Evaluate the equation 3/8h = 3/4

A) h= 1/2
B) h=1/4
C) h=1/8
D) h=2​

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Answer:

division

Step-by-step explanation:

2x/2=8/2=x=4

x=4

Answer:

The answer is 4/9. But I do not think that the options that you provided are true.

For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y

The correct condition that must be true if events A and B are independent is:

P(A ∩ B) = P(A) x P(B).

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.

In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.

When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.

Therefore, the correct answer is:

P(A ∩ B) = x*y

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Answer:

(-3,1)

Step-by-step explanation:

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer:

tell me the answer

rn

Step-by-step explanation:

1dgxr 3wa 4tws t

Answer:

b and d

Step-by-step explanation:

i just took the quiz

Answer:

C

Step-by-step explanation:

Since we know that squares have all equal sides the area of a square is just a side². So, we would square root 256 in order to find one side. And we know that there are 4 sides of a square so 16+16+16+16= 64. so the answer is C

The integral of cos(3πt)i + sin(2πt)j + \(t^3\)k with respect to t is (1/3π)sin(3πt)i - (1/2π)cos(2πt)j + (1/4)\(t^4\)k + c, where c is the constant of integration.

To evaluate the integral, we integrate each component separately.

The integral of cos(3πt) with respect to t is (1/3π)sin(3πt), where (1/3π) is the constant coefficient from the derivative of sin(3πt) with respect to t.

Therefore, the integral of cos(3πt)i is (1/3π)sin(3πt)i.

Similarly, the integral of sin(2πt) with respect to t is -(1/2π)cos(2πt), where -(1/2π) is the constant coefficient from the derivative of cos(2πt) with respect to t.

Thus, the integral of sin(2πt)j is -(1/2π)cos(2πt)j.

Lastly, the integral of \(t^3\) with respect to t is (1/4)\(t^4\), where (1/4) is the constant coefficient from the power rule of differentiation.

Hence, the integral of \(t^3\)k is (1/4)\(t^4\)k.

Putting it all together, the integral of cos(3πt)i + sin(2πt)j + \(t^3\)k with respect to t is (1/3π)sin(3πt)i - (1/2π)cos(2πt)j + (1/4)\(t^4\)k + c, where c represents the constant of integration.

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A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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Answer:

em sorry

Step-by-step explanation:

Answer:

$25.50

Step-by-step explanation:

We need to find 30% of 85:

30%*85

Convert 30% to a fraction to make the math easier:

\(\frac{30}{100}*85=\frac{3}{10}*85=25.5\)

She tipped the waiter $25.50

Answer:

3

Step-by-step explanation:

To calculate the amount that Mary pays in state income tax, we need to find 8% of her annual salary.

Given that Mary's annual salary is $147,362, we can calculate the state income tax as follows:

State Income Tax = (8/100) * Annual Salary

State Income Tax = (8/100) * $147,362

State Income Tax = $11,788.96

Therefore, Mary pays $11,788.96 in state income tax.

The correct answer is C) $11,788.96.

\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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Answer:

the 2.5 has is the bigger one

Step-by-step explanation:

if you are talking about "which one is greater" than i think its right

Paulo's claim that the first 6 is 10 times as great as the other six is false

The given parameters are:

Number = 6360

In the above number, we have the following place values

Next, we divide the place values of the first and the second 6.

So, we have the following quotient expression

Quotient = Place value of the first 6/Place value of the second 6

Substitute the known values in the above equation

Quotient = 6000/60

Evaluate the quotient

Quotient = 100

Hence, the first 6 is 100 times as great as the other six

This means that Paulo's claim that the first 6 is 10 times as great as the other six is false

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That when (x, y) = (0, 0), the function is defined to be 0, which corresponds to the origin in polar coordinates.

To describe the level curves of the function defined by f(x, y) = 2xy / (x^2 + y^2), where (x, y) ≠ (0, 0) and f(0, 0) = 0, we can convert the Cartesian coordinates (x, y) to polar coordinates (r, θ).

In polar coordinates, x = r cos(θ) and y = r sin(θ). Substituting these expressions into the function, we have:

f(r, θ) = 2(r cos(θ))(r sin(θ)) / (r^2 cos^2(θ) + r^2 sin^2(θ))

= 2r^2 cos(θ) sin(θ) / (r^2)

= 2r cos(θ) sin(θ)

Simplifying further, we get:

f(r, θ) = 2r cos(θ) sin(θ)

Now, let's consider the level curves, which are the curves in the xy-plane where f(x, y) is constant. In polar coordinates, this means we need to find values of r and θ such that f(r, θ) is constant.

Since f(r, θ) = 2r cos(θ) sin(θ), we can set a constant value k and rewrite the equation as:

k = 2r cos(θ) sin(θ)

Dividing both sides of the equation by 2 and rearranging, we have:

r = k / (2 cos(θ) sin(θ))

This equation represents the level curves of the function f(x, y) = 2xy / (x^2 + y^2) in polar coordinates. The level curves are given by the equation r = k / (2 cos(θ) sin(θ)), where k is a constant.

Note that when (x, y) = (0, 0), the function is defined to be 0, which corresponds to the origin in polar coordinates.

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Answer:

x = 2

Step-by-step explanation:

x2 + 6x - 13 = 3

first you add 13 to other side and get

x2 + 6x = 16

next you combine x's

8x = 16

then you divde the 8x by 16

and you get x = 2

Answer:

3,-2

Step-by-step explanation:

set y =0 and solve

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

the values 3, -2 solve the equation and are your x-intercepts

Discount is 0.354838, Discount percentage is 35.4838 %.

According to the question

A shop item is marked down from r 6.20 to r 4.

A discount is an amount that is subtracted from the regular price of an item.

Based on the given conditions

= \(\frac{6.2-4}{6.2}\)

Solving 6.2 - 4, we get 2.2

= 2.2/6.2

Discount = 11/31 = 0.354838

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred. For example, a percentage discount of 20% would mean that an item that originally cost $100 would now cost $80.

Discount percentage = \(\frac{11}{31}\) × 100

= 35.4838 %

Hence,

Discount is 0.354838, Discount percentage is 35.4838 %.

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From the triangle given, sin (B)= 0.74, cos (B)= 0.67 and tan (B)= 1.1 are the exact values according to the trigonometric functions.

From the given diagram,

a=65 and b =72 and c =97.

Given only according to the angle B.

Hypotenuse ( c ) = 97.

a. sin ( B ) = The length of the opposite side / The length of the hypotenuse

sin(B) = b/c

sin(B) = 72/97

sin(B) = 0.74

b. cos (B) = The length of the adjacent side / The length of the hypotenuse

cos (B) = a/c

cos (B) = 65/97

cos (B) = 0.67

c. tan (B) = The length of the opposite side / The length of the adjacent

tan (B) = b/a

tan(B)= 72/65

tan(B)=1.1

Therefore, from the triangle given, sin (B)= 0.74, cos (B)= 0.67 and tan (B)= 1.1 are the exact values according to the trigonometric functions.

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The 95% confidence interval for the slope will be B. (-0.308,-0.019).

The confidence interval based on the information and diagram will be:

= -0.1636 + 2.228 × 0.06488

= 0.019

Also, -0.1636 - 2.228 × 0.06488

= -0.308

In conclusion, the correct option is (-0.308,-0.019).

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A system of inequalities can be solved graphically.

See attachment for the required graph

The inequalities are given as

\(x + 3y > 6\\y \geq 2x + 4\)

The options are not given.

So, I have attached the graph that illustrates the solution to the system of inequalities.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

From the graph, we have the solutions as

\(x > -0.857\)

\(y\geq 2.276\)

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Answer:

The answer is 1,102

Step-by-step explanation:

First, we need to figure out how much per hour.

406 divided by 7 = 58

Now we multiply by the hours

58 x 19 = 1,102

Answer:

1,102 miles

Step-by-step explanation:

406=7

406/7= 58

1 hour = 58 miles

19 times 58 = 1,102

If the minimum 30 chairs were sold , then the minimum number of Tables sold is 10.

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 40

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 40        .......1

200 C + 600 T = 12000         .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 40 × 200

i.e 200 C + 200 T = 8000

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 8000

Or, 400 T =  4000

i.e T = 10

Put The value of T in eq 2

So, 200 C + 600 × 10 = 12000

or , 200 C + 6000 = 12,000

Or, 200 C = 12000 - 6000

Or, 200 C = 6000

i.e C = 30

The number of chair sold is 30

If the number of chair sold is 10 ,

Then the min number of table sold = 200 × 30 + 600 T = 12000

i.e 600 T = 12000 - 6000

or, 600 T = 6000

∴   T = 10

I.e T = 10

Hence, if the minimum 30 chairs were sold , then the minimum number of Tables sold is 10 .

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