Let y =tan(4x + 6). Find the differential dy when x = 3 and dx = 0.2 ______ Find the differential dy when x = 3 and dx = 0.4 ______

Answer:

Step-by-step explanation:

First calculate for the area of the trapezoid (the formula is (base + base / 2) x height):

60 cm + 90 cm = 150 cm

150 cm / 2 = 75 cm

75 cm x 30 cm = 2250 cm²

Now 1 cm² = 1 mL and 1000 mL = 1 L

2250 cm² = 2250 mL

2250 mL = 2.25 L

The volume of the aquarium of height 100 cm and area of 2250 cm sq is 225L.

An aquarium has a trapezoid base. The base is 90 cm long at the front, 60 cm long at the back, and 30 cm wide (from front to back). The height is 100 cm.

The area of the trapezoid is calculated by measuring the sum of the parallel sides divided by 2 and multiplying it with its height.

A = [(a + b)/2] × h

The volume of the trapezoid is the product of the area of the trapezoid and the height between the trapezoid's end.

The volume of trapezoid = area × height between trapezium ends

so, the area of the trapezoid, A = [ 90 + 60 ]/2 × 30

= 150 /2 × 30

= 75 × 30

= 2250 \(\rm cm^{2}\)

The volume of trapezoid = area × height between trapezium ends

The volume of the trapezoid = 2250 × 100

                                                = 225000 \(\rm cm^{3}\)

Now, 1 cm² = 1 mL and 1000 mL = 1 L

225000 cm² = 225000mL

225000 mL = 225 L

Therefore, the volume of the aquarium of height 100cm and area of 2250 cm sq is 225L.

Learn more about the volume of the trapezoid here:

https://brainly.com/question/16592149

The average of the three points A, B and C is M(x, y) = (- 7 / 9, 17 / 9).

In this problem we need to find the average of three points (A, B, C), each point has different weights. The average can be found by means of following expression:

\(M(x, y) = \frac{\sum\limits_{i = 1}^{n} w_{i}\cdot P_{i}(x, y)}{\sum \limits_{i = 1}^{n}w_{i}}\)

Where:

Then, the average of points A, B and C are described below:

M(x, y) = [1 · (8, - 6) + 4 · (9, - 5) + 4 · (- 6, 7)] / (1 + 4 + 4)

M(x, y) = [(8, - 6) + (9, - 5) + (- 24, 28)] / 9

M(x, y) = (- 7, 17) / 9

M(x, y) = (- 7 / 9, 17 / 9)

To learn more on weighted averages: https://brainly.com/question/28419561

#SPJ1

Answer:

40 cm 2 yes to Chou god cm,6 ja

Answer:

Step-by-step explanation:

I took the test

Answer:

75 sweets

Step-by-step explanation:

Given that

There is 120 sweets that are put into three different size boxis

And, the ratio of small box to medium box to large box is 1:2:5

We need to find out the no of sweets in the large box

So,

The number of sweets in a large box is

= 120 sweets × 5 ÷ (1 + 2 + 5)

= 120 sweets × 5 ÷ 8

= 75 sweets

In the group Z90⊕Z36, there are four cyclic subgroups of order 15. Each subgroup is generated by an element with a specific combination of residue classes modulo 90 and 36.

To determine the number of cyclic subgroups of order 15 in Z90⊕Z36, we need to find the elements whose powers generate subgroups of order 15.
The order of an element (a, b) in Z90⊕Z36 is given by the least common multiple of the orders of a and b. Since 15 is the desired order, the possible combinations of residue classes modulo 90 and 36 that satisfy this condition are: (3, 0), (23, 0), (33, 0), and (53, 0).
For example, the element (3, 0) generates a subgroup of order 15, denoted as ⟨(3, 0)⟩, where ⟨⟩ represents the subgroup generated by an element. Similarly, (23, 0), (33, 0), and (53, 0) also generate subgroups of order 15.
Therefore, in Z90⊕Z36, there are four cyclic subgroups of order 15, each generated by one of the elements (3, 0), (23, 0), (33, 0), and (53, 0).

Learn more about subgroup here
https://brainly.com/question/31432778



#SPJ11

Answer:

The area of the triangle is equal to half of the base times the height: A = b x h x 1/2 You could find the area of a triangle with base length of 4 inches and height of 3 inches as follows: A = 4 inches x 3 inches x 1/2 = 6 square inches

Step-by-step explanation:

The corresponding height is the length of a perpendicular segment from the base to the vertex opposite of it. The opposite vertex is the vertex that is not an endpoint of the base.

They can set up total 30 tables in 5 hours.

Multiply in mathematics refers to the continual addition of sets of same size.

2 × 3 = 6

It can be interpreted this way:

Three times two equals six.

Three times two equals six.

Six is two threes.

Given,

Andersons can set up 6 tables in 1 hour

Tables they can set up in 5 hours = 5 × 6

= 30

To learn more about multiplication from given link

https://brainly.com/question/4721701

#SPJ9

Answer:

There are 55 grams of sugar in a 20-ounce bottle of soda.

Step-by-step explanation:

So if your looking for a 68 ounce bottle of soda we know there would be about 165 grams of sugar just in 60 ounces. as then you would find the amount of 8 grams of sugar.

The time taken for 21000 spectators to vacate the stadium , if only 15 exits are functional is 28 minutes .

In the question ,

it is given that

the time taken to vacate the stadium = 20 minutes

number of exits = 25 exits

capacity of the stadium = 25000 spectators .

given that ,

time taken to exit the stadium varies directly with number of spectators and inversely with the number of exits .

time taken ∝ number of spectators ∝ 1/number of exits .

to remove the proportionality sign , we write the constant

time taken = k * (number of spectators)/(number of exits) .

20 = k * 25000/25

20 = k * 1000

k = 20/1000

k = 2/100

k = 1/50 = 0.02

So, to find the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional , we use the formula

time taken = (0.02)*(21000/15)

= 0.02*1400

= 28

Therefore , The time taken for 21000 spectators to vacate the stadium , if only 15 exits are functional is 28  minutes .

Learn more about Equation here

https://brainly.com/question/23633125

#SPJ1

Step-by-step explanation:

slope= -a/b

=-4/8

-1/2

500, 510, 520.20

500/100 = 5 or 1% of 500

5 x 2 = 10 or 2% of 500

500 + 10 = 510

From 500 to 510, we can see that it increase by 2%.

510/100 = 5.1 or 1% of 510

5.1 x 2 = 10.2 or 2% of 510

510 + 10.2 = 520.20.

From 510 to 520.20, we can see that it increase by 2%.

We can conclude that the investment is steadily going up by 2%.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.

The sampling method described in the scenario is called systematic sampling.

Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.

However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.

To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.

for more such question on relatively visit

https://brainly.com/question/29502088

#SPJ8

Equations for common surfaces:

1. Plane: Ax + By + Cz + D = 0

2. Sphere: (x - h)² + (y - k)² + (z - l)² = r²

3. (Elliptic) Paraboloid: z = ax² + by² + c

4. Hyperbolic Paraboloid: z = ax² - by² + c

5. (Circular) Cylinder: (x - h)² + (y - k)² = r²

6. Half Cone: z = √(x² + y²)

For each surface:

1. Plane: The easiest coordinate system to express the equation is the Cartesian coordinate system (x, y, z) since the equation involves linear terms in all three variables.

2. Sphere: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a sphere because it directly relates to the distance between the center of the sphere and any point on its surface.

3. (Elliptic) Paraboloid: The Cartesian coordinate system (x, y, z) is most convenient for expressing the equation of a (elliptic) paraboloid because it allows a direct representation of the quadratic terms in x and y.

4. Hyperbolic Paraboloid: Similar to the (elliptic) paraboloid, the Cartesian coordinate system (x, y, z) is best suited for expressing the equation of a hyperbolic paraboloid due to its direct representation of the quadratic terms.

5. (Circular) Cylinder: The cylindrical coordinate system (ρ, φ, z) is easiest to express the equation of a (circular) cylinder because it naturally separates the radial distance from the axis (ρ) and the angle in the xy-plane (φ).

6. Half Cone: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a half cone since it provides a direct representation of the relationship between the coordinates and the square root of the sum of their squares.

To know more about Plane, refer here:

https://brainly.com/question/29271728#

#SPJ4

a) We have shown that if x is even, then \(x^2 = 0\) or 4 (mod 8).

b) We have shown that if x is odd, then \(x^2 = 1\) (mod 8).

a) To prove that if x is even, then\(x^2 = 0\) or 4 (mod 8), we can use the fact that any even integer can be written in the form 2k, where k is an integer. Then, we have:

\(x^2 = (2k)^2 = 4k^2\)

Since k^2 is also an integer, we can write \(4k^2\)as 8m or 8m + 4, where m is an integer. This can be simplified as:

\(4k^2 = 8m or 4k^2 = 8m + 4\\2k^2 = 4m or 2k^2 = 2m + 1\\k^2 = 2m or k^2 = (2m + 1)/2\)

In the first case, \(k^2\) is even and so\(x^2 = 0\) (mod 8). In the second case, \(k^2\)is odd and so \(x^2 = 4\) (mod 8).

b) To prove that if x is odd, then \(x^2 = 1\) (mod 8), we can again use the fact that any odd integer can be written in the form 2k + 1, where k is an integer. Then, we have:

\(x^2 = (2k + 1)^2 = 4k^2 + 4k + 1\)

Since \(k^2\)and k are integers, we can write \(4k^2 + 4k\) as 8m or 8m + 4, where m is an integer. This can be simplified as:

\(4k^2 + 4k = 8m or 4k^2 + 4k = 8m + 4\\2k^2 + 2k = 4m or 2k^2 + 2k = 2m + 1\)

k(k + 1) = 2m or k(k + 1) = (2m + 1)/2

In the first case, either k or k + 1 is even, so k(k + 1) is even and \(x^2 = 0\)(mod 8). In the second case, k and k + 1 are consecutive integers, so one of them must be even and the other odd. Therefore, k(k + 1) is even and x^2 ≡ 4 (mod 8).

Finally, we have:

\(x^2 = 4m + 1 or x^2 = 4m + 5\)

In either case, \(x^2 = 1\) (mod 8), since 4m + 1 and 4m + 5 are both congruent to 1 modulo 8.

for such more question on even and odd

https://brainly.com/question/19180335

#SPJ11

Answer:

y=16x^12−72x^10+108x^8−54x^6

Step-by-step explanation:

We can use the concept of System of Equations to solve this question. The answer for part A is 0 and even for part B is 0.

A two-variable linear equation is one with the formula ax + by + c = 0, where a, b, c R, a, and b 0. By comparing the coefficients of the variables in the equations, we may determine how many solutions there are to a system of linear equations. Take into account the pair of linear equations involving x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here, the real numbers a2, b2, and c2 are all present.

Keep in mind that a12 + b12 0 and a22 + b22 0

1. There will be a singular solution if (a1/a2) (b1/b2).

2. There will be an endless number of solutions if (a1/a2) = (b1/b2) = (c1/c2).

3. There won't be a solution if (a1/a2) = (b1/b2) ≠(c1/c2).

Part A:

       4x+6y=24

       2x+3y=8 are the given solutions are they are in the form of linear equations.

a1/a2 =2 b1/b2=2 and c1/c2=3

So according to the condition 3 , there will no solution if both the lines are parallel and a1/a2 =b1/b2 ≠c1/c2.

∴ So No.of solutions are Zero.

Part B:

   In the updated system,

             12x+18y=72

              2x+3y=8

a1/a2 =6 b1/b2 =6 and c1/c2=9.

So according to the condition 3 , there will no solution if both the lines are parallel and a1/a2 =b1/b2 ≠c1/c2.

So they have same no.of solutions as the original system.

We can use the concept of System of Equations to solve this question. The answer for part A is 0 and even for part B is 0.

To refer more about System of Equations , visit:

https://brainly.com/question/13729904

#SPJ1

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

A quart means a quarter of gallon and is equal to 946.353 cubic centimeters. The volume of the cube is equal to the cube of the side lengt, then:

x³ = 946.353

x = ∛946.353

x ≈ 9.818

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

To learn more on volumes: https://brainly.com/question/1578538

#SPJ1

The area of the hexagon is 81 square meters, and the perimeter is 18√3 meters.

To calculate the area and perimeter of the given shape, we need to identify the shape. Based on the given dimensions of 3√3 m for one side and 6 m for another side, it appears that we are dealing with a regular hexagon.

A regular hexagon has six equal sides and six equal angles. The formula for the area of a regular polygon is A = ½ * a * P, where "a" is the length of one side and "P" is the perimeter.

Given that one side of the hexagon is 3√3 m, we can calculate the perimeter:

Perimeter = 6 * side length = 6 * (3√3) m = 18√3 m

To calculate the area, we use the formula:

Area = ½ * a * P = ½ * (3√3) * (18√3) = 27√3 * √3 = 27 * 3 = 81 m²

Therefore, the area of the hexagon is 81 square meters, and the perimeter is 18√3 meters.

To know more about Perimeter .

https://brainly.com/question/19819849

#SPJ11

\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 18}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( \frac{ - 3}{4} = \frac{x}{24} \)

➼ \( \: x = \frac{ - 3 \times 24}{4} \)

➼ \( \: x = \frac{ - 72}{4} \)

➼ \( \: x = - 18\)

Therefore the value of \(x\) is -18.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

\( \frac{ - 3}{4} = \frac{ - 18}{24} \)

➼ \( \: \frac{ - 3}{4} = \frac{ - 3}{4} \)

➼ L. H. S. = R. H. S.

Hence verified.

\(\bold{ \green{ \star{ \orange{Mystique35♨}}}}⋆\)

Answer:

14.3152173913

Step-by-step explanation:

Answer:

1317/92

Step-by-step explanation:

brainlest plz

Answer:

point b is located at -0.905 . If it was -0.95 then it would be point A

Answer:

point B

I hope it's helps you

Answer:

25,390

Step-by-step explanation:

The computation is shown below

Given that

There is a number i.e. 25387

Based on the above information

The given numbers should be written in 4 significant figures

So here the number after considering 4 significant figures is 25,390

Hence, the above represents the answer

(Hey, angles rock!)

Answer:

45 + 60 = 105

Step-by-step explanation:

ABC consists of two angles, angle ABD and angle DBC. Therefore, the sum of the measures of angles ABD and DBC is the measure of ABC.

45 + 60 = 105

Answer:

420

Step-by-step explanation:

if we add 30 to each of the length of speech, we get 420 seconds

The proportional relationships that model each relation are given as follows:

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:

y = kx.

Both items in this problem are represented by direct proportional relationships, we just have to identify the constants then graph the relations.

The graph of a proportional relationship is linear with slope given by the constant and intercept at 0, hence the graphs for each item are given at the end of the answer.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

The three (3) possible combinations are

Alex should 20 hats and 20 scarves

Let the number of scarves be x and y be the number of hats

He can make at most 20 hats and 30 scarves, but no more than 40 items altogether

x ≤ 20

y ≤ 30

x + y ≤ 40 (in time of market)

x + y ≥ 25

The possible combinations are

He should choose the third option x = 20, y = 20 this allows him to take more products to the show

Learn more about inequality graph at:

https://brainly.com/question/11234618

#SPJ1

On solving the provided question, we can say that equation that make the most sense to solve with the Zero Product Property is  4x² + 16x = 12

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

equation that make the most sense to solve with the Zero Product Property is

4x² + 16x = 12

as when putting x = 0 we get 12

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

\((2, \frac{7}{2} )\)

Step-by-step explanation:

The midpoint between two points is:

\((\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\) when the given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (1,6) and (3,1)

\(= (\frac{1+3}{2} , \frac{6+1}{2} )\\= (\frac{4}{2} , \frac{7}{2} )\\= (2, \frac{7}{2} )\)

Therefore, the midpoint between (1,6) and (3,1) is \((2, \frac{7}{2} )\).

I hope this helps!

Answer:

the answer is C your welcome!!!!

Step-by-step explanation:

Answer:

Let's denote O as center of circle.

=> Two isosceles triangles  AOB and EOF are congruent (SSS).

Because AO = BO = EO = FO = radius of circle O, AB = EF = 8

=> Arc AB = AOB = EOF = Arc EF = 65 deg.

Hope this helps!

:)