Find the intervals where f(x)=√x2−9​ is concave up/concave down. Provide the exact answers. 7. Find the equations of the tangent lines to the graph of x2+y2=25 which pass through the point (1, 8. Find the slope of the tangent line to the graph of Tan(x+2y)=x2+y−π2 at the point (π,0). Provide the exact and simplified answer.

The differential equation is first-order, there are no transient terms in the general solution.

The given differential equation is a first-order linear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)

where P(x) = sin(x)/cos(x) = tan(x) and Q(x) = 1.

Using the integrating factor method, we can find the general solution:

μ(x) = e^(∫P(x)dx) = e^(ln|cos(x)|) = |cos(x)|

Multiplying both sides of the differential equation by μ(x), we get:

cos(x)dy/dx + sin(x)y = cos(x)

Now, we can integrate both sides to get the general solution:

∫cos(x)dy + ∫sin(x)ydx = ∫cos(x)dx

y cos(x) - ∫sin(x)dy + C = sin(x) + D

y cos(x) + C' = sin(x) + D

y = (sin(x) + C')/cos(x)

where C' = C/|cos(x)| and D is an arbitrary constant of integration.

The largest interval over which the general solution is defined is (-π/2, π/2) since cos(x) = 0 at x = π/2 + nπ where n is an integer, and the integrating factor μ(x) is undefined at these points.

Since the differential equation is first-order, there are no transient terms in the general solution.

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Answer:60m^2

Step-by-step explanation:you have to find the height of the triangle first which is easy bc it’s been split in half so the are now two right triangles. use the pythagorean theorem to determine the height, the height is 12, the formula for the area of a triangle is 1/2bxa and half of the base is already given to you, 5 so 5 x 12 equals 60

Logan has 7 quarters and 14 dimes.

Let's start by setting up some equations to represent the problem.

Let:

x be the number of quarters Logan has

y be the number of dimes Logan has

We know that Logan has twice as many dimes as quarters, so we can write:

y = 2x

We also know that Logan has $3.15 worth of dimes and quarters. The value of x quarters is 0.25x dollars, and the value of y dimes is 0.10y dollars. So we can write:

0.25x + 0.10y = 3.15

Now we can substitute y = 2x into the second equation:

0.25x + 0.10(2x) = 3.15

Simplifying:

0.45x = 3.15

x = 7

So Logan has 7 quarters. We can use y = 2x to find y:

y = 2(7) = 14

So Logan has 14 dimes.

Therefore, Logan has 7 quarters and 14 dimes.

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The c is equal to half of the definite integral of the function over the interval [0, 2].

To determine c such that f(c) is the average value of the function on the interval [0, 2], we can use the formula for the average value of a function:

avg = 1/(b-a) * ∫(a to b) f(x) dx

In this case, a = 0 and b = 2, so the formula becomes:

avg = 1/2 * ∫(0 to 2) f(x) dx

We want to find the value of c such that f(c) = avg, so we can set these two expressions equal to each other and solve for c:

f(c) = avg
f(c) = 1/2 * ∫(0 to 2) f(x) dx

We can then use calculus to solve for c by finding the derivative of both sides with respect to c and setting them equal to each other:

f'(c) = 1/2 * (f(2) - f(0))

Solving for c gives us:

c = (1/2) * ∫(0 to 2) f(x) dx

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

The number 7 emerged in human history through cultural and mathematical developments.

The significance of the number 7 can be observed in various aspects of human history. One of the earliest instances is found in ancient Mesopotamia, where the Sumerians developed a base-60 numeral system called sexagesimal.

This system contributed to the use of 60 as a highly divisible number and influenced the concept of dividing the day into 24 hours, each consisting of 60 minutes.

In ancient Egypt, the division of the week into seven days was based on the observation of celestial bodies.

The Egyptians associated each day with a different planet or celestial object, namely Sunday (Sun), Monday (Moon), Tuesday (Mars), Wednesday (Mercury), Thursday (Jupiter), Friday (Venus), and Saturday (Saturn). These planetary associations were later adopted by the Romans, and their names in English still reflect these origins.

The number 7 also holds religious and symbolic significance. In Judaism, the seventh day of the week, Saturday, is considered a day of rest, known as the Sabbath.

This tradition is rooted in the biblical story of creation, where God rested on the seventh day. In Christianity, the Book of Genesis describes the world being created in six days, with the seventh day being designated as holy.

Furthermore, the number 7 appears in mathematics and geometry. The seven colors of the rainbow, the seven musical notes, and the seven wonders of the ancient world are all examples of the cultural significance attributed to this number.

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Answer:

The other integer is less than -80

Step-by-step explanation:

The given sum of the two integers < -57

The value of one of the integers = 23

Let 'b' represent the value of the other integer, we are given;

b + 23 < -57

Therefore, we have;

b < -57 - 23 = -80

Therefore, the other integer, b < -80.

Answer:

180 ft2

Step-by-step explanation: Trust (mark as brainliest)

Surface area of the ramp is 240ft².

"Surface area is defined as the total area covered by the surfaces of the 3 dimensional object."

Formula used

Area of the triangle = ( 1/ 2) ×base × height

Area of the rectangle = length × width

Total surface area

= 2(Area of triangular base)+Area of (rectangle1 + rectangle2 +rectangle3)

According to the question,

Given,

Ramp is in triangular prism shape

As given in the diagram,

Base of the triangle = 5ft

height of the triangle = 12ft

Substitute the value in the formula we get,

Area of the triangular base = (1 / 2) × 5 ×12

                                             = 30 ft²

Area of the 2triangular base = 2 × 30

                                               = 60ft²  ____(1)

length of rectangle1 = 6ft

width of rectangle 1 = 5ft

Substitute the value in the formula we get,

Area of the rectangle1 =  6 × 5

                                     = 30 ft²   _____( 2)

length of rectangle2 = 6ft

width of rectangle 2= 12ft

Substitute the value in the formula we get,

Area of the rectangle2 =  6 × 12

                                     = 72 ft²  _____(3)

length of rectangle3= 6ft

width of rectangle 3 = 13ft

Substitute the value in the formula we get,

Area of the rectangle3=  6 × 13

                                     = 78 ft²    _____(4)

Add  (1) , (2), (3) and (4) we get,

Total surface area = 60 + 30 +72 +78

                               = 240 ft²

Hence, surface area of the ramp is 240ft².

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The minimum number of integers that must be picked to ensure that at least two of them have the same remainder when divided by 5 is 6.

Grouping objects into equal parts is known as Division. The Division is an arithmetic operation. The division algorithm states that " when we divide a number by another number then relation Dividend = divisor × Quotient + Remainder is always satisfied"

Let "a" be an integer and "x" be a positive integer. Then there exist unique numbers "q" and "r" with 0 < r < d then,

                                        a   =   xq + r       → 1

where,   q = quotient and r = remainder

⇒ q   =   a div x   and    r   =   a mod x

The pigeonhole principle states that " if n items are put into m containers, with n > m, then at least one container must contain more than one item"

When the number is divided by 5, the remainder is r such that 0 ≤ r < 5. Then the possible remainders are = 0, 1, 2, 3 and 4. So, there are 5 possible remainders. If we select 5 integers, then it is possible to choose 5 integers with various remainders each. When we choose 6 integers, then at least two of the integers need to have the same remainder.

Therefore, 6 is the minimum number of integers that must be picked in order to be sure that at least two of them have the same remainder when divided by 5.

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Answer:

x = 6

Step-by-step explanation:

28/35 = 4x/30

140x = 840

x = 6

An acute triangle is made up of three acute angles. An obtuse triangle is formed by one acute angle and two obtuse angles.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. In Euclidean geometry, any three points identify a distinct triangle and, concurrently, a distinct plane if they are not collinear.

Three acute angles make up an acute triangle. One obtuse angle and two acute angles make form an obtuse triangle. Because in Euclidean geometry all angles in a triangle must be 180 degrees, a triangle cannot contain more than one obtuse angle.

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Answer:

11-n=5

Step-by-step explanation:

A null space calculator finds the null space of a matrix used in linear algebra.

An invalid space mini-computer is a web-based instrument used to track down the invalid space, otherwise called the portion, of a framework. The invalid space of a framework is the arrangement of all vectors that fulfill the condition Ax= 0, where An is the lattice and x is the vector of questions. The invalid space can be utilized to decide if an arrangement of straight conditions is steady or not, and to find the reason for the arrangement space. An internet based invalid space number cruncher permits clients to enter a network and get the invalid space, as well as different properties like the position, determinant, and eigenvalues of the framework. This can be helpful for understudies and experts in fields like science, physical science, and designing who need to address frameworks of straight conditions and dissect the properties of networks.

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Answer:

4

Step-by-step explanation:

d=2

\( \sqrt{ - 6 + 11(2)} \)

-6+22

16 square rooted

4

Answer:

When adding or subtracting a constant outside the radical sign, it only affects the overall value of the expression, but not the square root itself. The square root symbol only applies to the value inside it, so any constant added or subtracted outside will not change the result of the square root. For example:

√(9 + 4) = √9 + √4 = 3 + 2 = 5

√(9) + 4 = 3 + 4 = 7

As you can see, adding or subtracting a constant outside the radical sign only changes the final result of the expression, but not the value inside the square root.

Answer:

the effect is when graphing the constant determines how far up or down to move it, compared to the original parent function.

Step-by-step explanation:

The other vertices of the square will be at (-7 ,3)

A square is a polygon with four sides , four vertices and four angles .

The opposite sides are parallel and all sides are equal .

It is given that

The vertices of a square are at

(-4,0), (-7,0),(-4,3)

On Plotting the vertices we can see that to obtain a square , the other vertices will be at (-7 ,3)

It can be understood from the figure.

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The Pythagorean triplets for the given values of 'n' are as follows:

For n = 1: (3, 4, 5)

For n = 2: (5, 12, 13)

For n = 3: (7, 24, 25)

For n = 4: (9, 40,41)

To find the Pythagorean triplets for different values of 'n', we can use the formula that generates Pythagorean triples:

For any two positive integers 'm' and 'n' such that m > n, the Pythagorean triplets can be obtained as follows:

a = m^2 - n^2

b = 2mn

c = m^2 + n^2

where 'a', 'b', and 'c' represent the sides of a right-angled triangle.

Let's calculate the Pythagorean triplets for each given value of 'n':

For n = 1:

m = 2

a = m^2 - n^2 = 2^2 - 1^2 = 4 - 1 = 3

b = 2mn = 2 × 2 × 1 = 4

c = m^2 + n^2 = 2^2 + 1^2 = 4 + 1 = 5

Therefore, the Pythagorean triplets for n = 1 are (3, 4, 5).

For n = 2:

m = 3

a = m^2 - n^2 = 3^2 - 2^2 = 9 - 4 = 5

b = 2mn = 2 × 3 × 2 = 12

c = m^2 + n^2 = 3^2 + 2^2 = 9 + 4 = 13

Therefore, the Pythagorean triplets for n = 2 are (5, 12, 13).

For n = 3:

m = 4

a = m^2 - n^2 = 4^2 - 3^2 = 16 - 9 = 7

b = 2mn = 2 × 4 × 3 = 24

c = m^2 + n^2 = 4^2 + 3^2 = 16 + 9

Therefore, the Pythagorean triplets for n = 3 are (7, 24, 25).

For n = 4:

m = 5

a = m^2 - n^2 = 5^2 - 4^2 = 25 - 16 = 9

b = 2mn = 2 × 5 × 4 = 40

c = m^2 + n^2 = 5^2 + 4^2 = 25 + 16 = 41

Therefore, the Pythagorean triplets for n = 4 are (9, 40, 41).

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Answer:

436.25 I think

Step-by-step explanation:

4.2 hours take to screen-print a batch of 14 shirts.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

initial set-up time = 15 min

Additional time= 3 min

Total time to print T shirt= 15 + 3= 18 min

So, to print 14 T shirts the time will be taken

= 14 x 18

= 252 min

= 4.2 hours

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Answer:

57 minutes

Step-by-step explanation:

I just did it

It's given that 33.1% of all registered doctors were female, corresponding to 53700 female registered doctors.

It's required to find the total number of registered doctors.

The total number of doctors corresponds to 100%, so we use the inverse percentage calculation:

There were 162236 doctors in total

The measure of the angle that is complementary to angle B is 30°.

Complementary angles are a pair of angles whose measures add up to 90°(Right angle)

To find the measure of the angle that is complementary to angle B, we need to subtract the measure of angle B from 90 degrees.

Given measure of angle B is 60°

60°+x° = 90°

(Let x° be the complementary angle to ∠B)

x° = 90°-60°

x° = 30°

∴ The measure of the angle that is complementary to angle B is 30°.

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The equivalent effective bi-weekly rate is approximately 0.01456%.

To find the equivalent effective bi-weekly rate, we need to convert the given nominal rate \(i^{(2)} =1.45000\%\) to the effective rate for a bi-weekly period.

The formula to convert a nominal rate to an effective rate is \(i^{(m)} =(1+r/m)^{m}-1\), where \(i^{(m)}\) is the effective rate, r is the nominal rate, and m is the number of compounding periods per year.

In this case, we have a nominal rate \(i^{(2)}\) that corresponds to a semi-annual compounding (2 periods per year). We can plug the values into the formula and calculate the effective rate \(i^{(bi-weekly)}\) for a bi-weekly period.

\(i^{(bi-weekly)}=(1+1.45000/2/100)^{2}-1\)

Calculating the expression:

\(i^{bi-weekly}=(1+0.00725)^{2} -1\\i^{bi-weekly}= 1.0145640625-1\\i^{bi-weekly}= 0.0145640625\)

The equivalent effective bi-weekly rate is approximately 0.01456%.

Among the given options, none of them match the calculated value exactly.

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Answer: m = 24

Step-by-step explanation:

The right side of the table is the x value, and the left side is the y value.

Pick two points, I will pick (1,35) and (3,83).

Once you pick the points, input them in the rise over run formula:

y2-y1/x2-x1

83-35/3-1 = 48/2 = 24

The percentage of 7th graders students that spend less than an hour a day on social media is 51.8%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

7th graders:

Number of students that spend less than an hour = 29

Number of students = 56

The percentage of students that spend less than an hour.

= 29/56 x 100

= 51.785

= 51.8 %

Thus,

The percentage of students that spend less than an hour is 51.8%.

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The t-value for a 95% confidence interval is 2.08596 (Option C).

To determine the t-value, we need to calculate the standard error of the difference in means and then use it to calculate the t-value. The formula for the standard error of the difference in means is:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the standard deviations of the two samples, n1 and n2 are the sizes of the two samples.

In this case, for the first department, s1 = 3.5 and n1 = 12. For the second department, s2 = 3.4 and n2 = 9. Plugging these values into the formula, we get:

SE = sqrt((3.5^2 / 12) + (3.4^2 / 9)) ≈ 1.729133

The t-value is calculated by dividing the difference in means by the standard error:

t = (x1 - x2) / SE

Since we want a 95% confidence interval, we need to find the critical value corresponding to a two-tailed test with a significance level of 0.05. With the degrees of freedom calculated as df = n1 + n2 - 2 = 12 + 9 - 2 = 19, the t-value for a 95% confidence interval is 2.08596.

Therefore, the correct answer is option C, 2.08596.

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Answer:

1/4

Since there are 4 friends and 12 cookies, assuming they divide them equally, each friend gets 12/4=3 cookes and so the fraction would be 3/12 which would simplify to 1/4.

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\(\huge\textbf{Hey there!}\\\\\huge\boxed{\mathbf{Equation: \dfrac{4\ friends}{12\ friends}}}\\\\\\\huge\boxed{\mathbf{= \dfrac{12\ cookies}{4\ friends}}}\\\\\\\huge\boxed{\mathbf{= 4\ friends\div 12\ cookies}}\\\\\\\huge\boxed{\mathbf{= \dfrac{4\div4\leftarrow friends}{12\div4\leftarrow cookies}}}\\\\\\\huge\boxed{= \mathbf{\dfrac{1}{3}\ in\ all}}\\\\\huge\textbf{Thus, your answer is: \boxed{\mathsf{\dfrac{1}{3}}}}\huge\checkmark\)

\(\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{ your day!}\)

A. X is less than -1

Answer:

Step-by-step explanation:

what?

When the assumption in the Fixed Effects regression, which states that the covariance between the error terms (uit, uis) and the covariates (xit, xis) is zero for t ≠ s, is violated, the correct statement among the options provided is:

A) Using heteroskedastic-robust standard errors is not sufficient for correct statistical inference when using OLS.

The violation of the assumption leads to a situation called "clustered errors" or "within-group correlation." In this case, the ordinary least squares (OLS) estimator remains consistent, but the standard errors estimated by OLS become biased. Using heteroskedastic-robust standard errors addresses heteroskedasticity in the error terms but does not correct for the within-group correlation.

To obtain correct statistical inference in the presence of within-group correlation, researchers typically employ cluster-robust standard errors or adjust the standard errors using cluster-robust variance estimators.

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