Please help me fast thank you for your help I’ll give 50 points

The Length of the springs of the two pogo sticks will never be equal.

A pogo stick is an apparatus used for jumping off the ground. The pogo stick uses a spring to store energy when a user jumps on it. The spring is released when the user jumps off the ground.

The length of the spring is compressed when the user jumps on the pogo stick and non-compressed when not in use. The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after 8 seconds can be described by the function (0) = 2sine+√2.

Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)The non-compressed length is given by y = √2. When the pogo stick's spring is equal to its non-compressed length, the difference in length of the spring will be zero.2sine+√2 = √22sine = 0sine = 0The solutions to this equation are obtained by finding the values of θ for which sine = 0.

Therefore, the values of θ are given by:θ = nπwhere n is an integer.

Part B: If the angle was doubled, that is 0 became 20, what are the solutions in the interval [0, 2π)?How do these compare to the original function? (5 points)When the angle is doubled, the equation becomes:2sin2θ+√2 = √2By simplifying the equation, we obtain:2sin2θ = 0sin2θ = 0The solutions to this equation are obtained by finding the values of 2θ for which sine = 0.

Therefore, the values of θ are given by:θ = 0, π, 2πPart C: A toddler is jumping on another pogo stick whose length of its spring can be represented bythe function g(e)-1-cos² e+√2. At what times are the springs from the original pogo stick and thetoddler's pogo stick lengths equal? (5 points)The length of the spring of the toddler's pogo stick can be represented by the function g(e) = -1 - cos² e+√2.

The length of the spring of the original pogo stick is given by the function f(θ) = 2sinθ+√2.To find the times when the two springs are equal, we need to solve the equation:g(e) = f(θ)-1 - cos² e+√2 = 2sinθ+√2cos² e = 2sinθ2cos² e = sin2θ2(1-sin² e) = sin2θ2 - sin² e = sin2θsin² e + sin2θ = 1sin² e = 1 - sin2θ

Therefore, the equation reduces to:-1 - (1 - sin2θ) + √2 = 2sinθ + √2sin2θ = 0, sin2θ = -2The equation has no solutions since the value of sin2θ is less than or equal to 1.

Therefore, the length of the springs of the two pogo sticks will never be equal.

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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Answer:

30 cuzzo

Step-by-step explanation:

its 30 because 2 times 15 is 30

So the final answer is 8 x 10¹²which is (4/5) x 10¹³ in scientific notation.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we can simplify the expression by using the rules of exponents.

Recall that when you divide two numbers with the same base, you can subtract their exponents. That is:

\(a^m\) / aⁿ = \(a^{(m-n)}\)

Using this rule, we can simplify the given expression as follows:

4x10⁷ / 5x10⁻⁶ = (4/5) x (10⁷ / 10⁻⁶)

Now, we can simplify the expression inside the parentheses by using the rule of exponents that says:

a⁻ⁿ = 1/aⁿ

This means that:

10⁻⁶ = 1/10⁶

Substituting this in our expression, we get:

(4/5) x (10⁷ / 10⁻⁶) = (4/5) x (10⁷ x 10⁶)

Using the rule of exponents that says:

\(a^m\) x aⁿ =\(a^{(m+n)\)

We can simplify this expression as follows:

(4/5) x (10⁷ x 10⁶) = (4/5) x \(10^{(7+6)\)

= (4/5) x 10¹³

Therefore, So the final answer is 8 x 10¹² which is (4/5) x 10¹³ in scientific notation

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Answer:

\(x^{2} + 2x - 1\)

Step-by-step explanation:

We are solving for :

\(\frac{x^{3}+ 5x^{2} + 5x - 3 }{x + 3}\)

Factor \(x^{3} + 5x^{2} + 5x - 3 : (x + 3)(x^{2} + 2x - 1)\)

\(\frac{(x + 3)(x^{2} + 2x - 1)}{x + 3}\)

= \(x^{2} + 2x - 1\)

Taxes are rates or amount deducted from individuals.

The borrower paid $605.36 for county taxes

From the table, we have the following entry:

County taxes (half year)         (6)        $605.36

The above represents the amount paid for county taxes

Hence, the borrower paid $605.36 for county taxes

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Answer:

$605.36

$605.36

$605.36

$605.36

$605.36

$605.36

Answer:

x=3

Step-by-step explanation:

9x-6=3x+12

6x=18 |:6

x=3

Answer:

It’s A

Step-by-step explanation:

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

f(x) = (x − 1)2(x + 1)(x − 3)

Step-by-step explanation:

Look at where the red line crosses/ touches the x-axis. This will give you the zeros.

It crosses at -1, touches at 1, and crosses again at 3

This means the zeros are -1, 1 and 3

Now, you need to have (x+1) (x-3) and (x-1) as factors.

Therefore, the answer is f(x) = (x − 1)2(x + 1)(x − 3).

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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Answer:

24x + 15

Step-by-step explanation:

You multiply 24 and x together, then add 15 to the sum.

Answer:

Slope=−

2.000

4.000

=−2.000

s−intercept=

2

0

=0.00000

t−intercept=

1

0

=0.00000

t=0

s=0

Answer:

17, -3, -13, -18, -23

Step-by-step explanation:

Plug in the x side into the equation so

g(-4) = -5(-4) -3

g(-4) = 20-3

g(-4) = 17

Therefore that answer is 17

Then you do that for all of them, I don't have the time to do them all but that's the concept for all of them. Hope this helps and hopefully it's not too late. Sorry!

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°

Therefore;

b. Area of circular pie = π·r²

Where;

\(r = \mathbf{\dfrac{d}{2}}\)

Therefore;

\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)

\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)

\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)

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Answer:

SIMPLE INTEREST=PRT/100

P=300

R=5%

T=3

SI=300×5×3/100

SI=3×5×3

SI=45

Answer:

Principal(P) = R300 rate( r )=5% n=5 years

Total amount

= P(1+r/100)^n

= 300(1+5/100)^3

=R347. 2875

Interest

= Total amount - Principal amount

= 347.2875 - 300

= R47.2875

= R47.30( rounded up to 2

decimal places)

Answer:

y=3

Step-by-step explanation:

DFS can be used because the graph is directed and all of the edge weights are positive.

What is Algorithms?

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of IT employ algorithms extensively.

Steps can be taken. There may be a path from v to z* but not from z* to v or different from each with different weights, so we just need to apply DFS, dijkstras twice, starting with vertex v, to find the path length until z*. Then we need to add the path weights.

The problem is clear in that we need to find path weight from v to z* and z* to v. There may be more than one path that leads from v to z*, thus we must locate them all and store some of them because each loop will require a time complexity of O(V+E).

where, in the given graph, E stands for edges and V for vertex. When a graph is complete, meaning there is a path connecting every vertex to every other vertex, we must execute this technique V times to determine the total number of paths. As a result, the time complexity is O(V(V+E)).

Then we must repeat the process from z* to v, but this time we must choose every path whose weights satisfy the specified condition. In the worst case, we must repeat this process (V-1) times, thus the time complexity will be the same as before. As a result, our time complexity will be O(V(V+E)) overall.

Since the graph is directed and every edge weight is positive, DFS may be used.

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The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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Answer:

23552

Step-by-step explanation:

23, 92, 368...   is a geometric sequence.

first term = a = 23

common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4

nth term = \(ar^n^-^1\)

6th term = \(23*(4)^6^-^1\)

\(=23*4^5\)

\(=23*1024\)

\(=23552\)

Hope this helps :)

Pls brainliest...

Answer:

27% of the possible Z values are greater than 0.613

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 0, \sigma = 1\)

27% of the possible Z values are greater than

The 100 - 27 = 73rd percentile, which is X when Z has a pvalue of 0.73. So X when the z-score is 0.613.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.613 = \frac{X - 0}{1}\)

\(X = 0.613\)

27% of the possible Z values are greater than 0.613

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 2

Step-by-step explanation:

2/x^2-1 = 1/ x +1 + 1/ x-1

2/x^2-1 = 1

2=x^2-1

x^2 = 3

x= root 3

Answer:

$35,000

Step-by-step explanation:

In a proposed business venture, Serena estimates that there is a 65% chance that she will make $70,000

And also a 35% chance that she will loose $30,000

Therefore the expected value can be calculated as follows

E= 65/100 × 70,000 + 35/100 × (-30,000)

= 0.65 × 70,000 + 0.35(-30,000)

= 45,500 - 10,500

= $35,000

Hence the expected value is $35,000

Based on the probability of the payoffs, we can calculate that the expected value is $35,000.

The expected value is calculated as:

= ∑(Probability of payoff x Payoff)

The expected value here is therefore:

= (65% x 70,000) + (35% x -30,000)

= 45,500 - 10,500

= $35,000

In conclusion, the expected value is $35,000.

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Answer:

The statement that is true is:

All the equal parts must have the same area.

This is true because when a rectangle is divided into equal parts, it means that the area of each part is the same. The lines dividing the shape can be drawn in any direction (top to bottom, left to right, diagonal, etc.) and the shape of the parts can also be different( rectangles, squares or any shape).

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

the answer is 0 because both equations on either side cancel out thereby leaving in bare

The time required to grow a certain bacteria in a culture beginning with 20 bacteria is end of the day where B is the number of bacteria and t is the time in hours. End of 100th day is required to grow a culture of 13,500 bacteria

Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems. Some species can survive extreme conditions of temperature and pressure. The human body is full of bacteria, indeed it is estimated that there are more bacterial cells than human cells.

According to the Question:

We know that the number of bacteria doubles every hour.

Therefore, the number of bacteria after every hour will form a G.P.

with first term (a= 30) and common ratio (r= 2)

∴a³ = ar²

      = (20)(2)²

       = 80

Therefore, the number of bacteria at the end of 2nd hour will be 320.

a⁵ = ar⁴

   = (20)(2)⁴

   = 320

and in the end of the 100th day the bacteria will grow to 13500

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Answer:

57 seconds

Step-by-step explanation:

55.7 + 1.3 = 57 seconds