Cylinder A has a volume of 6 cubic units, and a height of 3 units. Cylinder B has the same base area and height,
but its slant height is 4 units. What is the volume of cylinder B?

The equation of a circle is used to calculate the radius and the center of the circle.

The equation of the circle is: \(\mathbf{(x + 4)\² + (y - 4)\² = 4\²}\)

The given parameters are:

\(\mathbf{y = 8 - x}\) --- center

Tangent to both axes

The equation of a circle is:

\(\mathbf{(x - h)\² + (y - k)\² = r\²}\)

where (h, k) is the center and

r is the radius.

If a circle is tangent to both axes, then

\(\mathbf{|h| = |k| = r}\)

Where h and k have different signs

i.e.

\(\mathbf{h = -k}\)

This means that:

\(\mathbf{y = 8 - x}\)

\(\mathbf{k = 8 -k}\)

\(\mathbf{k +k= 8}\)

\(\mathbf{2k= 8}\)

Divide both sides by 2

\(\mathbf{k= 4}\)

Recall that:

\(\mathbf{h = -k}\)

This means:

\(\mathbf{h = -4}\)

Recall that:

\(\mathbf{|h| = |k| = r}\)

This means that:

\(\mathbf{r = 4}\)

Recall that:

\(\mathbf{(x - h)\² + (y - k)\² = r\²}\)

Substitute values for h, k and r

\(\mathbf{(x + 4)\² + (y - 4)\² = 4\²}\)

Hence, the equation of the circle is:

\(\mathbf{(x + 4)\² + (y - 4)\² = 4\²}\)

See attachment for the graph of the circle

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Answer:

So we have this equation:

2   (3x-2) - 4x = 5x + 2

You can first operate the parenthesis, knowing that a(b+c) = ab + ac (conmutative)

2(3x-2) - 4x = 5x + 2

2 * 3x - 2 * 2 - 4x = 5x + 2

6x - 4 -4x = 5x + 2

Now, we can operate the x:

6x - 4 -4x = 5x + 2

2x - 4 = 5x + 2

And sum 4 in both sides and substract 5x in both too.

2x - 4 = 5x +2

2x - 4 + 4 - 5x' = 5x + 2 + 4 -5x

Now we can operate:

-3x = 6

And we can divide by -3 the two sides...

x = 6/-3 = -2

Answer:

both statements are true

Answer:

82in

Step-by-step explanation:

brainliest?

The formula for g(x) in terms of h(x) is: g(x) =  h(x - 5) -1

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The turning point (stationary point) of the curve.

the minimum point of a parabola that opens upwards

the maximum point of a parabola that opens downwards

To find the series of translations that transform the graph of y = h(x) onto y = g(x), compare the vertices of both graphs.

Vertex of h(x) = (-5, 7)

Vertex of g(x) = (0,6)

Find the difference of coordinates, the rule of translation right and up

x = 0 - (-5) = 5

y = 6- (7) = -1

h(x) translated 7 units right = h(x - 5)

h(x - 7) translated 5 units up = h(x - 5) -1

Therefore, the formula for g(x) in terms of h(x) is: g(x) =  h(x - 5) -1

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Answer:(7x + 2)(x + 4)

Step-by-step explanation:

Answer:

Heeeheeeeheee

Step-by-step explanation:

So right

Answer: about 17.7%

Step-by-step explanation:

The area of a trapezoid is ((b1+b2)/2)*h

Thus, the area of the trapezoid is 85 meters squared.  Thus, because the garden is 480 meters squared, the trapezoid occupies 85/480 of the garden, or about 17.7 percent.

Hope it helps <3

Answer:

17.7% rounded to the nearest tenth

Step-by-step explanation:

Well to find the percent of space the trapezoid takes up we need to find both areas.

To find the area of a Rectangle we do l*w.

So the l is 30 and the w is 16 so,

30*15 = 480m^2

To find the area of a Trapezoid \(\frac{b1 + b2}{2}h\).

So b1 is 20 and b2 is 14,

14 + 20 = 34

34/2 = 17

17 * h

17 * (5) = 85m^2

So now we make a fraction of the areas of the trapezoid and rectangle,

\(\frac{85}{480}\)

Now we simplify,

85/5 = 17

480/5 = 96

So 17/96 is in its simplest form so now we do 17/96 which is 0.1770833333

So to the following into a percent we move the decimal places 2 places to the right which is about 17.7% rounded to the nearest tenth.

Answer: The population would be the data of temperatures of all food served by the restaurant.

Step-by-step explanation:

In a statistical study, the term population refers to the largest group of all individuals related to the study or the objective of the study.

Here, the objective of the study= To check the temperatures of food just before serving.

Population = Data of temperatures of all dishes served by restaurant.

Hence, the population would be the data of temperatures of all dishes served by the restaurant.

Answer:

(a) = 10

(b) = 147

Step-by-step explanation:

Simple multiplication and division, if 9 stocks dropped 90$ of worth, every stock would have dropped 10$ in relation to that.

Yes, the equation C-1(A+X)B-1=In has a solution, X. To find the solution, first use C-1(A+X)B-1=In to simplify to C-1 AB-1=In+X. Next, use matrix multiplication to expand C-1AB-1 to In+X = AC-1B-1-B-1C-1. Subtract In from both sides of the equation to get X=AC-1B-1-B-1C-1-In. This is the solution for X, where A, B, and C are nan invertible matrices.

Given that A, B, and C are invertible nan matrices, we have to check if the equation C-1(A+X)B-1=In has a solution or not, and if there is a solution, we have to find X.

Let's solve it. Let's multiply both sides of the equation by B and C, respectively, we get C-1(A+X)B-1B = IB and C-1(A+X) = B. Now, we have to multiply both sides by C on the left, so we get C*C-1(A+X) = CB, which becomes A+X = CB.

Now we have to multiply both sides by B-1 on the right, so we get A + XBB-1 = CBB-1, which becomes A + XB-1 = CB-1.Now, we have to multiply both sides by C-1 on the left, so we get C-1A + C-1XB-1 = I.

Now, we have to multiply both sides by B and C, respectively, which results in C-1AC-1B + XC-1B = B. Finally, X = B(C-1AC-1B)B-1 - C-1B + I. We know that if A and B are matrices of the same order, then (AB)-1 = B-1A-1. By using this property, we can write the solution as X = B-1(A-1 + C-1)-1B-1 - C-1B + I. So, the solution exists for the given equation.

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Answer:

21

Step-by-step explanation:

\(\tt{Hey~there!\)

\(\tt{5\frac{7}{10}\times\frac{-5}{9}\)

\(\tt{Multiply:\)

\(\tt{5\frac{7}{10}\times\frac{-5}{9}=\frac{-19}{6}\)

\(\tt{Now~simplify~-19/6:\)

\(\tt{\frac{-19}{6} =-3\frac{1}{6}\)

\(\boxed{\tt{-3\frac{1}{6}}}\)

\(\tt{Hope~this~helps!\)

\(\boxed{\tt{-TestedHyperr}}\)

Answer:

57/18 or 3 1/6

Step-by-step explanation:

Step 1:

5 7/10 × - 5/9       Equation

Step 2:

57/10 × - 5/9    Change to Improper Fraction

Answer:

57/18 or 3 1/6

Hope This Helps :)

Answer:

B on edge

Step-by-step explanation:

The arrow is counterclockwise so its positive. The person above had the right idea but on edge is B.

Also I took the test and got 100% have a great day :D

Answer:

The answer is B

Explanation:

The arrow is counterclockwise so its positive.

Answer:

\( - 50 + 8i\)

Step-by-step explanation:

\(1. \: - 35 - 15i + 21i - 9 - (6 - 2i) \\ 2. \: - 35 - 15i + 21i - 9 - 6 + 2i \\ 3. \: ( - 35 - 9 - 6) + ( - 15i + 21i + 2i) \\ 4. \: - 50 + 8i\)

Answer: The pack of 20.

Step-by-step explanation:

It is because a pack of 20 sells for 2.50 for each pencil, and the pack of 12 sells for 2.51 per pencil, so that means the pack of 20 is cheaper.

The system formed by linear equations - 8 · x + 8 · y = 1 and - 32 · x + 32 · y = - 5 has no solution.

In this problem we find a system formed by two linear equations with two variables. There are three kinds of systems of linear equations:

First, write the system of linear equations:

- 8 · x + 8 · y = 1

- 32 · x + 32 · y = - 5

Second, multiply the first equation by 4:

- 32 · x + 32 · y = 4

Third, use transitive property:

4 = - 5 (CRASH!)

The system of linear equations has no solution.

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Answer:

How do you do 4+1346=? AnswerL 1350

600x787 and 675dividedby700= 472200  :D

Step-by-step explanation:

Answer:

4+1346=1350 ... 600x787=472200

675÷700=0.96

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

140%

Step-by-step explanation:

(24-10) / 10 = 14/10 = 140%

Answer:

140%

Step-by-step explanation:

A change from 10 to 24 represents a positive change (increase) to 140%.

Percent change = New-Old/Old x 100%

Percent change = 24-10/10 x 100% =

14/10 x 100 = 140% (increase)

Where 10 is the old value and 24 is the new value. In this case, we have a positive change (increase) of 140 percent because the new value is greater than the old value.

The dimensions of the framed picture would be "x + 2" centimeters for the width and "x + 8" centimeters for the length, where "x" represents the width of the original rectangular picture.

To determine the dimensions of the framed picture, we can use the information. Let's assume the width of the picture is "x" centimeters.

Since the rectangular picture is 6 centimeters longer than it is wide, the length of the picture would be "x + 6" centimeters.

When a frame 1 centimeter wide is placed around the picture, it adds 1 centimeter to each side of the picture.

Therefore, the width of the framed picture would be "x + 2" centimeters (2 additional centimeters for the frame on both sides) and the length would be "x + 6 + 2" centimeters (2 additional centimeters for the frame on both sides).

In simplified form, the dimensions of the framed picture would be width: "x + 2" centimeters and length: "x + 8" centimeters.

The complete question is "'A rectangular picture is 6 cm longer than it is wide. A frame 1 cm wide is placed around the picture. Write a polynomial that represents the area of the frame?"

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Answer:

Terry 108

300

Step-by-step explanation:

7a² - 4 if a = 4

7(4)² - 4

7(16) - 4

112 - 4

108

Terry 108

----------------------------

72/120 * 500

300

Answer:

$118

Step-by-step explanation:

If there are 59 students going on the field trip, and the cost is $2 per student, then the total cost for all the students to go on the field trip would be:

Total cost = Number of students × Cost per student

Total cost = 59 × $2

Total cost = $118

It would cost $118 in total for all 59 students to go on the field trip, assuming there are no taxes or additional fees involved.

The experimental Probability of stopping on a multiple of 3 is approximately 0.6667 or 66.67%.

The experimental probability of stopping on a multiple of 3 can be calculated by dividing the number of times the spinner stopped on a multiple of 3 by the total number of spins.

In this case, the spinner was spun 30 times and it stopped on a multiple of 3 twenty times.

Therefore, the experimental probability of stopping on a multiple of 3 is calculated as:

Experimental Probability = (Number of times spinner stopped on a multiple of 3) / (Total number of spins)

                      = 20 / 30

                      = 2/3

                      = 0.6667

So, the experimental probability of stopping on a multiple of 3 is approximately 0.6667 or 66.67%.

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Step-by-step explanation:

To find the vector parametric equation for the parabola from the origin to a point P, we need to express the position vector of P as a function of a parameter. Let's assume the coordinates of P are (x, y).

(a) Vector Parametric Equation for the Parabola: We can represent the position vector of P as a linear combination of two vectors. The first vector will point from the origin to P, and the second vector will be perpendicular to it.

Let's consider the vector from the origin to P as OP. Since P lies on the parabola, the magnitude of OP is given by the equation y = x^2. Therefore, the magnitude of OP is √(x^2 + (x^2)^2) = √(x^2 + x^4).

The unit vector in the direction of OP can be found by dividing OP by its magnitude: u = OP / √(x^2 + x^4).

To find a perpendicular vector, we can take the cross product of u with the vector (0, 0, 1) (which is perpendicular to the xy-plane). This will give us a vector perpendicular to the plane containing the parabola.

Let's call the perpendicular vector v. The cross product of u and (0, 0, 1) is given by: v = u × (0, 0, 1).

Finally, the vector parametric equation for the parabola from the origin to P is given by: r(t) = tu + tv, where t is the parameter ranging from 0 to 1.

(b) Line Integral along the Parabola: To find the line integral of a vector field F along the parabola from the origin to P, we need to evaluate the line integral: ∫(F · dr) from 0 to 1, where F is the vector field, dr is the differential vector along the parabola, and the integral is taken with respect to t.

The line integral can be calculated as follows: ∫(F · dr) = ∫(F · (du/dt) dt), where du/dt is the derivative of the unit vector u with respect to t.

Substituting r(t) = tu + tv into the above expression, we can find the line integral.

Please provide the vector field F so that I can assist you further in evaluating the line integral.

Answer:

4200 m²

Step-by-step explanation:

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the track. Shaded part

Solution:

The big semicircle has a diameter = 60 m + 10 m + 10 m = 80 m

The radius of the big semicircle = 80 m / 2 = 40 m

The area of the two big semicircles at both end of the big track = 2 * (1/2 πr²) = πr² = π(40)² = 5027 m²

The big track has semicircles at both ends and a rectangle. The length of the rectangle = 100 m, the width of the rectangle = diameter of big semicircle = 80 m

Area of big rectangle = length * width = 100 m * 80 m = 8000 m²

Area of big track = 8000 m² + 5027 m² = 13027 m²

The small semicircle has a diameter = 60 m

The radius of the small semicircle = 60 m / 2 = 30 m

The area of the two small semicircles at both end of the small track = 2 * (1/2 πr²) = πr² = π(30)² = 2827 m²

The small track has semicircles at both ends and a rectangle. The length of the rectangle = 100 m, the width of the rectangle = diameter of small semicircle = 60 m

Area of small rectangle = length * width = 100 m * 60 m = 6000 m²

Area of small track = 6000 m² + 2827 m² = 8827 m²

The area of track (shaded part) = Area of big track - Area of small track = 13027 m² - 8827 m² = 4200 m²

The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

Option 1 is true.

What is Quadratic equation?

An algebraic equation of the second degree in x is called Quadratic equation.

Given that;

The values of x and y are,

x = -1, 0, 3

y = -3, -3, 33

Let a quadratic function is,

y = ax² + bx + c     ... (i)

Then, It satisfy all the values given in table.

So, Substitute point (x, y) = (-1, -3) in equation (i) we get;

- 3 = a - b + c  ... (ii)

And, Substitute point (x, y) = (0, -3) in equation (i) we get;

-3 = c  .. (iii)

And, Substitute point (x, y) = (3, 33) in equation (i) we get;

33 = 9a + 3b + c ... (iv)

Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;

From (ii);

- 3 = a - b - 3

a - b = 0      ... (v)

From (iv);

33 = 9a + 3b - 3

Divide by 3;

11 = 3a + b - 1

3a + b = 12   .... (vi)

Solve equations (v) nd (vi) we get;

a = 3 and b = 3

Thus, Substitute the values a = 3, b = 3 and c = -3 in quadratic equation we get;

y = ax² + bx + c

y = 3x² + 3x - 3

So, The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

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