A conical container can hold 120 pie cubic centimeters of water the diameter of the base of the container is 12 centimeters the height of the containers centimeters. If the diameter and height were both doubled the containers capacity would be times its original capacity

Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

[tex] \frac{1}{ log(y) } = x[/tex]

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

The  system of equation: -x + 7 = -2x³ + 5x² + x - 2 has three solutions

The correct answer is option D.

To solve the system of equations:

-x + 7 = -2x³ + 5x² + x - 2

We need to simplify and rearrange the equation to find its solutions. Let's start by combining like terms:

-x + 7 = -2x³ + 5x² + x - 2

Simplifying the left side:

7 = -2x³ + 5x² - x - 2

Next, let's arrange the equation in descending order of the variable's exponent:

-2x³ + 5x² - x - 2 = 7

Now, let's move all terms to one side of the equation to set it equal to zero:

-2x³ + 5x² - x - 2 - 7 = 0

Simplifying further:

-2x³ + 5x² - x - 9 = 0

To determine the number of solutions, we can analyze the degree of the equation. Since it is a cubic equation, it can have a maximum of three real solutions.

The given system of equations is:

-x + 7 = -2x³ + 5x² + x - 2

To find the solutions, we need to set the equation equal to zero. Let's rearrange the terms:

2. -2x³ + 5x² - x - 9 = 0

Now, we can try to factor or use numerical methods to solve the equation. However, factoring a cubic equation can be complex and time-consuming. In this case, we'll use numerical methods to approximate the solutions.

One common numerical method is the Newton-Raphson method, which involves making an initial guess for the solutions and iterating to converge on a more accurate solution.

Using numerical software or calculators, we can find the approximate solutions of the equation as follows:

x ≈ -1.607, x ≈ 1.279, and x ≈ 3.328

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Answer:

D

Step-by-step explanation:

to find the coterminal angles add/ subtract 360° to the given angle

- 255° + 360° = 105°

- 255° - 360° = - 615°

The solution to the system is (a) (4/5, 5, -4, -4)

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

The augmented matrix

Where, we have

[tex]\left[\begin{array}{cccc|c}1&0&0&0&4/5\\0&1&0&0&5\\0&0&1&0&-4\\0&0&0&1&-4\end{array}\right][/tex]

From the above, we have the diagonals to be 1

And other elements to be 0

This means that the equation has been solved

So, we have

a = 4/5, b = 5, c = -4 and d =-4

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Both Roger and Jeff will have run a distance of 1/3 mile when Jeff catches up to Roger after 2 minutes.

To solve this problem, we can determine the relative speeds of Roger and Jeff.

Since Roger runs one mile in 9 minutes, his speed is 1/9 miles per minute.

Similarly, Jeff runs one mile in 6 minutes, so his speed is 1/6 miles per minutes.

Let's assume that Jeff catches up to Roger after t minutes.

In that time, Roger would have run (1/9) [tex]\times[/tex] t miles, and Jeff would have run (1/6) [tex]\times[/tex] t miles.

Since Jeff gives Roger a 1-minute head start, we can express their distances covered as:

Distance covered by Roger = (1/9) [tex]\times[/tex] (t+1) miles

Distance covered by Jeff = (1/6) [tex]\times[/tex] t miles

For Jeff to catch up to Roger, their distances covered must be equal. So we can set up the equation:

(1/9) [tex]\times[/tex] (t+1) = (1/6) [tex]\times[/tex] t

To solve for t, we can cross-multiply and simplify:

6(t+1) = 9t

6t + 6 = 9t

6 = 9t - 6t

6 = 3t

t = 2

Therefore, it will take 2 minutes for Jeff to catch up to Roger.

Substituting t = 2 back into the equations, we can find the distances covered by each:

Distance covered by Roger = (1/9) [tex]\times[/tex] (2+1) = 1/3 mile

Distance covered by Jeff = (1/6) [tex]\times[/tex] 2 = 1/3 mile

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The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.

Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.

The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.

Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.

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The values of x and y are 9√3 and 9. Thus, option C is the answer.

From the figure, we know that angle A = 60°, angle C = 30° and side AC =18 units.

We have to use trigonometric ratios to find the values of x and y.

sin30° = Opposite side/Hypotenuse  

But, we also know that sin30° = 1/2

Substituting the value in the above equation, we get

1/2 = y/18

Thus, the value of y = 18/2 = 9.

Now, sin60° = Opposite Side/ Hypotenuse

sin60° = √3/2

Substituting the value, we get

√3/2 = x/18

Thus, x = 9√3.

Therefore, the values of x and y in the given triangle are 9√3 and 9.

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The answer is:

3x + 12

Work/explanation:

To simplify this expression, we will use the distributive property:

[tex]\sf{3(x+4)}[/tex]

Distribute the 3:

[tex]\sf{3\cdot x + 3 \cdot 4}[/tex]

[tex]\sf{3x+12}[/tex]

Answer:

(x + 5)² + (y – 1)² = 25

Step-by-step explanation:

Note that the general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.

The circle is 10 units in diamater, so the radius is half this: r=10/2=5.

The circle goes from -10 to 0 along the x-axis, so the x-coordinate of its centre is halfway between this: h=(-10+0)/2=-10/2=-5

The circle goes from -4 to 6 along the y-axis, so the y-coordinate of its centre is halfway between this: k=(-4+6)/2=-2/2=1

Now that we know r, h, and k, we can sub these into the general formula to get our equation:

(x - (-5))² + (y – 1)² = 5²

(x + 5)² + (y – 1)² = 25

The perimeter of shape C is 30 cm shorter than the total perimeter of A and B.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter of each shape is given as follows:

Then the difference is given as follows:

34 + 26 - 30 = 30 cm.

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m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.

In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.

       We know that m∠BCD = (2x + 3)°

       Substituting x = 92/7, we get:

       m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°

       Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.

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Answer:

D. 1/2

Step-by-step explanation:

9^x - 1 = 2

9^x = 3

x = log{sub}9 (3)

x = 1/2 (9^(1/2)=3)

Answer:

if two parallel lines are cut by a transversal,then, exterior angles on the same side of the transversal are supplementary!

Step-by-step explanation:

I don't really know how to explain it but I hope this helped!

Step-by-step explanation:

b. To determine the coordinates of the points on the graph, we need to consider the information given.

At the beginning of the second lap, one minute and three seconds had passed. Since each lap is 4.7 kilometers long, we can calculate the distance traveled at the beginning of the lap using the formula:

Distance = (Number of laps - 1) × Length of each lap

For the beginning of the second lap:

Distance = (2 - 1) × 4.7 km = 4.7 km

At the beginning of the third lap, one minute and three seconds had passed. Therefore, the distance traveled at the beginning of the third lap is:

Distance = (3 - 1) × 4.7 km = 9.4 km

The coordinates of the points on the graph would be:

Point A: (4.7 km, 4.7 km)

Point B: (9.4 km, 9.4 km)

On the graph, the x-axis would represent the distance traveled at the beginning of the lap, and the y-axis would represent the distance traveled at the end of the lap.

c. To find the equation of the line between the two points, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

Using the coordinates of the two points (4.7 km, 4.7 km) and (9.4 km, 9.4 km), we can calculate the slope:

m = (y2 - y1) / (x2 - x1)

= (9.4 km - 4.7 km) / (9.4 km - 4.7 km)

= 4.7 km / 4.7 km

= 1

The slope of the line is 1.

Since the line passes through the origin (0, 0), the y-intercept (b) is 0.

Therefore, the equation of the line is:

y = 1x + 0

y = x

This line represents a one-to-one relationship between the distance traveled at the beginning of the lap and the distance traveled at the end of the lap.

d. To estimate how long it would take Fernando to finish the entire race if he continues to average the same speed, we need to find the time it takes for one lap.

In the given scenario, Brandon timed Fernando's lap for one minute and three seconds. Since there are 3 laps in total, we can divide the total time by the number of laps to find the average time per lap:

Average time per lap = Total time / Number of laps

= 1 minute and 3 seconds / 3

= 21 seconds

Since each lap is 4.7 kilometers long, we can calculate the speed:

Speed = Distance / Time

= 4.7 km / (1 minute + 21 seconds)

To estimate the time it would take Fernando to finish the entire race, we divide the total race distance by the speed:

Total race time = Total race distance / Speed

= 500 km / (4.7 km / (1 minute + 21 seconds))

To calculate the time, we need to convert 1 minute and 21 seconds to a decimal form:

1 minute + 21 seconds = 1 minute + (21 seconds / 60 seconds)

= 1 minute + 0.35 minutes

= 1.35 minutes

Substituting the values:

Total race time = 500 km / (4.7 km / 1.35 minutes)

= 500 km × (

1.35 minutes / 4.7 km)

= 500 km × 0.28723...

≈ 143.615 minutes

Therefore, it would take approximately 143.615 minutes for Fernando to finish the entire race if he continues to average the same speed.

Using the concept of scale factor, the value of t in polygon s is:  7.2

The amount by which the shape is expanded or contracted is referred to as the scale factor. This is usually utilized when 2D shapes such as circles, triangles, squares and rectangles need to be enlarged. If y = Kx is an equation, K is the scaling factor for x.

From the given image, since Polygon s is a scaled copy of polygon R, then we can say that using the concept of scale factor, we have:

9/t = 12/9.6

t = (9 * 9.6)/12

t = 7.2

Thus, we can be sure that is the value of t of the polygon S using the concept of scale factor

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Answer:

ok t means some thing but zero and seven should be solved

i) the original distance when the lighthouse is due West of the ship is 7 km

ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes

iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km

To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:

i) Finding the original distance when the lighthouse is due West of the ship:

The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.

To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:

Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).

ii) Finding the time in minutes when the lighthouse is due West of the ship:

To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:

Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).

To find the time, we can use the formula:

Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).

iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:

We can use the formula for relative velocity to find the distance:

Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)

Using the values we calculated earlier, we have:

Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).

Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.

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Part I- a) y = (x + 25)(x + 9)

b) y = x^2 + 34x + 225

c) y=  (x + 17)^2 - 64

d) The y-intercept is (0, 225), The y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.

g) y = 465 square yards

Part II- a) y = (6 + 2x)^2

b) 169 = (6 + 2x)^2

c) x = 3.5 feet

Part I:

y = (x + 25)(x + 9)

b) To rewrite the equation in standard form using the FOIL method:

y = x^2 + 9x + 25x + 225

= x^2 + 34x + 225

c) To rewrite the equation in vertex form by completing the square:

y = (x^2 + 34x) + 225

= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2

= (x^2 + 34x + 289) + 225 - 289

= (x + 17)^2 - 64

d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:

0 = (x + 17)^2 - 64

64 = (x + 17)^2

x + 17 = ±√64

x + 17 = ±8

x = -17 ± 8

x = -25, -9

Therefore, the x-intercepts are (-25, 0) and (-9, 0).

The y-intercept is obtained by setting x = 0 in the equation:

y = (0 + 17)^2 - 64

y = 17^2 - 64

y = 289 - 64

y = 225

Therefore, the y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.

g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).

h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:

y = (6 + 17)^2 - 64

y = 23^2 - 64

y = 529 - 64

y = 465 square yards

Part II:

a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:

y = (6 + 2x)^2

b) Substituting the area of the enclosed space (169 square feet) for y in the equation:

169 = (6 + 2x)^2

c) Solving the equation for x:

√169 = √((6 + 2x)^2)

13 = 6 + 2x

2x = 13 - 6

2x = 7

x = 7/2

x = 3.5 feet

Therefore, the width of the deck space around the hot tub is 3.5 feet.

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The exact values of csc(theta) and cot(theta) are: csc(theta) = 4√7/7

cot(theta) = -3√7/7.

To find the exact values of csc(theta) and cot(theta), given that cos(theta) = -3/4 and theta is an angle in quadrant two, we can use the trigonometric identities and the Pythagorean identity.

We know that cos(theta) = adjacent/hypotenuse, and in quadrant two, the adjacent side is negative. Let's assume the adjacent side is -3 and the hypotenuse is 4. Using the Pythagorean identity, we can find the opposite side:

[tex]opposite^2 = hypotenuse^2 - adjacent^2opposite^2 = 4^2 - (-3)^2opposite^2 = 16 - 9opposite^2 = 7[/tex]

opposite = √7

Now we have the values for the adjacent side, opposite side, and hypotenuse. We can use these values to find the values of the other trigonometric functions:

csc(theta) = hypotenuse/opposite

csc(theta) = 4/√7

To rationalize the denominator, we multiply the numerator and denominator by √7:

csc(theta) = (4/√7) * (√7/√7)

csc(theta) = 4√7/7

cot(theta) = adjacent/opposite

cot(theta) = -3/√7

To rationalize the denominator, we multiply the numerator and denominator by √7:

cot(theta) = (-3/√7) * (√7/√7)

cot(theta) = -3√7/7

Therefore, the exact values of csc(theta) and cot(theta) are:

csc(theta) = 4√7/7

cot(theta) = -3√7/7

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Answer:

Step-by-step explanation:

The given augmented matrix is already in reduced row echelon form. We can interpret it as a system of equations as follows:

1x + 0y + 0z + (4/5)w = 0

0x + 1y + 0z + 5w = 0

0x + 0y + 1z - 4w = 0

0x + 0y + 0z + w = -4

From the last row, we can see that w = -4. Substituting this value back into the previous rows, we get:

1x + 0y + 0z + (4/5)(-4) = 0

0x + 1y + 0z + 5(-4) = 0

0x + 0y + 1z - 4(-4) = 0

Simplifying these equations, we have:

x - (16/5) = 0

y - 20 = 0

z + 16 = 0

From the second equation, y = 20. From the third equation, z = -16. Substituting these values into the first equation, we get x - (16/5) = 0, which implies x = 16/5.

Therefore, the solution of the system is (16/5, 20, -16, -4).

So, the correct choice is:

A. The system has exactly one solution. The solution is

(16/5, 20, -16, -4)

Answer:

? = 220°

Step-by-step explanation:

the measure of the inscribed angle QRS is half the measure of its intercepted arc QS , then

QS = ? = 2 × QRS = 2 × 110° = 220°

To solve these problems, we can use Coulomb's Law, which states that the magnitude of the electric field produced by a charged particle is directly proportional to the charge and inversely proportional to the square of the distance from the particle.

a) Without finding the charge of the particle, we can use the inverse square relationship. If the electric field magnitude is 2.0 N/C at a distance of 50 cm, then at half the distance (25 cm), the electric field would be four times stronger. Therefore, the electric field at 25 cm would be 4 * 2.0 N/C = 8.0 N/C.

b) Doubling the charge would result in doubling the electric field magnitude. So, if the electric field at a distance of 50 cm was initially 2.0 N/C, it would become 4.0 N/C after doubling the charge.

c) To determine the magnitude of the particle's charge, we need to use the equation for the electric field:

E = k * (|q| / r^2)

where E is the electric field magnitude, k is the electrostatic constant, |q| is the magnitude of the charge, and r is the distance from the particle.

Using the known values of E = 2.0 N/C and r = 50 cm (or 0.5 m), we can rearrange the equation to solve for |q|:

|q| = E * r^2 / k

Substituting the values and the known value of k, we can calculate the magnitude of the charge.

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the answer is

w = -3/2 u + 2

A "⊂-maximal element" in set theory refers to an element in a set that cannot be strictly contained within any other element of the set, indicating a maximum extent or boundary within that set.

In the context of set theory and Tarski's notion of finiteness, a "⊂-maximal element" refers to an element within a set that cannot be strictly contained within any other element of the set. Let's break down the meaning of this term.

Consider a set S and a partial order relation ⊆ (subset relation) defined on the power set P(S) of S. A "⊂-maximal element" u of a set A ⊆ S is an element that is not strictly contained within any other element of A with respect to the subset relation. In other words, there is no element v in A such that u is a proper subset of v.

Formally, for any u ∈ A, if there is no v ∈ A such that u ⊂ v, then u is a ⊂-maximal element of A. This means that u is as large as possible within A and cannot be extended by including additional elements.

In the context of T-finite sets, the existence of a ⊂-maximal element in every nonempty subset of the set guarantees that the set has a well-defined structure and does not continue indefinitely without boundaries.

It ensures that there is a definitive maximum element within each subset, which is a key characteristic of finiteness.

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Answer:

be more clear of what u mean edit the question to explain more

Step-by-step explanation:

no explanation