The cost price of a book is Rs 20 . It is sold at 10% profit. Find its sale price

The value of lim f(x)g(x) as x approaches infinity is 0.

L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.

To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:

lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]

= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]

Applying L'Hopital's rule to the fraction in the numerator, we get:

lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]

= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]

= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]

= 0

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[tex]{\Large \begin{array}{llll} y=x^2+ax+b \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=-7 \end{cases}\implies -7=0^2+a(0)+b\implies \boxed{-7=b} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=7\\ y=0 \end{cases}\implies 0=7^2+a7+\stackrel{b}{(-7)}\implies 0=49+7a-7 \\\\\\ 0=42+7a\implies -42=7a\implies \cfrac{-42}{7}=a\implies \boxed{-6=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} y=x^2-6x-7 \end{array}}~\hfill[/tex]

now, let's get the "vertex" using the coefficients.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(1)}~~~~ ,~~~~ -7-\cfrac{ (-6)^2}{4(1)}\right) \implies \left( - \cfrac{ -6 }{ 2 }~~,~~-7 - \cfrac{ 36 }{ 4 } \right) \\\\\\ \left( 3 ~~~~ ,~~~~ -7 -9 \right)\implies {\Large \begin{array}{llll} (3~~,~-16) \end{array}}[/tex]

The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.

We have, The sides of a triangle have lengths of 15, 20, and 25.

To find, The length of the shortest altitude of the triangle.

Steps to solve the problem:

Area = 1/2 * base * height

Area of the triangle = 1/2 * 20 * h ⇒ 10h

A = √(s(s-a)(s-b)(s-c))

Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.

According to the given problem, the sides of the triangle are 15, 20, and 25.

s = (a + b + c)/2

= (15 + 20 + 25)/2

= 30

Therefore, the area of the triangle can be calculated as:

A = √(30(30-15)(30-20)(30-25))

= √(30*15*10*5)

= 150 sq. units

Therefore, we can write the formula for the area of the triangle as:

150 = 10 h

h = 15 units

Therefore, the length of the shortest altitude of the triangle is 15 units.

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To show that a function does not have a limit as (x, y) approaches (0, 0), we need to examine the limit along different paths .

How can we show that a function does not have a limit as (x, y) approaches (0, 0)?

To show that the function f(x, y) does not have a limit as (x; y) ! (0; 0), we need to examine the limit lim

(x;y)!(0;0) xy x y .

Convert the given limit into a more recognizable form. The given limit is

lim(x, y) -> (0, 0) (xy / (x + y)).

Analyze the limit along different paths. Let's examine the limit along two distinct paths - the

x-axis (y = 0)

and

the y-axis (x = 0).

For the x-axis (y = 0), the limit becomes

lim(x, 0) -> (0, 0) (x * 0 / (x + 0))

= lim(x, 0) -> (0, 0) (0) = 0.

For the y-axis (x = 0), the limit becomes

lim(0, y) -> (0, 0) (0 * y / (0 + y))

= lim(0, y) -> (0, 0) (0) = 0.

Compare the results of the two paths. Both limits along the x-axis and y-axis are equal to 0. However, this is not enough to conclude that the function f(x, y) has a limit as (x; y) ! (0; 0).

Examine another path, such as the line y = x. In this case, the limit becomes

lim(x, x) -> (0, 0) (x * x / (x + x))

= lim(x, x) -> (0, 0) (x^2 / 2x)

= lim(x, x) -> (0, 0) (x / 2)

= 0 / 2 = 0.

Consider another path, like

y = -x.

For this path, the limit becomes

lim(x, -x) -> (0, 0) (x * -x / (x - x))

which is undefined, since the denominator is zero.
Since we have found a path

(y = -x)

where the limit is undefined, we can conclude that the function f(x, y) does not have a limit as (x; y) ! (0; 0).

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The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.

Supplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.

Therefore, the supplementary angles of the given angles are:

Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]

Roots of quadrant equation have Samsame sign if product of roots >0.

[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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Answer:

y = -3/8x + 3

Step-by-step explanation:

The slope intercept form is y = mx + b

Our equation is 3x + 8y = 24

3x + 8y = 24

8y = -3x + 24

y = -3/8x + 3

So, the answer is y = -3/8x + 3

The domain of a step function is all real numbers. The equation G(x) = -[x] + 3 can be expressed as G(x) = { -x for x < 0; 3 for x ≥ 0}. The domain of G(x) is all real numbers.

To explain further, a step function can be expressed as two separate equations, one for x < 0 and one for x ≥ 0. The equation for x < 0 is G(x) = -x and the equation for x ≥ 0 is G(x) = 3. The domain of G(x) is all real numbers. This means that any x value, whether it is greater than or less than 0, will be included in the domain of G(x).

Answer:

7x+4y

Step-by-step explanation:

combine like terms

Answer:

4?

Step-by-step explanation:

Answer: x = 15

Step-by-step explanation:

Expand 1.4(x+5): 1.4x+7+1.6x = 52

Combine like terms: 3x+7 = 52

Subtract 7 from both sides: 3x = 45

Divide both sides by 3: x = 15

Answer:

The answer is x=15

Please give me Brainliest :)

1. Expand the expression

1.4x+7+1.6x=52

2. Simplify

3x+7=52

3. Separate the constants and variables

3x=52−7

4. Add or subtract numbers

3x=45

5. Divide both sides by 3

6. Simplify

x=15

The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.

Given that:

P(A) =0.65

P(A∩B) = 0.33

And event A and B are independent.

Using the probability formula:

  P(B) = 1 - P(A) + P(A∩B)

⇒ P(B) = 1 - 0.65 + 0.33

⇒ P(B) = 0.68

Therefore , the probability of event B is 0.68.

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Answer:

b: 70

Step-by-step explanation:

10 times 5 is 50 and 4 times 5 is 20. 50 plus 20 is 70

Answer:

Step-by-step explanation:

71/8*9 which it 639/8 feet long

Answer:30

Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.

Answer:

345.6

Or 345 full cubes

Step-by-step explanation:

To answer this question we first need to find the volume of the cuboid!

To find volume we use the equation...

For the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...

We now need to the the volume of the cube which we can just do by cubing the value given

We now need to divide the two results together to find out how many cubes would fit...

Hope this helps, have a lovely day!

From the use of the angle of elevation, the length of ladder is 47 feet.

The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.

We know that we have to use the idea of the angle of elevation in this case. We know that;

Cos 65 = 20/x

x is the length of the ladder

x =20/Cos 65

x = 20/0.4225

x = 47 feet

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We can solve this problem by using proportions.  20/16 = x/10 =>  x = 12.5  Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.

what is   proportions ?

proportions are statements that two ratios or fractions are equal. A ratio is a comparison of two quantities, typically expressed as the quotient of one quantity divided by the other. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges is 5/3.

what is  height  ?

Height typically refers to the measurement of how tall or high something is, usually from its base to its top. In geometry, height is often used to refer to the perpendicular distance

In the given question ,

Let x be the height of the maple tree in feet. Then we have:

(height of statue) / (length of statue's shadow) = (height of maple tree) / (length of maple tree's shadow)

Substituting the given values, we get:

20/16 = x/10

on solving  this equation, we can cross-multiply to get:

16x = 200    =>      x = 12.5

Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.

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Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Answer:

an = a1 + (n-1)d

Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:

an = 4 + (n-1)3

a5 = 4 + (5-1)3

a5 = 4 + 12

a5 = 16

Jadi, suku ke-5 dari barisan ini adalah 16.

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It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.

Answer:

-3+[tex]4x^{2}[/tex]

Step-by-step explanation:

The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.

To determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.

We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).

Here's how to solve the problem:

1 pound = 16 ounces

Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces

The weight of one toy car is 7 ounces.

Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):

448 ÷ 7 = 64

Therefore, the bin can hold 64 toy cars.

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Move all terms that don't contain [tex]y[/tex] to the right side and solve.

the 7th number is 8. Answer B is correct. The sum of the first 6 numbers can be found by multiplying the average by the number of numbers:

sum of first 6 numbers = 6 x 15 = 90

Let the 7th number be x. Then the sum of all 7 numbers is:

sum of all 7 numbers = sum of first 6 numbers + 7th number = 90 + x

The new average is 1 less than the original average, so:

new average = 15 - 1 = 14

This means that the sum of all 7 numbers divided by 7 is 14:

(sum of all 7 numbers)/7 = 14

Substituting the expression we found for the sum of all 7 numbers, we get:

(90 + x)/7 = 14

Multiplying both sides by 7, we get:

90 + x = 98

Subtracting 90 from both sides, we get:

x = 8

Therefore, the 7th number is 8. Answer B is correct.

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