find the solution to the differential equation dydt=y2(4 t), y=8 when t=1.

The function f(x) is 3/x³ if f'(x) is 1/x²

Given that,

f'(x) is 1/x²

To find : f(x)

Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the  x.

f(x) ---> differentiation  ------> f'(x)

f'(x)---> integration ------> f(x)

f(x) = ∫ f'(x)

f(x) = ∫ 1/x²

f(x) = 3/x³

Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .

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If a paper company needs to ship paper to a late printing business. 12 small boxes were shipped and 8 large boxes were shipped.

Using a system of equations to represent the problem.

Let x represent the number of small boxes shipped

Let  y represent the number of large boxes shipped.

We know that:

x + y = 20 (the total number of boxes shipped)

8x + 21y = 264 (the combined volume of all boxes )

Solving the first equation for y: y = 20 - x

Substituting this expression for y into the second equation:

8x + 21(20 - x) = 264

8x + 420 - 21x = 264

-13x = -156

x = 12 (small boxes)

So,

y = 20 - x

y = 20 -12

y = 8 (Large boxes)

Therefore 12 small boxes were shipped and 8 large boxes were shipped.

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Answer:

x = 1/a

Step-by-step explanation:

To solve 7ax + 8ax = 9ax + 6 for x, we can start by combining like terms on both sides of the equation:

7ax + 8ax = 9ax + 6

becomes

15ax = 9ax + 6

Next, we can subtract 9ax from both sides of the equation:

15ax - 9ax = 9ax + 6 - 9ax

becomes

6ax = 6

Finally, we can divide both sides of the equation by 6a to find the value of x:

6ax / 6a = 6 / 6a

becomes

x = 1/a

So, the solution for x is x = 1/a.

Answer: Graph A is your answer

Step-by-step explanation:

Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.

Answer:

3:10

Step-by-step explanation:

In order to find the ratio of red to green sweets, we first need to find the ratio of yellow to green sweets. We know that the ratio of yellow to green is 1:5 and we also know that the ratio of red to yellow is 3:2.

We can use this information to find the ratio of red to green by cross-multiplying the ratio of red to yellow and the ratio of yellow to green.

So (3:2) x (1:5) = (3:10)

This means the ratio of red to green is 3:10.

Alternatively, we can find the ratio of red to green by using the following formula:

(red:yellow) x (yellow:green) = (red:green)

So (3:2) x (1:5) = (3:10)

The ratio of red to green is 3:10.

Answer:

Step-by-step explanation:

The ratio of red : yellow = 3:2 and yellow:green = 1:5

So, the ratio of red : yellow : green = 3:2:5

To find the ratio of red: green, we can find the ratio of red : yellow : green and then divide the red and green portions.

So, the ratio of red: green = (3/(3+2+5)) : (5/(3+2+5)) = 3/10 : 5/10 = 3:5

To determine the cosine of an angle, use the Cos Theta Formula in mathematics.The Answer is 3.

If arctan(2)=, then let the angle be.In this case, tan = 2.

We get =63.43 when we plug the value into the arctan(x) graph.

We do this by using the x=2 line and examining where it crosses the arctan graph (x).

To determine the cosine of an angle, use the Cos Theta Formula in mathematics.

The symbol for it is Cos(), and it has the following form:

adjacent/hypotenuse = cos().

f(θ) = tan(θ) = 3

Note that

tan (x+y ) = tan x +tan y/1-tan x tan y

Note that tan(π) = 0.

Therefore

f(θ + π) = tan(θ+π)

           = (tanθ + tan π)/(1 -tanθ tan π)

           = 3/1 = 3

Answer is 3.

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Answer: x/4+2=5

Step-by-step explanation:

Answer:

I think the y= (-7)

Answer: The last option.

Step-by-step explanation:

         The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;

             m∠1 + m∠2 = m∠2 + m∠3

       This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.

The domain of y = sin x is the set of all real numbers.

The sine function, represented by y = sin x, is defined for all real numbers, meaning that any real number can be plugged into the function as the input (x) and will produce a valid output (y). Therefore, the domain of y = sin x is the set of all real numbers.

The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.

Although the question does not specify the options, but I have specified my answer as follows:

Given:

The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.

Account Opening Charges: $10

Starting amount: $d

The total amount in the account: $m

Let us say the depositor deposits an amount $k for 'i' number of months

Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.

I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.

The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time

⇒m=d-10+k×i

This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.

Therefore, the following equation is m=d-10+k×i.

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(a) The domain of the function-

[tex]g(t)=sin(e^{-t})[/tex]

is (-∞,∞)

(b) the domain of the given function -

[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)

(a) The domain of the function-

[tex]g(t)=sin(e^{-t})[/tex]

is (-∞,∞)

(b) the domain of the function -

[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)

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Answer:

j(x) = f(g(x)) = f(0.25x) = 0.75x - 5

According to the scatter plot below, when x = 5, the value of y is 1.

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).

Here,

Based on the scatter plot below, when x=5 then value of y is 1.

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Answer:

The percentage error in x can be calculated as follows:

Percentage error = (Estimated value - Actual value) / Actual value * 100

Let x be the actual value and y be the estimated value such that y > x.

Percentage error = (y - x) / x * 100

This formula calculates the absolute error in terms of a percentage of the actual value.

The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon

Ms. Avila ordered 120 blue ribbons from the smart start school supplier.

Smart start reduced the price of each blue ribbon by $0.75.

The total came to $60.

To express the problem in equation we have to read the question carefully and write the equation according to question.

Let the price of 1 blue ribbon = b

If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)

She buy total blue ribbons = 120

So the price of 120 blue ribbons = 120(b - 0.75)

But the total cost is $60.

So the equation is:

120(b - 0.75) = 60

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The value of y if (1, y, −9) is perpendicular to vector v is  38/5.

Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k

In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero

So,  vector v.vector c = 0

(2i - 5j - 4k ).(i + yj - 9k)  = 0

                    2(1) - 5(y) - 4(-9) = 0

                           2 - 5y + 36 = 0

                                    5y = 38

                                      y = 38/5

Hence, the value of y is 38/5.

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Answer:

a

Step-by-step explanation:

Answer:

a. a student who was not absent during unit should score about 98

The surface area of the whole solid will be 144 square inches.

The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.

The surface area will be calculated as:-

SA = SA of cuboid + SA of cube

SA = 6 x ( 11 x 2 ) + 6 x 2

SA = 132 + 12

SA = 144 square inches

Therefore, the surface area of the whole solid will be 144 square inches.

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The volume of the cylinder is 1413 cubic cm. Then the mass of the carbon will be 2741.22 grams.

The density is the ratio of mass to volume of any substance. Let m be the mass of the object and v be the volume of the object.

Then the density D will be

D = m / v g/cm³

The volume of the cylinder is given as,

V = (π/4) d²h

V = (π/4) x 10² x 18

V = 1413 cm³

Then the mass of the carbon is given as,

1.94 = m / 1413

m = 2741.22 grams

The mass of the carbon will be 2741.22 grams.

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Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.

Let the number of ml of 40% sugar be x and 85% sugar used be y

System of equations is given as:

x + y = 1800mL ....... (1)

x = 1800 - y

40% × x + 85% × y = 60% × 1800mL

0.4x + 0.85y = 1080.... (2)

We substitute 1800 - y for x in (2)

0.4(1800 - y) + 0.85y = 1080

simplifying the above equation, we get

720 - 0.4y + 0.85y = 1080

- 0.4y + 0.85y = 1080 - 720

0.45y = 360

y = 360/0.45

y = 800mL

Solving for x

x = 1800 - y

substitute the value of y in the above equation, we get

x = 1800 - 800

x = 1000mL

Therefore, the number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL.

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Step-by-step explanation:

What we have is...

[tex]4(-4.6+w) = 22.24[/tex]

What we'll first do is distribute the 4 into the -4.6 and w

-18.4+4w = 22.24

Next we add 18.4 to both sides to get rid of it on the right side

4W = 22.24+ 18.4

4W = 40.64

Last thing to get W alone, we will divide both sides by 4

W = 10.16

Answer:

2300000

Step-by-step explanation:

Step-by-step explanation:

The data displayed below is numerical data.

Tally Chart:

10 |

19 |

17 |

14 |

11 |

18 |

16 |

17 |

18 |

15 |

13 |

12 |

14 |

15 |

16 |

18 |

19 |

20 |

16 |

15 |

11 |

10 |

15 |

20 |

12 |

14 |

Note: The above tally chart is just a representation of the data, the actual tally chart should be made on paper with tally marks.

Applying the two-tangents theorem, the value of x is: 5.

The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.

Since point J is formed by the two tangents, KJ and MJ, therefore:

KJ = MJ

Substitute:

4x + 7 = 7x - 8, find x

Combine like terms:

4x - 7x = -7 - 8

-3x = -15

-3x/-3 = -15/-3

x = 5

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The time when the projectile has an instantaneous velocity of zero is a = 10 seconds.

The instantaneous velocity of a projectile at time t can be found by taking the derivative of its position function with respect to time. The velocity function is given by:

v(t) = ds(t)/dt = -32t + 320

The time at which the projectile has an instantaneous velocity of zero is when the velocity function is equal to 0. We can find this time by solving the equation:

-32t + 320 = 0

32t = 320

t = 10

Therefore, the time at which the projectile has an instantaneous velocity of zero is a = 10.

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--The given question is incomplete; the complete question is

"A projectile is fired vertically upward and has a position given by s(t) = -16T^2+320t+336 for 0 ≤ t ≤ 21.

Identify the time at which the projectile has an instantaneous velocity of zero; call this time = a."--

Answer:

Salvador has traveled 584 - 396 = 188 kilometers so far.

The measure of arc FQ is given as follows:

155º.

The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.

From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.

Applying the two secant theorem, the angle measure of arc FQ is given as follows:

(FQ - 75)/2 = 40

FQ - 75 = 80

FQ = 75 + 80

FQ = 155º.

Meaning that the last option represents the correct option in the context of this problem.

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Answer:

the 45 tickets

Step-by-step explanation:

In the 20 tickets deal, you'll spend USD 1.333333333333333 per ticket; in the 45 tickets deal, you pay USD 0.6 per ticket.