[/tex] ) / 2

y = (-2 ± 10 ) / 2

y = (-2 + 10 ) /2  ,     y = (-2 - 10 ) /2  

y = 8/2  ,                  y = -12/2

y = 4   ,                     y = -6

y = 4 and y = -6

Then, integral to calculate area will be with limits -6<y<4:

A = [tex]\int\limits^[/tex] 12 - [tex]\frac{y^{2} }{2}[/tex] - y dy

A = 12y - [tex]\frac{y^{3} }{6}[/tex] - [tex]\frac{y^{2} }{2}[/tex]

A = 12*4 - [tex]\frac{4^{3} }{6}[/tex] - [tex]\frac{4^{2} }{2}[/tex] - [12(-6) - [tex]\frac{-6^{3} }{6}[/tex] - [tex]\frac{-6^{2} }{2}[/tex] ]

A = 48 - 10.6 - 8 - [ -72 + 36 - 18 ]

A = 48 - 10.6 - 8 + 72 - 36 + 18

A = 83.4

Therefore,

The area of the enclosed region is 83.4 square units.

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Answer:

Step-by-step explanation:

Solve the problem 4p-32=p+7

4p - 32 = p + 7

3p = 39

p = 39 : 3

p = 13

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

4 x 13 - 32 = 13 + 7

20 = 20

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Households with negative or zero net worth may have high credit card debt due to financial distress, using credit to cover everyday expenses, or difficulty managing finances.

Financial distress: Households with negative net worth may be in financial distress and may be relying on credit cards to cover their basic expenses. This can lead to high levels of credit card debt as they continue to use their credit cards to pay for necessities such as food, housing, and utilities.

Financing everyday expenses: Households with zero net worth may also have high levels of credit card debt if they are using their credit cards to finance their everyday expenses. This can happen if they do not have sufficient income to cover their expenses, or if they have high levels of fixed expenses such as mortgage or rent payments.

Difficulty managing finances: Households with negative or zero net worth may also have a harder time managing their finances and may be more prone to making financial mistakes such as missing credit card payments or making late payments. This can lead to higher levels of credit card debt as they incur late fees and interest charges.

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Households with net worth in the negative or zero have the highest average credit card debt due to the lack of other financing options available to them.

The reason why households with net worth in the negative or zero have the highest average credit card debt is likely due to the fact that they have less access to other financing options and thus rely more heavily on credit cards. When a household has no net worth, they are unable to turn to other sources of borrowing such as home equity loans or personal loans, as they have no equity to borrow against. Therefore, they are more likely to use credit cards to cover unexpected expenses or emergency needs. In addition, households with zero or negative net worth may have lower income and less access to savings, causing them to rely heavily on credit cards for daily expenses.

To illustrate this concept, let’s assume that there are two households with different levels of net worth. Household A has a net worth of $10,000 and Household B has a net worth of -$2,000. Both households have monthly expenses of $1,000 and an income of $2,000. Household A has more financial flexibility because they can turn to other sources of borrowing to cover their expenses, such as home equity loans or personal loans. Household B, however, is unable to borrow against their negative net worth and must rely solely on credit cards to cover their monthly expenses. This makes them more likely to accumulate higher levels of credit card debt due to their limited access to other financing options.

Therefore, it is evident that households with net worth in the negative or zero have the highest average credit card debt due to the lack of other financing options available to them.

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Explanation:

When working on complicated problems, it's best to break things down as much as possible.

Toby knows how to work with 2 terms, so let's start with that.

Ignore the 8^2 for now.

Focus on the first 2 exponential terms 8^7 and 8^3.

Multiply them to get: 8^7*8^3 = 8^(7+3) = 8^10

Which Toby should know how to do. The general rule is

a^b*a^c = a^(b+c)

Add the exponents but only when the bases are the same.

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

This means

8^7* 8^3*8^2

is the same as

8^10*8^2

Then apply that rule again to get

8^10*8^2 = 8^(10+2) = 8^12

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

So overall, 8^7*8^3*8^2 = 8^12

In other words, we add the exponents to get 7+3+2 = 12 as the final exponent. The base stays at 8 the entire time.

Monique can make 5 Vase with 4 Daisies and 5 Roses in each.

The greatest number among all the common factors of the given numbers is the HCF (Highest Common Factor) of two numbers.

For example, the HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36.

Given:

Daisies = 20

Roses = 25

Monique obviously wants to use all the flowers so she does not any left over. She needs to find a number which divides into 20 and 25,

So, the HCF of 16 and 24, which is 5.

Factors of 20 = 2, 4, 5, 10, 20.

Factors of 25 = 5, 25

So, She will be able to make 5 bouquets.

and, Each bouquet will have 4 Daisies and  5 Roses.

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The Complete Table that missing in the table is

Flower Type Number

Daisies 20

Roses 25

If variation in a process results from common causes alone, the process is said to be in statistical control.

When talking about control charts, being in-control means your process is exhibiting common cause variation and is predictable.

Variation due to the inherent variability in a system of operation is called. special or assignable causes.

Industrial control systems are used by a discipline known as industrial process control in continuous manufacturing processes to produce at a level of consistency, economy, and safety that is impossible to achieve exclusively through manual human control. Process control systems make guarantee that industrial activities are carried out efficiently, dependably, and with as little fluctuation as is practical. They are installed in industrial settings to guarantee throughput, quality, yield, and energy efficiency. Ensure that work is done profitably and safely according to established procedures.

Therefore,

If variation in a process results from common causes alone, the process is said to be in statistical control.

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Answer:

21 cm

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of the 3 sides. We already know all 3 lengths. The base is 6 cm, and the other two sides are 7 cm and 8 cm. 6+7+8 = 21. The perimeter is 21 cm.

perimeter of the triangle when base=6cm , height=6cm and side=7cm:

perimeter =6+6+7= 19cm.

perimeter of the triangle when base=6cm , height=6cm and side=8cm:

perimeter =6+6+8= 20cm.

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The expression is a polynomial expression that has 3 terms

The constant is 1/10

the leading coefficient is 1

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial with an exponent of 1 is, for instance, 2x + 5.

The given polynomial is written as -x + 1/10 + x⁴

x⁴ - x + 1/10

the number of terms are 3

the constant term is 1/10

the leading coefficient is the coefficient of x⁴ which is 1

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Answer: the answer is £12.

Step-by-step explanation:

To solve this problem, we can set up an equation to represent the information given in the problem. Let's call the amount of money Hasim had at the beginning of the day x.

We know that Hasim gave his brother 1/3 of his money, so we can represent that with the equation:

x / 3 = y

Where y is the amount of money Hasim gave to his brother.

We also know that Hasim spent £12 on a present for his sister, so we can subtract that amount from x to find the amount of money he had left:

x - 12 = z

Where z is the amount of money Hasim had left after buying the present.

Finally, we are told that the amount of money Hasim had left is half of what he had at the beginning of the day, so we can represent that with the equation:

x / 2 = z

Now we have three equations that all involve the variable x. We can solve for x by substituting the first equation into the second and third equations:

x / 3 = x - 12

x / 2 = x / 3

Solving these equations, we find that x = 36.

This means that Hasim had £36 at the beginning of the day, and gave his brother £36 / 3 = £<<36/3=12>>12.

People hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

Theories of human labor motivation and management include Theory X and Theory Y.

They were invented by Douglas McGregor in the 1950s while he was a faculty member at the MIT Sloan School of Management, and they underwent further development in the 1960s.

Consider work a natural part of life, and come up with creative solutions for workplace issues.

According to Theory X, individuals despise their jobs, desire to escape them, and detest having to be accountable.

According to Theory Y, people are self-driven and enjoy having responsibilities placed on them.

Therefore, people hate their jobs, want to get away from them, and hate having to be responsible, claims Theory X. People are independent and appreciate having obligations placed on them, claims Theory Y.

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The general form of an exponential decay function is f(a) = P . (1 - r)ᵃ, hence a function is an exponential decay if the factor (1 - r) is less than 1.

The general exponential decay function can be written as:

f(a) = P . (1 - r)ᵃ

Where:

P = initial quantity

f(a) = remaining quantity at time a

a = time period

r  = decay rate

(1 - r) = decay factor

On the other hand, the general exponential growth function can be written as:

f(a) = P . (1 + r)ᵃ

Hence, the difference between decay function and growth function is: the factor in decay faction is less than 1, while in growth function, the factor is greater than 1.

Example:

f(a) = 6 . (0.25)ᵃ

This is an exponential decay function because the factor is less than 1, that is 0.25

f(a) = 10 . (3)ᵃ

This is not an exponential decay function, but a growth function,  because the factor is greater than 1, that is 3

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Use identity:

Modify it as follows:

Substitute a = p, b = 1/p and evaluate:

Proved

The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Three pupils will be chosen from a class of 12 girls and 10 males to sit on a school advisory council. Here are four distinct approaches to choosing.

The total number of students is given as,

Total = 12 + 10 = 22

Then the best sampling method, among these four will be given as,

¹²C₃ × ¹⁰C₀, ¹²C₂ × ¹⁰C₁, ¹²C₁ × ¹⁰C₂, ¹²C₀ × ¹⁰C₃

The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

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Answer:

V=whl=3·7·4=84

Step-by-step explanation:

The cylinder has a height of 18 in, a base radius of 7 in, and a volume of 2769.5 in³.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been a solid in three dimensions. In elementary geometry, it is regarded as a prism with a circle as its basis.

V = πr²h is the formula for computing a cylinder's volume.

where ;

Replace the specified arguments to obtain:

V = π(7)² * 18

V = 2769.5 in³

Therefore, the cylinder's volume, which has a base radius of 7 inches and a height of 18 inches, is 2769.5 in³.

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The value of the given logarithm ln(x²y⁵) in terms of u and v will be 2u + 5v thus option (D) is correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

As per the given expressions,

u = ln x and v = ln y

Take anti-log as

x = [tex]e^{u}[/tex] and y = [tex]e^{v}[/tex]

Thus, x² = [tex]e^{2u}[/tex] and y⁵ = [tex]e^{5v}[/tex].

Multiply both as

x²y⁵ =  [tex]e^{2u}[/tex][tex]e^{5v}[/tex]

Take logarithms on both sides,

ln(x²y⁵) = ln( [tex]e^{2u}[/tex][tex]e^{5v}[/tex])

By log property that ln(A x B) = lnA + lnB

ln(x²y⁵) = ln  ([tex]e^{2u}[/tex]) + ln([tex]e^{5v}[/tex])

ln(x²y⁵) = 2u ln e + 5v ln e

ln(x²y⁵) = 2u + 5v



Hence "In terms of u and v, the value of the given logarithm ln(x²y⁵) will be 2u + 5v.".

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Answer:

No its not but each time a car come you need to move to your side of the lane

The tangent to the graph f,  f(x) = [tex]5x^4[/tex]/4 + 15/4.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Given:

f '(x) = 5x³

and, line: 5x + y= 0

We integrate to get f(x) = ∫5x³ dx = [tex]5x^4[/tex]/4 + C.

As, tangent line is y = - 5x,

then f'(x) = 5x³ = - 5, x³ = -1 and x = -1 is x-coordinate of tangent point.

So, the y-coordinate of tangent point is

f(-1) = 5[tex](-1)^4[/tex]/4  + C

      = 5/4 + C.

and, the equation of tangent line is

y - 5/4 - C = - 5(x + 1)

y = - 5x - 15/4 + C.

Thus,  -15/4 + C = 0,

C = 15/4 and f(x) = [tex]5x^4[/tex]/4 + 15/4

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Answer:

m= slope - - = +. formula is m=y2-y1

Answer:(-5/0) (y,x) (rise/run)

Step-by-step explanation:

Assuming that those are two points, the slope is -5/0.

(y1-y2)       Rise

over         over

(x1-x2)       Run

Answer:

D. y ≤ -1/4x - 3

A. y < 2/3x + 3

Step-by-step explanation:

For the first question, the answer would obviously be either B or D because the y-intercept is -3. The slope of the graph is -1/4 so the answer is D.

For the second question, the answer would be A or B because its a dashed line. Next, the slope is 2/3 so the answer is A.

g(2) is -1/4 for function g(x)= 1-x/x².

A relation is a function if it has only One y-value for each x-value.

The given function is  g(x)= 1-x/x²

g of x equal to one minus x divided by x square

g(x)= 1-x/x²

Now we need to find the value of g(2).

Replace the x with 2

g(2)=1-2/2²

When two is subtracted from one we get minus one and two square is four

g(2)=-1/4

Hence, g(2) is -1/4 for function g(x)= 1-x/x².

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Point (80, 185) represents the location of the beetle 5 seconds after starting.

An equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used. For instance, the equation y = x2 can be expressed as a pair of equations in parametric form, x = t and y = t2, rather than the Cartesian form of y = x2. Parameterization, which transforms a function into a parametric form, greatly improves the efficiency of differentiating and integrating curves.

The parametric equations for the path of the beetle are:

x(t) = 28t

y(t) = 84t + 10

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Answer:

it’s not 80,185 I got it wrong on edge

Step-by-step explanation:

ugh