Write 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 as a power of 10 using exponents.
A) 10'3
B) 10'6
C) 10'9
D) 10'10

It's geometric sequence:

[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]

Calculate the common ratio:

[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]

The explicit formula of geometric sequence:

[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]

Substitute:

[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]

Answer: "f(x) = 1.2(2.5)x-1"

Answer:

Step-by-step explanation:

100% righttt

This question deals with the physics of projectile motion and rocket trajectories. By analyzing the given equations for acceleration and position over time, we can determine the units of constants and describe the motion of the rockets, emphasizing their parabolic paths.

The question at hand involves understanding the motion of two rockets using principles of physics and applying mathematical functions to describe their trajectories. For rocket A, the given quadratic function A(t) = −(t − 8)2 + 535, describes its height as a function of time, indicating a parabolic trajectory, which is typical for projectiles under gravity's influence.

In rocket motion, the acceleration can sometimes be described by an equation of the form a(t) = A - Bt1/2. Here, A and B are constants that determine the rocket's changing acceleration over time. The units of A would be meters per second squared (m/s2), since it represents acceleration, and the units of B would have to be meters per second to the power of five halves (m/s5/2) to ensure the units of time (t) cancel out correctly. When a rocket starts from rest, its velocity changes over time, initially increasing but then possibly decreasing if the acceleration is negative due to the subtraction of the term involving Bt1/2.

If the initial position is set to zero, the rocket's position as a function of time can be found by integrating the velocity function, which is the integral of the acceleration function with respect to time. This integration process accounts for the initial conditions and gives a complete description of the rocket's motion.

In the context of projectile motion, the trajectory is indeed parabolic, represented by the equation y = ax + bx2. To prove this, we use the kinematic equations that separately describe the horizontal and vertical motions (x = Voxt for horizontal and y = Voyt - (1/2)gt2 for vertical motion) and eliminate the time variable to find y as a function of x.

Solution:

The given inequality is :

3 x - 2 y ≤ 6

To draw the graph we will first draw the graph of line : 3 x - 2 y = 6

The graph of this function i.e 3 x - 2 y = 6 will be a straight line.

Then we will check whether origin lies on which side of line .

Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain

LHS = 0 ≤ 6

It means the line will contain the Origin.

Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]

Answer:

3/4z-1/4z+1=2/4z+1

Combine like terms to get

1/2z+1=1/2z+1

Subtract one from both sides to get

1/2z=1/2z

Multiply both sides by 2 to get

z=z.

This is D, has infinitely many solutions because any number you enter as z will equal itself.

Ex. 5 as z would be 5=5 which is true with any number.

Answer:

2 times

Step-by-step explanation:

Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only  will work, thus, there are  positive integer values of  such that this function is less than 20.

In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.

In science, the four ways to incorporate proof into the research paper are:

1.    If the research you are investigating has been with other research paper before.

2.    There is an experimental proof that the evidence is true.

3.    The research published belongs to a reliable source.

4.    There are citations of the evidence that you are investigating

Answer:

$162.97 is the exact answer.

Step-by-step explanation:

Final answer:

The velocity of the ball at t = 1 second is found by taking the derivative of the position function s(t) and evaluating it at t = 1. The derived velocity function is v(t) = -32t + 20, and the velocity at t = 1 second is 8 ft/sec.

Explanation:

The student wants to find the velocity of a ball at t = 1 second when thrown vertically upward from the top of a 100-foot tower with an initial velocity of 20 ft/sec. The position function given is [tex]s(t) = -16t^2 + 20t + 100[/tex]. To find velocity, we need to take the derivative of the position function with respect to time, which represents the velocity function v(t).

The derivative of the position function is:
v(t) = −32t + 20.

To find the velocity at t = 1 second, substitute 1 for t:
v(1) = −32×1 + 20 = −12 + 20 = 8 ft/sec.

Therefore, the velocity of the ball at t = 1 second is 8 ft/sec.

The mathematical rule (x,y) to (x-2, y-7) signifies a transformation in the coordinate plane shifting points 2 units to the left and 7 units down. To apply this rule to any point, subtract 2 from the x-coordinate and 7 from the y-coordinate.

The rule (x,y) to (x-2,y-7) in Mathematics signifies a specific transformation in a coordinate plane. This is essentially a rule used in graph transformations to shift a point in the coordinate plane. In this specific rule, every point (x, y) is shifted 2 units to the left and 7 units down to get the new point (x-2, y-7). For example, if we take a point, (5,10), applying this rule means we subtract 2 from the x-coordinate and 7 from the y-coordinate resulting in a new point (3,3). Therefore, simplifying this process, to apply the rule (x,y) to (x-2,y-7) to any point, all you need to do is subtract 2 from the x-coordinate and 7 from the y-coordinate of the point.

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Answer:

50.24 square units

Step-by-step explanation:

Hope this helps.

Answer:

The answer is C

[tex]3x-y=14\\-9x+3y=-42[/tex]

Step-by-step explanation:

In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.

I have attached an image that shows different systems of two lines.

So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:

[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]

This system has infinitely solutions.

C(n,r)=C(7,6) 

Final answer:

There are 7 different ways to select a committee of 6 people from a group of 7 candidates, calculated using the combinations formula C(7, 6) = 7! / (6! * (7 - 6)!) = 7.

Explanation:

The question is asking to determine the number of different ways a committee can be selected from a group of candidates, which is a common problem in combinatorics, a branch of mathematics. To find the number of different ways a committee of 6 people can be selected from a group of 7 candidates, you can use combinations. Since the order in which the committee is chosen does not matter, you calculate combinations and not permutations. The formula for combinations is:

C(n, k) = n! / (k! * (n - k)!)

Applying the formula:

C(7, 6) = 7! / (6! * (7 - 6)!) = 7 / 1 = 7

Therefore, there are 7 different ways to select a committee of 6 people from a group of 7 candidates.

Answer: The height of the stacked boxes is 31 meters.

Step-by-step explanation:

Since, the Volume of a cube = (side)³

The volume of first box = 1331 cubic meters,

⇒ (side)³ = 1331

⇒

Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )

Now, the volume of third box = 729 cubic meters

⇒ ⇒ (side)³ = 729

⇒

Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box

= 11 + 11 + 9

= 31 meters.