Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). Find [tex]\frac{dy}{dt}[/tex] when x= [tex]\frac{\pi }{10}[/tex], given
[tex]\frac{dx}{dt}[/tex] = -4 when x= [tex]\frac{\pi }{10}[/tex]
Enter an exact answer.
[tex]\frac{dy}{dt}[/tex]=______

Answer: A

Step-by-step explanation:

The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.

As per the given,

Principle amount P = ​$25,000

APR = 9% = 0.09

Time period T = 20 years

a) Monthly payment will be given as,

⇒ P(r/12)/(1 -(1 +r/12)^(-12t))

⇒ 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20))

⇒ $161.20

b) After 20 years the amount as,

$161.20 x 240 = $38,688

c) (22500/38688)·100% = 58.2% is paid toward principal

The remaining amount, 41.8% is paid toward interest.

Hence "The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest".

For more information about compound interest,

brainly.com/question/26457073

#SPJ1

An expression that represents the ADDITION of the two number lines is: B. -10x - 5x + 30x.

Each segment equals 5x and the first arrow is 30x long.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Based on the number line shown above, we can reasonably infer and logically deduce that each of its segment is equal to 5x with the longest arrow measuring 30x on the number line.

Read more on number line here: brainly.com/question/21832213

#SPJ1

Answer:

the answer will be the option 2

1. Parallel

2. Perpendicular

3. Skew

4. Parallel

5. Perpendicular

6. ↔QW, ↔SW, ↔TZ

7. ↔YZ, ↔ST

8. ↔RQ, ↔QW, ↔ST, ↔TZ

9. Plane TQW, plane SRX, plane ZWX

10. Plane WXY

11. Corresponding

12. Alternate exterior

13. Alternate interior

14. Consecutive interior

15. Alternate exterior

16. Alternate interior

17. ↔OL ║↔VN

18. ↔VN ⊥ ↔RT

19. No; the markings do not indicate that the lines are parallel

The monthly payment (R) needed to have a sinking fund accumulate the future value (A) is equal to $325.08

What is Future Value?

Here, the given values are:

A=$4,000;

r=5.5%=0.055

t=1 year

And it is given that the interest is compounded monthly.

So, n=12

Using the formula for Future Value, [tex]A=\frac{R[(1+\frac{r}{n})^{nt}-1] }{\frac{r}{n}}[/tex]

Substituting the given values in the above equation, we get

[tex]4000=\frac{R[(1+\frac{0.055}{12})^{12 \times 1}-1] }{\frac{0.055}{12}}\\\implies 4000=\frac{R[(1+0.0046)^{12}-1] }{0.0046}\\\implies 4000=\frac{R \times 0.0566 }{0.0046}\\[/tex]

Rearranging the above expression  in terms of the monthly payment, we get

[tex]R=\frac{4000 \times 0.0046}{0.0566} \\\implies R=325.08[/tex]

Therefore, the monthly payment (R) needed to have a sinking fund accumulate the future value (A) is $325.08

To learn more about the future value from the given link

https://brainly.com/question/24703884

#SPJ1

The expression that shows how many charms Jenny's older sister has is

c + 5.

What are algebraic expressions?

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Expressions are made up of terms.

According to the given question:

Jenny has c charms on her bracelet.

Her older sister has 5 more charms than Jenny.

To write an expression that shows the number of charms her older sister has. we simply add 5 extra charms to the number of charms Jenny has

Therefore, Jenny's older sister has c + 5 charms.

In this expression c represents the number of charms Jenny has.

The complete question is as follows:

Jenny has c charms on her bracelet. Her older sister has 5 more charms than Jenny. Write an expression that shows how many charms her older sister has.

To know more about algebraic expressions visit

https://brainly.com/question/12739821

#SPJ1

The wheel will travel 904.32 inch when it take 4 rotation

How do you calculate distance using radius and revolutions?

Hint: To calculate the wheel's circumference, use the formula 2πr, where r is the radius and π=3.14 , to first determine the distance covered in one revolution. To determine the distance traveled, multiply the distance covered in one revolution by 200. In the end, multiply it by 100 to get the distance in meters.

In mathematics, what is the circumference?

The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian.

The circle's circumference must be known in order to compute the distance covered during one rotation. C=2πr is the formula for the circumference.

The radius, designated as r, is 36 inches. As a result, C=2π36 = 72π. The distance covered in one rotation is 226.08 inches because (pi) =3.14159, C=226.08 inches. So when we rotate this 4 times the it travels 226.08 * 4 = 904.32 inch

Learn more about circumference

https://brainly.com/question/27447563

#SPJ1

Answer:

Hello there, I think this is the answer

a = - 2

b = - 9

Answer:5 miles per hour

Step-by-step explanation:

By subtraction, we can see that the second time was 10-8=2 hours  and covered 52-42=10 miles.  10 miles/2hours = 5 miles per hour.  So that was her constant (or average) speed throughout the trip.

A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

x= -2, x=7

Given,

P(x) = 0

This polynomial function has the roots,

x= -2, x=7

So,

(x+2)(x-7)

We have to multiply both of them we get,

P(x)=(x+2)(x-7)

0=x²-5x-14

x²-5x-14=0

Therefore, P(x)=x²-5x-14 is the polynomial function.

To know more about polynomial function, visit:

https://brainly.com/question/12976257

#SPJ1

True, The dimension of the eigenspace for each eigenvalue equals the multiplicity.

Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.

When a linear transformation is done to an eigenvector, a set of eigenvectors called an eigenspace is created for each eigenvalue. In many cases, the linear transformation uses a square matrix (a matrix that has the same number of columns as it does rows).

yes, it is true that the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.

to learn more about eigenvalue visit:

https://brainly.com/question/29565569

#SPJ4

As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.

Confidence interval,

in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.

Given,

in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.

Here we need to find the given statement is true or false.

While we looking into the given question, we have identified that the value of

Confidence interval = 95%

Sample size = 20

Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).

Therefore, the statement is in correct.

To know more about confidence interval here.

https://brainly.com/question/24131141

#SPJ4

The term that is the −20,155,392 in the sequence is a₁₀.

A sequence is defined as an arrangement of numbers in a particular order.

The given sequence is 2, -12, 72, -432

a = first term

n = number of terms

r = common ratio

r = -12 / 2 = 72 / -12 = -432 / 72 = -6

a = 2

Therefore, nth term = arⁿ⁻¹

−20,155,392 = 2 × -6ⁿ⁻¹

−20,155,392 / 2 = -6ⁿ⁻¹

- 10077696 =  -6ⁿ⁻¹

6ⁿ⁻¹ = 10077696

6ⁿ⁻¹  = 6⁹

n - 1 = 9

n = 9 + 1

n = 10

Hence, it's the 10th term.

learn more on sequence here:

brainly.com/question/22696821

#SPJ1

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and the angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2abcos(C)

In this problem, we are given the measure of angle C and the lengths of sides b and c. We can use this information to find the length of side a and the measures of angles A and B.

First, we can use the Law of Cosines to find the length of side a. Plugging in the given values, we get:

a^2 = c^2 - b^2 + 2bc cos(C)

Substituting in the given values, we get:

a^2 = 151^2 - 181^2 + 2 * 151 * 181 * cos(60.0°)

Solving this equation gives us a = 143 m.

Now that we have the length of side a, we can use the Law of Sines to find the measures of angles A and B. The Law of Sines states that for a triangle with sides a, b, and c and angles A, B, and C opposite these sides, the following equation holds:

a/sin(A) = b/sin(B) = c/sin(C)

We are given the lengths of sides a and b and the measure of angle C. We can use this information to find the measures of angles A and B.

First, we can use the Law of Sines to find the measure of angle A. Plugging in the given values, we get:

a/sin(A) = b/sin(B)

Solving for sin(A), we get:

sin(A) = a * sin(B) / b

Substituting in the given values, we get:

sin(A) = 143 m * sin(B) / 181 m

To find the measure of angle A, we can use the inverse sine function (sin^-1). This gives us:

A = sin^-1(sin(A))

= sin^-1(143 m * sin(B) / 181 m)

Similarly, we can use the Law of Sines to find the measure of angle B:

B = sin^-1(143 m * sin(A) / 181 m)

Since we have two unknowns (A and B) and two equations, there is a unique solution for this triangle.

Therefore, the number of solutions is 1, and the measures of angles A and B are A = 38.5° and B = 101.5°. The length of side a is 143 m.

The answer is 64

If you need a breakdown I don't know how to help.

Confident, In contrast to any stillness he had ever felt on land, he felt a sense of calm when the water was calm. and "He gave two weeks' notice at his job and immediately sailed off again."

fishing vessel Place on list Share. fishing boat definitions. a fishing vessel with a well for preserving the catch. A boat and a fishing smack are potential candidates. both sorts of draggers and trawlers. Fishing ships or boats are used to remove aquatic creatures from bodies of water.

A trawl is a type of fishing net that is currently dragged along or through the ocean floor at specific depths. Since trawlers are frequently bigger than fishing boats and struggle to maneuver when necessary, they are given special qualities in ror.

Thus, options A and A, B are correct.

To know more about fishing vessel, visit:

https://brainly.com/question/26399526

#SPJ1

Answer:

Part a: confident

Part b: "The calmness that he felt when the water was placid wasn’t like any stillness that he experienced on land." and "He had spent most of his life on the sea; he knew the habits and nuances of the water like it was his closest friend."

Step-by-step explanation: I took the test :)

option c)   4x⁴ -2x³ -2x² +3x -10

On subtracting we will get

(3x²₋ 2x + 4x⁴) - (5x²+2x³-5x+10)

= 3x²- 5x²- 2x -2x³+ 4x⁴+ 5x -10

= -2x² + 3x  -2x³ + 4x⁴- 10

= 4x⁴ -2x³- 2x² + 3x - 10

The given sum belongs to quadratic equation

Quadratic equation definition:

When a, b, and c are real-world coefficients, a second-order equation is said to be quadratic if it is represented as ax²+ bx + c = 0.

The Characteristics of Quadratic Equations' Roots

The discriminant of the quadratic equation ax2+bx+c=0 is (b2-4ac), which determines whether or not the equation has real roots.

The quadratic equation ax2+ bx + c= 0 hence

If b2-4ac >0, two different real roots

If b2-4ac= 0, there are two equal real roots.

To see similar problem on quadratic equation click on given link below

brainly.com/question/28183293

#SPJ1

By using the concept of demand and supply, it can be concluded that-

The price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.

What is demand and supply?
Demand is the amount of good which the customer wants to purchase during a particular time at a particular price.

Supply is the total amount of goods made available to the customer at a particular time

Equilibrium price is the price at which the quantity demanded is equal to the quantity supplied

So the price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.

To learn more about demand and supply, refer to the link-

https://brainly.com/question/4804206

#SPJ1

Answer:

8/4, or 2

Step-by-step explanation:

Brainliest, Please!

Like fractions are fractions that have the same denominator.

To add like fractions, you must add the numerators and keep the same denominator. Finally, the result is simplified if possible.

The procedure for this addition of fractions is as follows:

[tex]\begin{gathered} \sf \frac{3}{4} + \frac{5}{4} = \\ \\ \sf \frac{3 + 5}{4} = \\ \\ \boxed{ \sf\frac{ \red8}{ \red4} }= \sf \blue2\end{gathered}[/tex]

Therefore, the result of the sum of fractions is two.

The completed table and the graph of the proportional relationship are given by the image shown at the end of the answer.

The proportional relationship in this problem is defined as follows:

s=2 b.

The variables are defined as follows:

Then the graph of the proportional relationship is that of a linear function with these following features:

Then the numeric values that complete the table are calculated as follows:

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

The range of the cluster shown in the graph is [1, 6]

What is range of a graph?

The range is all the values of the graph from down to up or on the x-axis.

Solution :

∵ Range is calculated from x-axis

∴ Range  {1,2,3,4,5,6} = 6-1

                                     = 5

#SPJ4

The range of the cluster shown in the graph is [1, 6]

The range is all the values of the graph from down to up or on the x-axis. The possible output values are displayed on the y-axis and make up the range. Remember that the domain and range of the graph could be larger than the visible values if it extends beyond the area that can be seen.

Solution :

∵ Range is calculated from x-axis

∴ Range  {1,2,3,4,5,6} = 6-1

                                    = 5

To learn more about range visit:

https://brainly.com/question/29794762

#SPJ4

Your knowledge of the percentage 47.728 is already complete.4772.8% is the percentage equivalent of 47 7 2 8.

To compute 47.728 as a percentage of a given number x, divide 47.728 by x and multiply the result by 100.

For instance, the ratio of 47.728 to 10 is equal to (47.728 / 10) times 100%, or 477.28%.

Use the decimals to percents converter found below at your convenience.

Place your value in the "% of" area after entering 47.728 in the number field.

Press reset first if you want to restart.

At this point, an automatic conversion to 47.728 in percent will take place.

The answer has been rounded to ten decimal places, as you can see.

To learn more about  percentage refer

https://brainly.com/question/24304697

#SPJ1

The graphs of the equations are drawn ad attached here.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equations are (i) y = x-4, (ii) y = 2x-4, (iii) y = 3x-4.

The equations are given in the slope-intercept form.

(i) The given equation is y = x-4.

   the y-intercept of the equation is (0,-4).

Now, substitute y = 0 into the given equation:
0 = x - 4

x = 4

Hence, the line y = x-4 passes through points (0,-4) and (4,0).

Now, draw a line passing through the points (0,-4) and (4,0).

Using the same procedure, the graphs of the other two equations are also drawn.

Hence, the graphs of the equations are drawn ad attached here.

To learn more about the slope-intercept form of a line, click here:

https://brainly.com/question/9682526

#SPJ1

The gross pay for Riddler for working 47 hours will be $783.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours.

The overtime cost = 1/2 x 18

The overtime cost = $9

The gross pay will be calculated as,

Gross pay = ( 40 x 18 ) + ( 7 x 9 )

Gross pay = 720 + 63

Gross pay = $783

To know more about an expression follow

https://brainly.com/question/13178740

#SPJ1

Answer:

52

Step-by-step explanation:

Substitute the value -4 into the expression and simplify:

3(-4)^2 - (-4)

3(16) + 4

48 + 4

52

From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT.

When an angle appears simultaneously in multiple geometric figures, it is referred regarded as being a common angle. Two figures with shared vertices points and angle edges are said to have a common angle.  

Here we have  

ΔPQT and ΔRSQ    

The internal angles of ΔPQT are

=> ∠PQT,  ∠PTQ, and ∠QPT

The internal angles of ΔRSQ are

=> ∠SRQ, ∠RSQ, and ∠SQR

Where ∠PQT = ∠SQR

From above information

The common angles of ΔPQT and ΔRSQ are ∠PQT and ∠SQR    

Therefore,

From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT  

Learn more about Common angles at

https://brainly.com/question/19569101

#SPJ1  

Complete Question:

What is the common angle of ΔPQT and ΔRSQ from the given figure?

The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 ​million in 15.82258467 years and the doubling time is 25.55035862 years

The exponential growth function is of the form P = P₀(1+r)^t

where P₀ is the current population, r is the growth rate and t is the time

Given: P₀ =  6.51 million, r = 2.75​% per year

a) The exponential growth function

P = 6.51 (1+0.0275)^t

P = 6.51 (1.0275)^t

​b) The population of the city in 2018

t = 2018-2012 = 6 years

P = 6.51 (1.0275)^t

P = 6.51 (1.0275)⁶ = 7.66 million

​c) When the population of the city will be 10 ​million

P = 6.51 (1.0275)^t

10 =  6.51 (1.0275)^t        (Solve for t)

(1.0275)^t =10/6.51

log (1.0275)^t = log(10/6.51)

t × log (1.0275) = log(10/6.51)

t = [log(10/6.51)] / [log (1.0275)]

t = 15.82258467 years

d) The doubling time

P =  6.51 (1.0275)^t will become:

2 = 1 (1.0275)^t

1.0275^t = 2

log(1.0275)^t = log 2

t log(1.0275) = log 2

t = log 2 / log 1.0275

t = 25.55035862 years

Learn more about population growth function on:

brainly.com/question/25896797

#SPJ1

Answer:

QR = 49

Step-by-step explanation:

QR = QP

3x + 22 = 10x - 41

x = 9

10(9) - 41

= 49