A car worth Rs. 210000 depreciated by 10%. Find its value after one year.

The car will travel approximately 11.829 if its wheels revolve 10,000 times without slipping.

First, we need to find the circumference of the wheel, which is given by the formula:

circumference = pi x diameter

where pi is approximately equal to 3.14.

So, the circumference of the wheel = 3.14 x 24 = 75.36 inches.

Next, we need to find the distance traveled by the car in one revolution of the wheel, which is equal to the circumference of the wheel.

Distance traveled by the car in one revolution of the wheel = 75.36 inches = 0.0011829 miles (1 inch = 0.000015783 miles).

Therefore, the distance traveled by the car in 10,000 revolutions of the wheel = 0.0011829 x 10,000 = 11.829 miles.

Rounding this answer to two decimal places, we get the final answer as approximately 11.829.

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The two sets of possible dimensions (length and width) of the rectangular plot are:  Length = 21 meters, Width = 13 meters

                                    Length = 8.5 meters, Width = 38 meters

Let L be the length and W be the width of the rectangular plot. We know that the perimeter of the rectangular plot is 55 meters, which can be expressed as:

2L + W = 55

We also know that the area of the rectangular plot is 342 square meters, which can be expressed as:

L * W = 342

We can use these two equations to solve for L and W:

W = 55 - 2L

L * (55 - 2L) = 342

Expanding the left side of the equation and rearranging terms, we get:

2L² - 55L + 342 = 0

We can solve this quadratic equation for L using the quadratic formula:

L = (55 ± √(55² - 42342)) / (2*2)

L = (55 ± √(841)) / 4

L = (55 ± 29) / 4

L = 21 or L = 8.5

Substituting these values of L back into the equation 2L + W = 55, we can solve for the corresponding values of W:

When L = 21, W = 55 - 2L = 13

When L = 8.5, W = 55 - 2L = 38

Therefore, the two sets of possible dimensions (length and width) of the rectangular plot are:

Length = 21 meters, Width = 13 meters

Length = 8.5 meters, Width = 38 meters

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Answer:

7

Step-by-step explanation:

87 - 80 = 7

The value of the double integral is 27/16.

We can solve this problem by converting the double integral to polar coordinates.

The circle \(x^2 y^2 = 9\) can be rewritten as \(r^2 = 9/(x^2)\), which simplifies to r = 3/|x|. The line y = \(\sqrt{(3)}\)x can be rewritten as theta = pi/3.

Thus, the limits of integration are:

0 ≤ r ≤ 3/|cos(theta)|

0 ≤ theta ≤ pi/3

The integrand is:

\(r^3 \times (cos(\theta))^3 \times (sin(\theta))^3\)

So the double integral becomes:

∫∫d \((x^2 y^2) ^3/2\) dA = ∫\(0^(\pi/3)\) ∫0^(3/|cos(theta)|) \(r^3\) \(\times\) (cos(theta)\()^3\) \(\times\) (sin(theta)\()^3\) dr d(theta)

We can simplify this integral by factoring out the constants and making a substitution u = 3cos(theta)/r:

∫0^(pi/3) ∫0^(3/|cos(theta)|) \(r^3\) \(\times\) (cos(theta)\()^3\) \(\times\)(sin(theta)\()^3\) dr d(theta)

= (27/4) ∫0^(pi/3) \(cos^3\)(theta) sin^3(theta) d(theta) ∫3cos(theta)/3 3cos(theta)/\(r^2\) dr

= (27/4) ∫0^(pi/3) \(cos^3\)(theta) \(sin^3\)(theta) d(theta) [u]^∞_(3cos(theta)/3)

= (27/4) ∫0^(pi/3) \(cos^3\)(theta) \(sin^3\)(theta) [1 - cos(theta)] d(theta)

We can evaluate this integral using integration by substitution (letting u = cos(theta)):

(27/4) ∫0^(pi/3) \(cos^3\)(theta) \(sin^3\)(theta) [1 - cos(theta)] d(theta)

= (27/4) ∫\(0^1 u^3 (1 - u^2) du\)

= (27/4) \([u^4/4 - u^6/6]_0^1\)

= (27/4) [1/4 - 1/6]

= 27/16

Therefore, the value of the double integral is 27/16.

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Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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Answer:

x = 6 or x = 0 or x = -8

Step-by-step explanation:

Solve for x over the real numbers:

2 x^3 - 4 x^2 - 96 x = -8 x^2

Add 8 x^2 to both sides:

2 x^3 + 4 x^2 - 96 x = 0

The left-hand side factors into a product with four terms:

2 x (x - 6) (x + 8) = 0

Divide both sides by 2:

x (x - 6) (x + 8) = 0

Split into three equations:

x - 6 = 0 or x = 0 or x + 8 = 0

Add 6 to both sides:

x = 6 or x = 0 or x + 8 = 0

Subtract 8 from both sides:

Answer: x = 6 or x = 0 or x = -8

The value of c that makes f(x) a valid density function over [0, 2] is c = 1/4.

The function given to us is f(x) = cx, and we are asked to find the value of c that makes this a valid density function over the interval [0, 2]. To be a valid density function, a function must satisfy two properties:

The function must be non-negative over the interval.

The integral of the function over the interval must be equal to 1.

Let's first check the first property. For f(x) to be non-negative over the interval [0, 2], c must be non-negative as well. This is because x³ is always non-negative, and multiplying it by a negative value of c would make f(x) negative for some values of x.

So, we can conclude that c ≥ 0.

Now let's check the second property. We need to find the value of c that makes the integral of f(x) over [0, 2] equal to 1:

∫₀² cx³ dx = 1

We can solve this integral using the power rule of integration:

(c/4) [x⁴]₀² = 1

(c/4) (2⁴ - 0⁴) = 1

16c/4 = 1

4c = 1

c = 1/4

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Answer:

3b^4−2b^2+8b+6

Answer:

Correct answer is B.

Step-by-step explanation:

They are equal.

Answer:

  $2.40

Step-by-step explanation:

sales tax = 30 * .08 = $2.40

Answer:

all you have to do is Just divided the numbers

Step-by-step explanation:

÷

Answer:

y = x + 1

Step-by-step explanation:

The line y = x  goes through the origin, and forms a perfect 45 degree angle with the x axis.

This is that same line, moved upward 1 unit, so the y value comes out 1 unit more.

Also, in y = mx + b form (slope-intercept form), we see slope m = 1 and y-intercept b = 1, so

y = 1x + 1 = x + 1

y = x + 1

Answer:

x = 25.2

Step-by-step explanation:

\(\frac{5}{18} =\frac{7}{x}\)

5x = 126

x = 25.2

By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.

According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.

1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

220000

Step-by-step explanation:

2000x110=220000

Why does he have so man though???

Answer:

200 cards

Step-by-step explanation:

Given: Jackson has 2,000 baseball cards in his collection. Gabe has  as many baseball cards in his collection as Jackson.

To Find: How many baseball cards does Gabe have in his collection.

Solution:

Total number of cards Jackson has in his collection

Let number of cards Gabe has =

Now,

Answer:

\(\huge\boxed{\sf No}\)

Step-by-step explanation:

Evan spent 20 hours doing homework last week

25 hours were spent this week.

Let's see what 125% of 20 equals:

= (125 / 100) * 20

= (125 / 10) * 2

= 125 / 5

= 25 hours

But,

It is written that Evan thought he spent 125 % more than the last week which means:

= (125% of 20) + 20

= 25 + 20

= 45 hours

He should've said that he has given 25% more time than the last week.

(Note that: 25 % of 20 equals 5 so 25 % more than last week will be equal to (25 % + 20) = (5+20) = 25)

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

x = 7 and - 1

Step-by-step explanation:

f(x) = (x - 7) (x + 1)

x - 7 = 0

x - 7 + 7 = 0 + 7

x = 7

x + 1 = 0

x + 1 - 1 = 0 - 1

x = - 1

Answer:

a) x= -3 y=0

x= -2 y=8

x= -1 y=6

x= 0 y=0

x= 1 y= -4

x= 2 y= 0

x= 3 y= 18

b) x³ + x² - 6x=0

x* (x² + x -6)=0

x( x(x-2) +3(x-2))=0

x=0

x-2=0 x=2

x+3=0 x= -3

x= 0, x=2, x=-3

The surface area and volume of a cube with different edge length are

When a cube with edge length 4inches ,

Surface area = 96 square inches and Volume =64 cubic inches.

Cube dilated by scale factor 0.25 ,  

Surface area = 6 square inches and Volume =1 cubic inches.

The surface area of a cube is = 6 times the area of one face.

Each face of this cube has an area equals to

= (4 inches) x (4 inches)

= 16 square inches,

So the total surface area is,

Surface area

= 6 x 16 square inches

= 96 square inches

The volume of a cube =  length of one edge cubed.

Here, the edge length is 4 inches,

Volume

= (4 inches)^3

= 64 cubic inches

When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.

This implies,

The edge length of the image cube is

0.25 x 4 inches = 1 inch.

Surface area of the image cube =  6 times the area of one face.

Each face of the image cube has an area of

= (1 inch) x (1 inch)

= 1 square inch,

So the total surface area is,

Surface area

= 6 x 1 square inch

= 6 square inches

Volume of the image cube = length of one edge cubed.

Here, the edge length is 1 inch,

Volume

= (1 inch)^3

= 1 cubic inch

Therefore, the surface area and volume for the given dimensions are

For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.

For scale factor 0.25 ,  Surface area = 6 square inches and Volume =1 cubic inches.

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Answer:

dilation

Step-by-step explanation:

i passed the class

The line integral of F around the circle of radius a = 1, centered at the origin and transversed counterclockwise, is 2π + 28.

To calculate the line integral, we need to parameterize the circle. Let's use polar coordinates (r, θ), where r = 1 and θ varies from 0 to 2π.

The unit tangent vector T(t) is given by T(t) = (cos t, sin t), where t is the parameterization of the curve.

Substituting the parameterization into the vector field F, we get:

F(r, θ) = (6(1)²(cos θ)(sin θ) + 2(sin θ)³ + 7e(1*cos θ)) i + (2e(sin² θ) + 150(1)) j

Now we evaluate the dot product of F and T:

F • T = (6(cos θ)(sin θ) + 2(sin θ)³ + 7e(1*cos θ))(cos t) + (2e(sin² θ) + 150)(sin t)

Integrating this dot product with respect to t from 0 to 2π, we obtain the line integral as 2π + 28.

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the complete question is:

F=( 6x²y + 2y³ + 7 eˣ) i + (2eʸ² + 150x )j, Consider the line integral of F around the circle of radius a, centered at the origin and transversed counterclockwise.

Find the line integral for a = 1

Answer:

y = 8√2

Step-by-step explanation:

First, we can use the 30-60-90 triangle rule on the rightmost triangle. This states that:

So, we can solve for the middle line (I will call it L) on this triangle:

L = 16 / 2

L = 8

Next, we can solve for y using the rule with 45-45-90 triangles:

So, we can solve for y:

y = 8 · √2

y = 8√2

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

15

Step-by-step explanation:

- 7 + m = 8

m - 7 = 8

m = 8 + 7

m = 15

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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Answer:

2sqrt(7)/5

Step-by-step explanation:

sqrt(28/25)

sqrt(28)/sqrt(25)

2sqrt(7)/sqrt(25)

2sqrt(7)/5

Answer:

c

Step-by-step explanation:

because this is very easy and i got it right on the test got it right on edge