Expression for calculation divided 10 in half and subtract from 50 divided into fifth

To find the base of the triangle with a known area and height, apply the formula for the area of a triangle and solve for the base, resulting in 12 ft.

The base of the triangle can be found using the formula for the area of a triangle:

To calculate the volume of a cylinder with a diameter of 28 units and a height of 28 units, use the formula V = πr²h. The calculated volume is approximately 17240.896 cubic units.

To find the volume of a cylinder, we use the formula:

V = πr²h

Here, the diameter of the cylinder is 28 units. To find the radius, we divide the diameter by 2:

r = 28 / 2 = 14 units

The height of the cylinder is given as 28 units. Substituting the values into the formula, we get:

V = π × (14)² × 28

V = π × 196 × 28

V = 5488π

Using the approximation π ≈ 3.142,

V ≈ 5488 × 3.142 ≈ 17240.896 cubic units

Therefore, the volume of the cylinder is approximately 17240.896 cubic units.

The area of the circle in square centimeters is [tex]\( 36\pi x^{18}y^{10} \)[/tex] cm².

The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.

Given that the radius [tex]\( r \)[/tex] of the circle is [tex]\( 6x^9y^5 \)[/tex] cm, we can substitute this value into the formula to find the area.

[tex]\( A = \pi (6x^9y^5)^2 \)[/tex]

Now, we square the radius:

[tex]\( (6x^9y^5)^2 = (6x^9y^5)(6x^9y^5) \)[/tex]

[tex]\( = 36x^{18}y^{10} \)[/tex]

Substituting this back into the area formula:

[tex]\( A = \pi \cdot 36x^{18}y^{10} \)[/tex]

[tex]\( A = 36\pi x^{18}y^{10} \)[/tex]

Therefore, the area of the circle in square centimeters is [tex]\( 36\pi x^{18}y^{10} \)[/tex] cm².

Final answer:

To verify the divergence theorem for the given vector field and region e, we need to calculate the flux through each face of the cube and sum them up. By calculating the flux through each face and summing them, we can verify that the flux of the vector field through the region e is 0.

Explanation:

The divergence theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the volume enclosed by the surface.

In this case, the vector field is given by f(x, y, z) = 4xi + xyj + 4xzk. The region e is a cube bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, and z = 2.

To verify the divergence theorem, we need to calculate the flux of the vector field through each face of the cube and sum them up.

Let's go step by step to calculate the flux through each face:

Flux through the x = 0 plane: The unit normal vector of this plane is -i. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is -4x. The integral becomes: integral[0 to 2] integral[0 to 2] -4x dy dz = -16.

Flux through the x = 2 plane: Similar to the previous case, the unit normal vector of this plane is i. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is 4x. The integral becomes: integral[0 to 2] integral[0 to 2] 4x dy dz = 16.

Continue with steps 3-6, calculating the flux through the rest of the faces and summing them up.

Flux through the y = 0 plane: The unit normal vector of this plane is -j. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is -xy. The integral becomes: integral[0 to 2] integral[0 to 2] -xy dx dz = -8.

Flux through the y = 2 plane: Similar to the previous case, the unit normal vector of this plane is j. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is xy. The integral becomes: integral[0 to 2] integral[0 to 2] xy dx dz = 8.

Flux through the z = 0 plane: The unit normal vector of this plane is -k. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is -4xz. The integral becomes: integral[0 to 2] integral[0 to 2] -4xz dx dy = -16.

Flux through the z = 2 plane: Similar to the previous case, the unit normal vector of this plane is k. The flux through this plane is given by the surface integral of f dot dS, where dS is the area element of the plane. Since f(x, y, z) = 4xi + xyj + 4xzk, the dot product is 4xz. The integral becomes: integral[0 to 2] integral[0 to 2] 4xz dx dy = 16.

Finally, to verify the divergence theorem, we sum up the flux through each face:

-16 + 16 + (-8) + 8 + (-16) + 16 = 0

The flux of the vector field f through the region e is 0

The points that satisfy both inequalities are:

B) (0.5, 2)

D) (−2, 4)

To identify which points are solutions to the system of inequalities:

2x + 3y > 6

3x + 2y < 6

We need to check each point to see if it satisfies both inequalities.

2(1.5) + 3(1) = 3 + 3 = 6 - Not a solution

3(1.5) + 2(1) = 4.5 + 2 = 6.5 Not a solution

2(0.5) + 3(2) = 1 + 6 = 7 This a solution

3(0.5) + 2(2) = 1.5 + 4 = 5.5 -  This a solution

2(-1) + 3(2.5) = -2 + 7.5 = 5.5 - Not a solution

3(-1) + 2(2.5) = -3 + 5 = 2 - Not a solution

2(-2) + 3(4) = -4 + 12 = 8 -  This a solution

3(-2) + 2(4) = -6 + 8 = 2-  This a solution

Complete question

Identify any solutions to the system shown here.

2x+3y>6

3x+2y<6

A) (1.5,1)

B) (0.5,2)

C) (−1,2.5)

D) (−2,4)

Final answer:

The equation according to Dolbear's law is T = 0.25x + 40. For 100 chirps, the temperature is 65°F. For a temperature of 96°F, the cricket would make 224 chirps.

Explanation:

According to Dolbear's law, the relationship between the temperature and the number of chirps made by a snowy tree cricket can be used to predict the temperature. We are given that at 50°F, a cricket chirps 40 times in one minute, and for each increase of 0.25°F, there is one additional chirp per minute. To write an equation in slope-intercept form (T = mx + b), where m is the slope and b is the y-intercept, we must find these values. Since we know that 40 chirps correspond to 50°F, we can use this as our starting point (b). Also, because each additional chirp represents a 0.25°F increase in temperature, the slope (m) is 0.25. Therefore, the equation is:

T = 0.25x + 40

If you count 100 chirps in one minute, to find the temperature, simply plug in the value for x in the equation:

T = 0.25(100) + 40

T = 25 + 40

T = 65°

The temperature is 65°F.

If the temperature is 96°F, to find the number of chirps (x), we rearrange the equation to solve for x:

96 = 0.25x + 40

x = (96 - 40) / 0.25

x = 224 chirps

You would expect the cricket to make 224 chirps.

Answer:

16.5 feet is the amount of the length

Answer:

Chiara has 2 penny coins and 24 nickel coins

Step-by-step explanation:

Let

p ----> the number of penny coins

n ---> the number of nickel coins

Remember that

[tex]1\ penny=\$0.01[/tex]

[tex]1\ nickel=\$0.05[/tex]

Chiara has 26 coins that equal 34 cents

so

[tex]p+n=26[/tex]

isolate the variable x

[tex]p=26-n[/tex] ----> equation A

34 cents=$0.34

[tex]0.01p+0.05n=0.34[/tex]

Multiply by 100 both sides

[tex]p+5n=34[/tex]

isolate the variable x

[tex]p=34-5n[/tex] -----> equation B

Create a table  to guess

assume  different values of n and determine the value of p in equation A and equation B

The solution is when the value of p in the equation A must be equal to the value of p in equation B

1) For n=1

equation A

[tex]p=26-1=25[/tex]

equation B

[tex]p=34-5(1)=29[/tex]

[tex]29\neq 25[/tex]

2) For n=2

equation A

[tex]p=26-2=24[/tex]

equation B

[tex]p=34-5(2)=24\\24=24[/tex]

therefore

The solution is (2,24)

Chiara has 2 penny coins and 24 nickel coins

Answer:

Step-by-step explanation:

Sorry I'm late but the other person is wrong this is the answer

Final answer:

To find out what fraction of all shapes are red stars in Lucy's design, multiply the fraction of stars (1/4) by the fraction of red stars among them (8/9) to get 2/9 of all shapes being red stars.

Explanation:

The question asks us to determine what fraction of all the shapes in Lucy's design are red stars. To solve this, we need to multiply the fraction of shapes that are stars by the fraction of those stars that are red. Lucy has stars that make up 1/4 of all shapes, and 8/9 of these stars are red. By multiplying these two fractions, we can find the fraction of all the shapes that are red stars.

Here is the step-by-step calculation:

Multiply the fractions: (1/4) × (8/9) = 8/36.

Simplify the fraction: 8/36 can be simplified by dividing both the numerator and the denominator by the greatest common factor, which is 4. So, (8 ÷ 4)/(36 ÷ 4) = 2/9.

Therefore, 2/9 of all the shapes in Lucy's design are red stars.

To determine the amount of salt in the tank at time t, we need to consider the inflow and outflow of the brine solution over time. The inflow rate is given as 3 gal/min, and the concentration of salt in the inflow varies with time according to the equation cin(t) = 2 + sin(t/4) lb/gal. The outflow rate is also 3 gal/min.

To determine the amount of salt in the tank at time t, we need to consider the inflow and outflow of the brine solution over time. The inflow rate is given as 3 gal/min, and the concentration of salt in the inflow varies with time according to the equation cin(t) = 2 + sin(t/4) lb/gal. The outflow rate is also 3 gal/min.

To find the amount of salt in the tank at time t, we need to integrate the product of the inflow rate and the concentration of salt over the interval [0, t]. This will give us the total amount of salt that has entered the tank up to time t. We can then subtract the amount of salt that has been pumped out of the tank over the same interval to get the amount of salt remaining in the tank at time t.

a(t) = ∫[0,t] (3 gal/min * cin(t)) dt - 3 gal/min * t.

To determine the amount of hardener needed for 14 containers of resin, multiply the amount of hardener needed for one container (55mL) by the number of containers (14), resulting in 770mL of hardener.

To determine the amount of hardener needed for 14 containers of resin, we can use the given formula of adding 55mL of hardener to each container. We can multiply the amount of hardener needed for one container (55mL) by the number of containers (14).

Calculation:

Therefore, 770mL of hardener should be added to 14 containers of resin.

To calculate the total amount of hardener needed for 14 containers of resin, multiply the 55 mL required per container by 14, resulting in 770 mL of hardener needed.

You are asked to determine how much hardener should be added to 14 containers of resin if it is known that 55 mL of hardener is required for each container. To find the total amount of hardener needed for 14 containers, you would use multiplication:

Total hardener needed = Hardener per container × Number of containers

So, Total hardener needed = 55 mL/container × 14 containers

Now by multiplying 55 by 14, we get:

Total hardener needed = 770 mL

Therefore, 770 mL of hardener is needed for 14 containers of resin.

The average value of v(x) for the interval 1≤x≤8 is calculated by summing up the products of the average values each times their respective lengths of interval, and dividing by the total length of the interval, which results in 4.2857 approximately.

The average value of v(x) for 1≤x≤8 can be calculated using the formula for the average of a function over an interval, which is the sum of the function values times their respective lengths of interval, divided by the total length of the interval. For the first interval, 1≤x≤6, the average value of y is 4, and the length of the interval is 6-1=5. Hence, the sum of the product of the average value times the length of the interval is 4*5=20.

For the second interval, 6≤x≤8, the average value of y is 5, and the length of the interval is 8-6=2. Hence, the sum of the product of the average value times the length of the interval is 5*2=10.

Summing up these two products, we get 20+10=30. The total length of the overall interval 1≤x≤8 is 8-1=7. Hence, the average value of v(x) for 1≤x≤8 is 30/7=4.2857, approximately.

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Answer:

284.4

Step-by-step explanation:

Given is a picture of a circle as earth and radius = 3959 mi.

THe horizon is the tangent with length unknown x

The hypotenuse of the right triangle is 3959+10.2 = 3969.2 mi.

Hence we get

x using Pythagorean theorem

[tex]x^2+3959^2=3969.2^2\\x^2= 10.2(7928.2)\\x=284.37[/tex]

Round off to nearest 10th

Since ii digit after decimal is 7 >5 we add 1 to the digit after decimal

Answer is 284.4

Tea reaches half concentration after 5 hours; at 4 hours, it's a quarter.

To solve this problem, we can use the fact that the cable between the towers forms a parabolic shape. Since the cable touches the sides of the road midway between the towers, the cable forms a parabola with its vertex at the midpoint between the towers and its axis of symmetry being parallel to the road.

Let's denote the midpoint between the towers as the origin  (0, 0). Then, the vertex of the parabola is at (640, 160) since the towers are 1280 meters apart and rise 160 meters above the road.

The general equation of a parabola in vertex form is:

[tex]\[ y = a(x - h)^2 + k \][/tex]

Where:

-  (h, k)  is the vertex of the parabola.

- ( a ) determines the "width" of the parabola.

Since the parabola is symmetric, we know that it opens either upwards or downwards. Given the geometry of the situation (the cable hanging between the towers), we know it opens downwards. Therefore, ( a ) will be negative.

To find the equation of the parabola, we need to find the value of ( a ). We can use the point  (640, 0). which is the midpoint between the towers.

Let's plug in the values:

[tex]\[ 0 = a(640 - 640)^2 + 160 \]\[ 0 = 160a \][/tex]

From this, we find that ( a = 0 ).

This indicates that the parabola is a horizontal line, which is not the shape of a cable between the towers. We made an error. The equation of a parabola is  [tex]\( y = a(x - h)^2 + k \),[/tex] but for this problem, we should use the equation of a downward-opening parabola, which is [tex]\( y = ax^2 + bx + c \).[/tex]

Let's correct the approach and use the new equation to solve the problem. We'll find the coefficients  [tex]\( a \), \( b \), and \( c \)[/tex]  using the given information. Once we have the equation of the parabola, we can find the height of the cable at a distance of 200 meters from a tower. Let's do it step by step.

Complete the chart:

Dimension What Can Be Measured Example Object

Zero Nothing Point

One Length Line

Two Length, Width Polygon

Three Length, Width, Height Solid

Zero Dimensions:

What Can Be Measured: Nothing. Zero dimensions imply a mathematical point without any length, width, or height.

Example Object: Point. A point in geometry is a location represented by a dot and has no size or dimensions.

One Dimension:

What Can Be Measured: Length. In one dimension, objects have only length and can be measured in a straight line.

Example Object: Line. A line is a straight path that extends infinitely in both directions. It is characterized by its length.

Two Dimensions:

What Can Be Measured: Length, Width. Two-dimensional objects have both length and width. They are flat and can be measured in both directions.

Example Object: Polygon (e.g., Square). A polygon is a closed two-dimensional shape with straight sides, and a square is an example with equal length and width.

Three Dimensions:

What Can Be Measured: Length, Width, Height. Three-dimensional objects have length, width, and height. They are solids and occupy space.

Example Object: Solid (e.g., Cube). A cube is a three-dimensional shape with equal length, width, and height. It represents a solid object.

For such more question on Dimensions

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