The formula for the volume of a cylinder is V = arh.
Solve v = 12h for h, the height of the cylinder.

The calculated equation of the graph is f(x) = 3(x - 2)(x - 1)(x + 2)²

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a polynomial graph with the following zeros and multiplicities

The equation is then represented as

y = a(x - zero) to the exponent of the multiplicities

So, we have

y = a(x - 2)(x - 1)(x + 2)²

Using the y-intercept, we have

a(0 - 2)(0 - 1)(0 + 2)² = 24

This gives

a = 3

So, we have

y = 3(x - 2)(x - 1)(x + 2)²

Hence, the equation of the graph is y = 3(x - 2)(x - 1)(x + 2)²

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Answer: is not / is one x-value

Step-by-step explanation:

The relation is not a function because there is one x-value corresponding to multiple y-values.

For a function, each point on the domain is mapped into only one point on the range.

In this relation we can see the points:

(1, 4), (3, -1), (-1, -2), and (1, -3).

Then we can see that the element of the domain "1" is being mapped into two different elements of the range (4, and -3).

Then the relation is not a function because there is one x-value corresponding to multiple y-values.

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The factors of the given expression are (a-b)(m+1).

A factor is one of two or more expressions multiplied together.

Given that, an expression, a(m+1) + b(-m-1), we need to find the factors of the expression,

a(m+1) + b(-m-1)

Opening the brackets and using distributive property,

am+a-bm-b

Rearranging according to terms,

a-b+am-bm

= a-b+m(a-b)

= (a-b)(m+1)

Hence, the factors of the given expression are (a-b)(m+1).

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The equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

What is Equation in Spherical Coordinates?

A mathematical equation that is represented in terms of the spherical coordinates of a point is known as an equation in spherical coordinates. A three-dimensional coordinate system known as spherical coordinates makes use of two angles, typically represented by symbols and a radial distance (r), and a coordinate system to find points in space.

\($r^2 = 81$\)

To represent the equation in spherical coordinates, we substitute the Cartesian coordinates \($x = r\sin(\phi)\cos(\theta)$, $y = r\sin(\phi)\sin(\theta)$, and $z = r\cos(\phi)$\) into the equation. After substitution and simplification, we have:

\($r^2\sin^2(\phi)\cos^2(\theta) + r^2\sin^2(\phi)\sin^2(\theta) + r^2\cos^2(\phi) = 81$\)

Since \(r^2 = 81,\) we can substitute it into the equation:

\($81\sin^2(\phi)\cos^2(\theta) + 81\sin^2(\phi)\sin^2(\theta) + 81\cos^2(\phi) = 81$\)

Finally, we divide the equation by 81 to simplify:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

So, the equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

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Answer:

x = -7

Step-by-step explanation:

f(x) = -3x + 2

= -3(3) + 2

= -9 + 2

= -7

Answer:

-30c

Step-by-step explanation:

now:-25

noon - 10pm +10 (got 10c hotter)

-25c-10=-35c(opposite of rise)

midnight - noon: -5c

so do the opposite which is +5

-35+5=-30c

Answer:

Y

Step-by-step explanation:

Look at Y and look at the input and output it shows which one is it and how to find it you welcome :)

Answer:

Step-by-step explanation:

Let's call one leg of the triangle "x" and the other leg "2x-4". We can use the Pythagorean theorem to solve for the lengths of the legs:

x^2 + (2x-4)^2 = 10^2

x^2 + 4x^2 - 16x + 16 = 100

5x^2 - 16x - 84 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring gives us:

(5x + 14)(x - 6) = 0

So x = -14/5 or x = 6. We can discard the negative solution since we're dealing with lengths. Therefore:

x = 6

2x - 4 = 8

The lengths of the legs are 6 feet and 8 feet.

Step-by-step explanation:

She has 1050

400 of that is the DB fee

Now she has 650 dollars

650/50 per person is 13

She can have 13 people

Answer:

B. no, the relation is not a function

Step-by-step explanation:

The truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

The statement q(x) is x² = 2x. Now, we will check the truth value of each statement in terms of q(x):

(i) q(0): \(0^2=2\times 0\)

   q(0): 0 = 0; so, the statement q(0) is true.

(ii) q(1): \(1^2=2\times 1\)

    q(1): 1 = 2; so, the statement q(1) is false.

(iii) q(-2): \((-2)^2=2\times (-2)\)

     q(-2): 4 = -4; so, the statement q(-2) is false.

(iv) q(2): \(2^2=2\times 2\)

     q(2): 4 = 4; so, the statement q(2) is true.

So, the truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

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Answer:

4.62 sq ft

Step-by-step explanation:

Area of rectangle = 2.5 x 1 = 2.5

To get area of triangle we must use the altitude theorem to find the height:

let 'x' = altitude (or height)

x/1.5 = 2/x

cross-multiply to get:

x² = 3

x = \(\sqrt{3}\)

Area of triangle = 1/2(2.5)(\(\sqrt{3}\))

= 1.25\(\sqrt{3}\) which is approx 2.12

Total area = 2.5 + 2.12 = 4.62

The answer is C. 1/10 of a centimeter.

Answer:

C. x=18

Step-by-step explanation:

note that PQ is the diameter of circle O. this means that angle QRP is a 90 degree angle. now we have 5x=90 so x=18

Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

Let's define the variables:

We know that we want to make 200ml, then:

x  + y = 200

And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:

x*0.5 + y*0.8 = 200*0.68

(the concentrations are written in decimal form)

Then we have the system of equations:

x  + y = 200

x*0.5 + y*0.8 = 200*0.68

To solve it we start by isolating x in the first equation:

x = 200 - y

Replacing that in the other equation we get:

(200 - y)*0.5 + y*0.8 = 200*0.68

Now we can solve this for y, we will get:

100 - y*0.5 + y*0.8 = 136

y*0.3 = 136 - 100 = 36

y = 36/0.3 = 120

So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

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The mass of the porcelain table top is approximately 4,608 grams. To calculate the mass of the porcelain table top, we need to find its volume and then multiply it by the density of porcelain.

The table top is in the shape of a rectangular prism with dimensions given as length = 12 inches, width = 12 inches, and height = 1.5 inches.

The volume of a rectangular prism is given by the formula: volume = length × width × height. Substituting the given values, we have volume = 12 inches × 12 inches × 1.5 inches.

To convert the volume from cubic inches to cubic centimeters, we use the conversion factor: 1 cubic inch = 16.3871 cubic centimeters.

So, the volume of the table top in cubic centimeters is calculated as follows:

volume = 12 inches × 12 inches × 1.5 inches × 16.3871 cubic centimeters/cubic inch.

Next, we multiply the volume by the density of porcelain, which is given as 2.4 grams per cubic centimeter.

mass = volume × density = (12 inches × 12 inches × 1.5 inches × 16.3871 cubic centimeters/cubic inch) × 2.4 grams/cubic centimeter.

Calculating this expression gives the mass of the table top as approximately 4,608 grams when rounded to the nearest gram.

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Hi!! I'd love to help!!

The slope of your points is 2.

When we use the slope intercept formula (y=mx+b), we get y=2x-2.

So the answer to your question is C

Hope this helps!! Let me know if you need any more help or have questions/concerns.

Step-by-step explanation:

The question implies the two angles are equal because of the positioning of the named vertices. m∠A = m∠E so to say.

You can substitute the values and solve the inequality to find x, then solve for m∠A.

m∠A = m∠E; Given (Inferred)

6x - 8 = 4x + 1; Substitution

6x = 4x + 9; Addition Property of Equality

2x = 9; Subtraction Property of Equality

x = 4.5; Division Property of Equality

m∠A = 6x - 8; Given

m∠A = 6(4.5) - 8; Substitution

m∠A = 19; Solve

Hope this helps!!

To solve this problem, we need to use some trigonometry. We can use the tangent function to find the length of the magma below sea level.

Let's define the following variables:

• x: the length of magma below sea level (what we want to find)

• y: the total length of magma (which we don't know)

• θ: the angle of elevation, which is 40°

We can set up a right triangle with the hypotenuse representing the total length of magma (y), the opposite side representing the length of magma below sea level (x), and the adjacent side representing the distance from the volcano to the point where the magma rises above sea level (which we don't need to calculate).

Using the tangent function, we can write:

tan(θ) = x / y

Rearranging this equation, we get:

x = y * tan(θ)

Now we just need to plug in the values we know:

• θ = 40°

• y = 15 kilometers (since the magma reservoir is located 15 kilometers beneath the Chijiwa Bay)

Using a calculator, we can evaluate tan(40°) to be approximately 0.8391.

Plugging in these values, we get:

X = 15km*0.8391, X = 12.5865km

Therefore, the length of magma below sea level is approximately 12.5865 kilometers



Answer:

A. 45 + 42p

Step-by-step explanation:

Answer:

Most ancient societies had symbols to represent numbers, but they did not have symbols to represent operations or unknown quantities. Thus, the problems and solutions to the problems had to be written in word form.

Step-by-step explanation:

Sample response :)

Answer:

Most ancient societies had symbols to represent numbers, but they did not have symbols to represent operations or unknown quantities. Thus, the problems and solutions to the problems had to be written in word form.

Step-by-step explanation:

Answer:

here it is on a graph

Step-by-step explanation:

Answer:

I attached a png with my answer.

Step-by-step explanation:

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

b= 50

Step-by-step explanation:

the entire angle equals 80 degrees and a portion of it equals 30. therefore the portion that equals b = 50 because 30+50=80 hope this helps.

Answer:

True

Step-by-step explanation:

Yes, A proportional relationship is linear.

Answer: 38 3/4 or 38.75

Step-by-step explanation:

multiply 3 1/2 * 5 = 17 1/2

multiply 4 1/4 * 5 = 21 1/4

add the 2

=38 3/4

The length of the curve y = sin(3x)

from x = 0

to x = π/6 is given by

\(\frac{1}{3}(\sqrt {10} + 3\ln (2 + \sqrt 3 ))\)

The length of the curve y = sin(3x)

from x = 0

to x = π/6 is given by:

 \($\int\limits_0^{\pi/6} {\sqrt {1 + {({y^{'}})^2}} dx}$\)
Given, the curve is y = sin(3x)
We have to find the length of the curve from x = 0

to x = π/6 using the formula

\($\int\limits_0^{\pi/6} {\sqrt {1 + {({y^{'}})^2}} dx}$\)
We know that the derivative of y with respect to x is y',

so y' = 3cos(3x)
Using the formula we get,

\($\int\limits_0^{\pi/6} {\sqrt {1 + {({y^{'}})^2}} dx}\)

=\(\int\limits_0^{\pi/6} {\sqrt {1 + 9{{\cos }^2}3x} dx} $\)
Now, substitute u = 3x,

then \($\frac{du}{dx} = 3$\)

and \($dx = \frac{1}{3}du$\)
Hence, the integral becomes

\($\int\limits_0^{\pi/6} {\sqrt {1 + 9{{\cos }^2}3x} dx}\)

= \(\frac{1}{3}\int\limits_0^{\pi/2} {\sqrt {1 + 9{{\cos }^2}u} du}\)

Let's substitute \($t = \tan u$\),

then dt =\({\sec ^2}udu$ and $\sec^2 u\)

=1 + \tan^2 u

=\(1 + {t^2}$\)

Also, when $u = 0,

t =\(\tan 0\)

= 0

and when \($u = \frac{\pi}{6},\)

t =\(\tan \frac{\pi}{6}\)

= \(\frac{\sqrt 3 }{3}$\)
Hence, the integral becomes

\($\frac{1}{3}\int\limits_0^{\pi/2} {\sqrt {1 + 9{{\cos }^2}u} du}\)

=\(\frac{1}{3}\int\limits_0^{\sqrt 3 /3} {\sqrt {1 + {{\sec }^2}{\tan ^{ - 1}}t} dt} \\\)

=\(\frac{1}{3}\int\limits_0^{\sqrt 3 /3} {\sqrt {1 + {{(1 + {t^2})}^2}} dt} \frac{1}{3}\int\limits_0^{\sqrt 3 /3} {\sqrt {1 + {{(1 + {t^2})}^2}} dt}\)

On simplifying and solving the integral, we get the length of the curve from x = 0

to x = π/6 is given by

\(L = \frac{1}{3}(\sqrt {10} + 3\ln (2 + \sqrt 3 ))\)

Therefore, the length of the curve y = sin(3x) from x = 0 to x = π/6 is given by \($\frac{1}{3}(\sqrt {10} + 3\ln (2 + \sqrt 3 ))$\)

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