The explicit rule for a sequence is given.

an= 2/5 (5)^n−1

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]

where [tex]v_{0}t[/tex] is the initial upwards velocity and

[tex]h_{0}[/tex] is the initial height from which the object was launched.  Filling in that equation with those values gives you

[tex]s(t)=-16t^2+64t+3[/tex].  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

[tex]-16t^2+64t=-3[/tex]

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

[tex]-16(t^2-4t)=-3[/tex]

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

[tex]-16(t^2-4t+4)=-3[/tex]

BUT since you added in a 4*-16 on the left you have to add it in on the right:

[tex]-16t^2(t^2-4t+4)=-3-64[/tex]

which simplifies to

[tex]-16(t-2)^2=-67[/tex]

Now bring the 67 over by addition and you have your vertex:

[tex]s(t)=-16(t-2)^2+67[/tex].

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

Answer:

The solution is (-3, 10.8)

Step-by-step explanation:

While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.

To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):

-0.18x + y = -6.54

-2.8x - y = -2.4

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

-2.98x = -8.94

Dividing both sides by -2.98, to isolate x, yields:  x = -8.94 / (-2.98) = -3.

Then x = 3.  Find y from -2.8x - y = -2.4:  -2.8x + 2.4 = y, and here,

y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8

Then the solution is (-3, 10.8)

Find the area of the square, which has a side length of 2.

Area of square = 2 x 2 = 4  

Now multiply the area by the length b

Volume = 4 x 5 = 20 square units total.

Answer:

$2950

Step-by-step explanation:

Add together the following three items:

Materials:  $2000 plus 15%, or 1.15($2000), or $2300

Labor:  $500

Equipment Rental:  $150

Total:  $2300 + $500 + $150 = $2950

Answer:

- The center of hyperbola is (-2 , 3)

- The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

- The other vertex is (2 , 3)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1, Where

- The length of the transverse axis is 2a

- The coordinates of the vertices are (h ± a , k)

- The length of the conjugate axis is 2b

- The coordinates of the co-vertices are (h , k ± b)

- The coordinates of the foci are (h ± c , k), where c² = a² + b²

* Now lets solve the problem

∵ (x + 2)²/4² - (y - 3)²/5² = 1

∵  (x - h)²/a² - (y - k)²/b² = 1

∴ a = 4 , b = 5

∴ h = -2 , k = 3

∵ The center of the hyperbola is (h , k)

∴ The center of hyperbola is (-2 , 3)

∵ The coordinates of the vertices are (h + a , k)  , (h - a , k)

∴ The coordinates of the vertices are (-2 + 4 , 3)  , (-2 - 4 , 3)

∴ The coordinates of the vertices are (2 , 3)  , (-6 , 3)

∴ The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

∴ The other vertex is (2 , 3)

The center of a hyperbola is determined by the coordinates (h, k) in its equation. The vertices are the points where the hyperbola intersects its major axis, and their positions depend on whether the hyperbola opens horizontally or vertically. If it opens horizontally, the left vertex is at (h - A, k), and if it opens vertically, the bottom vertex is at (h, k - B).

In the equation of a hyperbola, the center of the hyperbola can be found by identifying the coordinates (h, k). These are the constants in the denominators of the fractions on the left-hand side of the equation. For instance, in the equation ((x-h)²/A²) - ((y-k)²/B²) = 1, the center would be at the point (h, k).

The vertices of the hyperbola are the points where the hyperbola intersects its major axis. If the hyperbola opens horizontally, the left vertex will be located at the coordinate (h - A, k), and the other vertex will be at (h + A, k). If the hyperbola opens vertically, the bottom vertex will be at the coordinate (h, k - B), with the other vertex at (h, k + B).

Remember, A represents the distance from the center to a vertex along the major axis, and B represents the distance from the center to a vertex along the minor axis.

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In converting to spherical coordinates, we use

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

so that

[tex]\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

Then the integral is

[tex]\displaystyle\iiint_Ey^2\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^3\rho^4\sin^2\theta\sin^3\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta=\boxed{\frac{162\pi}5}[/tex]

To evaluate the expression using spherical coordinates, express the given solid hemisphere in spherical coordinates by replacing x, y, and z with r, θ, and φ. Substitute the volume element in spherical coordinates, and integrate over the limits specified by the solid hemisphere. Finally, evaluate the expression numerically.

To evaluate the expression ∫ey2dv using spherical coordinates, we first need to express the solid hemisphere in spherical coordinates. The given condition for the solid hemisphere is x2 + y2 + z2 ≤ 9 and y ≥ 0. In spherical coordinates, the equation for the solid hemisphere becomes r ≤ 3 and 0 ≤ θ ≤ π/2.

The volume element dv in spherical coordinates is dV = r2sinθdrdθdφ. Substituting this into the original expression, we have ∫ey2dv = ∫e(r*sinθcosφ)2r2sinθdrdθdφ. Since we are integrating over the solid hemisphere, the limits of integration for r, θ, and φ are r = 0 to r = 3, θ = 0 to θ = π/2, and φ = 0 to φ = 2π.

After substituting the expressions for y and dv in terms of spherical coordinates and integrating over the given limits, we can find the numerical value of the given expression.

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Answer:

[tex](x+3)^2 + y^2 =25[/tex]

Step-by-step explanation:

The general equation of a circle has the form:

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

Where the point (h, k) is the center of the circle and r is the radius

In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]

So [tex]h=-3\\k=0[/tex]

Finally the equation of the circle is:

[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]

[tex](x+3)^2 + y^2 =25[/tex]

(X+3)^2 +y^2 =25

This is the correct answer

Check on Desmos

Cosidering the ray BC.

It is clear that:

1) A ray starts from one point and extends infinitely in ONE direction.

2) The ray BC cannot be measured. But the line-segment BC can be Measured.

3) B and C are the only two points on the given ray.

Hence the statement: "There are only two points on the entire ray" is the correct one.

Hope it helps...

Regards;

Leukonov/Olegion.

The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered so options (A), and (D) are true.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given,

A ray is passing through points B and C.

(A) The ray extends infinitely in one direction which is True.

(D) There are only two points on the entire ray which is also true.

Hence, The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered.

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Answer:

2

Step-by-step explanation:

Kelly ran at an average speed of 8 miles per hour. If she finished the race in one and a half hours that means she ran 12 miles.

8=x

?=3/2x

12=x

We now know the road is 12 miles long. Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2

It takes Ava to finish the race in 2 hours.

Kelly ran at an average speed of 8 miles per hour.

If she finished the race in one and a half hours that means she ran 12 miles.

The average speed is the distance traveled divided by the time taken.

8=x

12=x

We now know the road is 12 miles long.

Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2hours

Therefore, It takes Ava to finish the race in 2 hours.

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Answer:

Final answer is E. 10

Step-by-step explanation:

Apply Pythagorean theorem to the given right triangle.

[tex]\left(Hypotenuse\right)^2=\left(Leg_1\right)^2+\left(Leg_2\right)^2[/tex]

[tex]\left(h\right)^2=\left(5\sqrt{2}\right)^2+\left(5\sqrt{2}\right)^2[/tex]

[tex]\left(h\right)^2=50+50[/tex]

[tex]\left(h\right)^2=100[/tex]

take square root of both sides

[tex]h=10[/tex]

Hence final answer is E. 10

ANSWER

E. 10

EXPLANATION

Using Pythagoras Theorem, which says the hypotenuse squared is equal to the sum of squares of the two shorter legs.

[tex] {h}^{2} = {(5 \sqrt{2} )}^{2} + {(5 \sqrt{2} )}^{2} [/tex]

Evaluate the squares on the RHS.

[tex] {h}^{2} = 25 \times 2 + 25 \times 2[/tex]

[tex] {h}^{2} = 50 + 50[/tex]

Simplify:

[tex] {h}^{2} = 100[/tex]

Take positive square root.

[tex]h = \sqrt{100} [/tex]

[tex]h = 10[/tex]

The hypotenuse is 10 units.

The correct answer is E

To solve for Sydney's age, we used an equation based on the relationship that Devaughn is 11 years younger than Sydney and the sum of their ages is 83. Solving the equation 2S - 11 = 83, we found that Sydney is 47 years old.

To find Sydney's age, we need to set up and solve an equation based on the information given: Devaughn is 11 years younger than Sydney, and the sum of their ages is 83.

Let's let Sydney's age be represented by S and Devaughn's age be represented by D. Given that Devaughn is 11 years younger than Sydney, we can express Devaughn's age as D = S - 11.

The sum of their ages is given as 83, so we can write the following equation: S + D = 83.

Substituting Devaughn's age in terms of Sydney's age, we get: S + (S - 11) = 83. This simplifies to 2S - 11 = 83. Solving for S, we add 11 to both sides, resulting in 2S = 94, and then we divide by 2 to find S = 47.

Therefore, Sydney's age is 47 years old.

Answer:

A.

Step-by-step explanation:

The question is on laws of logarithms

For example to find the log₁₀ 100

⇒log₁₀ 100 = 2................how?

we take In 100 / 1n l0 = 2

where  10²=100

⇒Thus   logₓ y = In y / In x

Answer:

True

Step-by-step explanation:

A negative exponent turns into positive when it is put into fraction form.

5^-2 = 1/5^2

5^-2 = 1/25

Answer:

Step-by-step explanation:

It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example

(5/3)^(-2) = (3/5)^2 = 9/25

Answer:

Step-by-step explanation:

m = megs age

v = vectors age

meg is 2 years older than vector   + 2

therefore

m = v +2

Answer:

20/28 which is about 71%

Step-by-step explanation:

so first you add up how many balls there are. 8+20=28. So 28 is the denominator for the fraction. there are 20 black balls, so that is the numerator. so 20/28 is the fraction. then you divide 20 by 28 to get the rounded percent.

Answer:

The length of MN is [tex]\sqrt{5}[/tex] units.

Step-by-step explanation:

The given Quadrilateral KLMN has vertices at K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4).

We use the distance formula to find the length of MN.

[tex]|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We plug in the values to get

[tex]|MN|=\sqrt{(-4--2)^2+(-4--5)^2}[/tex]

[tex]|MN|=\sqrt{(-2)^2+(1)^2}[/tex]

[tex]|MN|=\sqrt{4+1}[/tex]

[tex]|MN|=\sqrt{5}[/tex]

The length of MN is [tex]\sqrt{5}[/tex] units.

Answer:

B

Step-by-step explanation:

the answer is 3 I bet the oven is hot tbh

Title: The Infallible Logic of 1 + 1 = 2

Introduction:

The seemingly simple equation, 1 + 1 = 2, holds a profound and fundamental place in mathematics and logic. Its truth is evident, self-evident, and indisputable, serving as a cornerstone for mathematical reasoning and human understanding. In this essay, we explore the underlying principles and irrefutable logic behind the statement that 1 + 1 equals 2.

Body:

Basic Arithmetic Principles:

At its core, mathematics is a system of rules and principles that govern the manipulation of numbers and quantities. The equation 1 + 1 = 2 is a fundamental expression of these principles. It demonstrates the addition of two individual units (1) to form a collective sum (2). This is a foundational concept in arithmetic.

Axiomatic Truth:

In the realm of mathematics, certain statements are considered axioms—self-evident truths that do not require proof. 1 + 1 = 2 is one of these axioms. It is a statement that is true by definition and serves as a building block for more complex mathematical operations.

Logical Proof:

One way to understand why 1 + 1 equals 2 is through logical proof. We can start with the premise that we have one unit (1) and add another unit (1) to it. The result, by definition, is two units (2). This logical progression is simple and irrefutable.

Set Theory:

In set theory, a branch of mathematics that deals with sets and their relationships, the equation 1 + 1 = 2 is rigorously defined. In set theory, 1 represents a set containing a single element, and adding another set with one element results in a set with two elements. This is a formalized representation of why 1 + 1 equals 2.

Real-World Application:

The equation 1 + 1 = 2 has practical applications in various fields, including science, engineering, economics, and everyday life. It reflects the way we count and aggregate objects, making it essential for quantitative analysis and problem-solving.

Conclusion:

The equation 1 + 1 = 2 is not merely a mathematical expression; it is a reflection of the logical and axiomatic foundation upon which mathematics and much of human reasoning are built. Its undeniable truth serves as a testament to the precision and consistency of mathematics. The simple act of adding one to one resulting in two exemplifies the elegance and power of mathematical logic, making it an enduring principle in our understanding of the world. In a universe governed by mathematical laws, 1 + 1 will always equal 2, and this irrefutable truth is a testament to the beauty and reliability of mathematics.

5 5/8= 45/8

1 1/2= 3/2

45/8 divided by 3/2

Or

45/8 times 2/3

15/4 or 3 3/4

Answer:

C

Step-by-step explanation:

Using the coefficients of each term and evaluating for h = - 4

- 4 | 1   - 7   - 7   20

      ↓   - 4   44   - 148

     ---------------------------

      1   - 11   37   - 128 ← remainder

Quotient = x² - 11x + 37 , R - 128

Answer:18.66

Step-by-step explanation:

By the inscribed angle theorem,

[tex]12y-1=9y+11[/tex]

[tex]3y=12[/tex]

[tex]y=4[/tex]

So the angles have measure

[tex](12\cdot4-1)^\circ=\boxed{47^\circ}[/tex]

The measure of the angle is 47 degrees. Thus, the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angles at the periphery made by the same chord will be equal.

The equation is given as,

12y - 1 = 9y + 11

Simplify the equation, then we have

12y - 1 = 9y + 11

12y - 9y = 11 + 1

3y = 12

y = 4

Then the measure of the angle is given as,

Angle = 12 x 4 - 1

Angle = 48 - 1

Angle = 47

Thus, the correct option is B.

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Answer:

I can tell you that B is NOT correct as I got it wrong.  I bet the right answer is C as it is holding steady at 1:95.

Step-by-step explanation:

These are the choices for Plato

A. The exchange rate between the U.S. dollar and the yen changes from 1:95 to 1:102.

B. The exchange rate between the U.S. dollar and the euro changes from 1:95 to 1:92. - Wrong answer

C. The exchange rate between the U.S. dollar and the euro remains 1:95

Answer:

Associative property of multiplication

Explanation:

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

Answer:

$6.48

Step-by-step explanation:

Answer:

D) No, corresponding angles are not congruent and corresponding sides are not proportional.

;]

Step-by-step explanation:

Answer:

the answer is D i just answered it with D and its correct

good luck on your assignment :)

Step-by-step explanation:

Answer:

  [4, 8]

Step-by-step explanation:

You want to find t such that ...

  T ≥ 69

  24t − 2t^2 + 5 ≥ 69

  t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

  (t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

  t ∈ [4, 8]

Final answer:

This question pertains to calculating the volume of a triangular pyramid using given measurements of the base edge, base height, and volume.

Explanation:

The subject of this question involves calculating the volume of a triangular pyramid and understanding its geometric properties. Given the volume (56 cubic centimeters), base edge (8 centimeters), and base height (7 centimeters), one can determine various other properties of the pyramid. In geometry, the formula to calculate the volume of a pyramid is V = (1/3)*Base Area*Height, where the Base Area for a triangular pyramid is ½ times the base length times the base height. The challenge here would involve determining the height of the pyramid based on the given volume and base dimensions.

Check the picture below.

Answer:

B. 7.5 square units.

Step-by-step explanation:

We have been given an image of a right triangle. We are asked to find area of our given triangle.

We can see that base of our given triangle is 5 units as difference between point S and point T is 5 units.

[tex]2--3=2+3=5[/tex]

The height of our given triangle (RT) is 3 units.

[tex]1--2=1+2=3[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times \text{5 units}\times \text{3 units}[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times 15\text{ units}^2[/tex]

[tex]\text{Area of triangle}=7.5\text{ units}^2[/tex]

Therefore, area of our given triangle is 7.5 square units and option B is the correct choice.

So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.

36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)

51000 x .36 = 18360

So you simply subtract 18360 from 51000, which is 32,640.