Question 13 (1 point)
Hans is jumping on a trampoline. His distance from the ground, in metres, in terms of time, is modelled by the
equation () - 1.5 sm(360s)" + 2. What does the 2 in this equation represent?
Solve

Answer:

What do you need help with?

Step-by-step explanation:

Answer:

AC = 8.7 cm (nearest tenth)

Step-by-step explanation:

Given:

To find AC:

\(\implies \tan(30)=\dfrac{5}{b}\)

\(\implies b=\dfrac{5}{\tan(30)}\)

\(\implies b=5\sqrt{3}\)

⇒ b = 8.7 (nearest tenth)

Therefore, the length of AC is 8.7 cm (nearest tenth)

\(\\ \rm\Rrightarrow tan30=\dfrac{5}{b}\)

\(\\ \rm\Rrightarrow 1/\sqrt{3}=5/b\)

\(\\ \rm\Rrightarrow b=5\sqrt{3}\)

\(\\ \rm\Rrightarrow b=8.66=8.7cm\)

Answer:

17.5 is the answer fjdjidbdbd

Answer:

D) 3

Step-by-step explanation:

Recall the formula for a Taylor Series of a function f(x) centered at x=a:

\(\displaystyle f(x)=f(a)+f'(a)(x-a)+\frac{f''(a)(x-a)^2}{2!}+\frac{f'''(a)(x-a)^3}{3!}+...+\frac{f^n(a)(x-a)^n}{n!}\)

Therefore, the coefficient of x² would come from determining \(\displaystyle \frac{f''(a)(x-a)^2}{2!}\):

\(\displaystyle \frac{f''(0)(x-0)^2}{2!}=\frac{\frac{6}{(1+0)^4}x^2}{2}=\frac{6x^2}{2}=3x^2\)

So, the coefficient would be 3.

The coefficient of x² in the Taylor series expansion for 1/(1+x)² about x = 0 can be determined by taking the derivative of the function and evaluating it at x = 0. The correct option is c.

To find the Taylor series expansion of 1/(1+x)², we can start by expanding the function using the geometric series:

1/(1+x)² = (1 - x + x² - x³ + ...)² = 1 - 2x + 3x² - 4x³ + ...

By inspecting the expansion, we can see that the coefficient of x² is 3. Therefore, the correct option is (c) 1.

In summary, the coefficient of x² in the Taylor series for 1/(1+x)² about x = 0 is 3, which corresponds to option (c).

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Answer:

allie saw 68 near sighted patients

sam saw 59 near sighted patients

Step-by-step explanation:

40% of 170 = 68

0.4 × 170 = 68

25% of 236 = 59

0.25 × 236 = 59

Answer:

Step-by-step explanation:

x = 75°

75° + 75° + a = 180°

a + 150° = 180°

a = 180° - 150°

a = 30°

y + 30° = 90°

y = 90° - 30°

y = 60°

I hope I've helped you

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The required values are ~

\( \boxed{x = 75 \degree}\)

and

\( \boxed{y = 60 \degree}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

As it's shown in the figure, the sides opposite to x and Angle 75° are equal. So the corresponding Angles are also equal to one another.

that is ~

I have taken an angle and marked it as " m " in the attachment.

So, according to Angle sum property of a triangle,

now, it's given that the sum of Angle y and Angle m is 90°

hence,

Answer:

11x + 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

4x + 4 + 7x + 9

Step 2: Simplify

The rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

To find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form, the rectangular coordinates of the above points are given below:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

The rectangular coordinates of the point(s) of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ) can be found by converting the polar equations to rectangular form and solving for the x and y coordinates.

To convert the polar equations to rectangular form, we can use the relationships x = rcos(θ) and y = rsin(θ). Substituting these expressions into the given polar equations, we get:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

To find the points of intersection, we need to set the x and y coordinates of both equations equal to each other and solve for θ. However, solving this system of equations algebraically can be complex due to the trigonometric functions involved.

Graphing the polar curves and visually inspecting the points of intersection may provide a more intuitive approach to finding the rectangular coordinates. By plotting both polar curves on a graph, the points where the curves intersect can be determined by their shared coordinates.

In summary, to find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

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Answer:

m (Slope) = 3

Step-by-step explanation:

Slope formula:

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

= (24 - 3) / (9 -2)

= 21 / 7

=3

The inequality of the graph can be written as x ≥ -1

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. We have different inequality signs e.g greater than (>), less than(<), less than or equal to (≤) and greater than or equal to (≥)

Given the graph attached, in order to write the inequality we need to know where the arrow is pointing at. If the arrow is pointing to the right, the inequality will be  greater than (>) and If the arrow is pointing to the left, the inequality will be less than(<)

Also, we need to know the position of the small circle and whether the circle is shaded or not. If it is not shaded, the inequality will be greater than (>) or less than(<). But if it is shaded, the inequality will be less than or equal to (≤) and greater than or equal to (≥)

Considering our graph now, the circle is at -1 (it's one step behind the thick line(0) ) and it is not shaded. Also, the arrow is pointing to the right. Using variable x:

Therefore, the inequality of the graph is x ≥ -1

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Answer:

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

100 dozen add 20% is:

Answer/Step-by-step explanation:

43 = (4 * 101) + (3 * 100)

43 = (4 * 10) + (3 * 1)

43 = 40 + 3

In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.

Hence, the correct option is D.

The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.

To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.

9.5 - 7.0 = 2.5

Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents

10^(2.5) = 316.2

Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.

Hence, the correct option is D.

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Answer:d

Step-by-step explanation:

its d

Answer:

5,5 m and 12 m

Step-by-step explanation:

Let's assume, the length of the rectangle is x and the width is y meters

Let's write 2 equations and put them in a system:

{x × y = 66,

{x = 2y + 1;

Let's replace x in the 1st equation with its value from the 2nd equation:

(2y + 1) × y = 66

\(2 {y}^{2} + y = 66\)

\(2 {y}^{2} + y - 66 = 0\)

a = 2, b = 1, c = -66

Let's solve this quadratic equation:

\(d = {b}^{2} - 4ac = {1}^{2} - 4 \times 2 \times ( - 66) = 1 + 528 = 529 > 0\)

\(y1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 1 - 23}{2 \times 2} = \frac{ - 24}{4} = - 6\)

Since y has to be a natural number (side lengths cannot have negative units), we cannot take this as an answer

\(y2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 1 + 23}{2 \times 2} = \frac{22}{4} = 5.5\)

y = 5,5

x = 2 × 5,5 + 1 = 12

the dimensions of the rectangle are 5.5 meters by 12 meters.

The question states that the area of a rectangle is 66 m², and the length of the rectangle is 1 meter more than twice the width. We need to find the dimensions of the rectangle.

Let’s assume the width of the rectangle as “x”.

Then, according to the given information, the length will be (2x + 1).

Area of the rectangle = Length × Width

66 = (2x + 1) × x ⇒ 2x² + x - 66 = 0

Now we have to solve this quadratic equation. We can solve it by factoring or using the quadratic formula. Let’s use the quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2aHere, a = 2, b = 1, and c = -66

Therefore,x = [ -1 ± √(1² - 4(2)(-66)) ] / 2(2)x = [ -1 ± √(1 + 528)) ] / 4x = [ -1 ± √529 ] / 4

When we solve this, we get two possible solutions:

x = (-1 + 23) / 4 or x = (-1 - 23) / 4x = 22/4 or x = -24/4x = 5.5 or x = -6

The width of the rectangle cannot be negative. Therefore, the width of the rectangle is 5.5 meters.Length of the rectangle = 2 × 5.5 + 1= 11 + 1= 12 meters

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Answer:  greatest number of bunches using all balloon is 48, using purple ballon is 27

Step-by-step explanation:

Given:

Let x=34 miles

y=44 miles

\(\frac{dy}{dt}=41 miles/hr\)

To find:

\(\frac{d\theta}{dt}\)

Solution:

\(Hypotenuse=\sqrt{(base)^2+(Perpendicular\;side)^2}\)

Using the formula

\(Hypotenuse=\sqrt{(34)^2+(44)^2}=55.6 miles\)

\(sec\theta=\frac{Hypotenuse}{Base}\)

Using the formula

\(sec\theta=\frac{55.6}{34}\)

\(tan\theta=\frac{Perpendicular\;side}{Base}\)

Using the formula

\(tan\theta=\frac{y}{34}\)

Differentiate w.r.t t

\(sec^2\theta\frac{d\theta}{dt}=\frac{1}{34}\frac{dy}{dt}\)

Using the formula

\(\frac{d(tanx)}{dx}=sec^2 x\)

Substitute the values

\((\frac{55.6}{34})^2\times \frac{d\theta}{dt}==\frac{1}{34}\times 41\)

\(\frac{d\theta}{dt}=\frac{41\times (34)^2}{34\times (55.6)^2}\)

\(\frac{d\theta}{dt}=0.45 rad/hour\)

Answer:

Step-by-step explanation:

sum of 3 numbers = 57

let

the numbers be x, y and z.

x + y + z = 57

let z be the largest and x be the smallest.

z - x = 47

x+y = 16

Answer:

7

Step-by-step explanation:

42/6=7

Hi! Your answer is q = -9

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

Since we want to solve for q-term. That means we are going to isolate q-term.

\(\huge{3q+4+9=-14}\)

We can add 4 and 9 together.

\(\huge{3q+13=-14}\)

Because we want to know the value of q. That means we have to isolate q-term by subtracting both sides by 13.

\(\huge{3q+13-13=-14-13}\\\huge{3q=-27}\)

We are reaching to the final step where we divide the whole equation by 3.

\(\huge{\frac{3q}{3}=-\frac{27}{3}}\\\huge{q=-9}\)

Finally, the solution for this equation is q = -9. But what if you are not certain or sure about the answer? Let's check it out!

To check the answer, simply substitute q = -9 in the equation.

\(\huge{3q+4+9=-14}\\\huge{3(-9)+13=-14}\\\huge{-27+13=-14}\\\huge{-14=-14}\)

Notice that the equation is true for q = -9. Hence, we can conclude that the solution for this equation is q = -9.

Hope this helps!

The volume of the reduced globe is 523.3 in³ .

Given,

Diameter of globe = 20 inches .

Now,

The volume of a sphere is equal to

V = 4/3 ×π×r³

we have

r = d/2

the radius is half the diameter

Substitute,

The volume of the original globe is

V = 4/3 × π × 10³

V = 4186.7 in³

step 2

If the dimensions of the globe were reduced by half,

then

The new radius is equal to

r = 10/2

r = 5 in

The volume of the reduced globe is

V = 4/3 ×π × 5³

V = 523.3 in³

therefore

The volume of the reduced globe is  523.3 in³

Compare the volumes

4186.7 in³ /   523.3 in³

= 8

Remember that

If two solids are similar, then the ratio  of its volumes is equal to the scale factor elevated to the cube.

The scale factor is 1/2

so

(1/2)³ = 1/8

Hence,

The original globe is eight times the volume of the reduced globe

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I'm not that good at explaining but here are my answers:

1- 170

2-340

3- 9 months for $140 and 14 months for $190

4- 10

5-If the x (or months savings) goes up or down, so does the y (or account balance)

6- 70y +20n= 2x

explanation:

1- 150 + 20 = 170

2- 170*2= 340

3-the number always goes up by 20, if it's something like an uneven number, let's say 3, which is after 2, add 10.  

4- can't explain this, I used a calculator

5- i don't think I have to explain

6- I don't know, I just took a random equation and "plugged in" the numbers from the equation I was working on.

0(zero) crates weigh more than 99. 5 pounds.

The distance between the median and the third quartile on the plot is equal to the interquartile range,

IQR.IQR = Q3 − Q1

Using the values given in the plot:

Q1 = 99.5Q3

     = 143IQR

     = 143 − 99.5

     = 43.5

The upper bound of the plot can be determined by adding 1.5 times the interquartile range to the third quartile.

UPPER = Q3 + 1.5(IQR)

UPPER = 143 + 1.5(43.5)

UPPER = 209.25

Since the upper bound of the plot is 209.25, any crate weighing more than 209.25 pounds is an outlier, which means that all crates on the plot are within the reasonable range.

To determine the number of crates weighing more than 99.5 pounds, we need to look at the box-and-whisker plot again.

We can see that the crate's weight starts at 84 and ends at 170.

So, we need to determine how many crates weigh more than 99.5 pounds, which is the third value on the plot.

From the plot, we can see that 170 is the largest weight and the next-largest weight is 143, which is less than 170.

Thus, there are no crates weighing more than 170 pounds.

Therefore, the number of crates weighing more than 99.5 pounds is the same as the number of crates weighing more than 143 pounds.

This means that no crate weighs more than 99.5 pounds. So the answer is 0.

There are zero crates weighing more than 99.5 pounds, and this can be written as 0 in numerals. This answer can be verified by looking at the plot.

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180|                               |                                              |                                            |                             |

     |                               |                                              |                                            |                             |

     |                               |                                              |                                            |                             |

     |                               |_____________________|                                            |                             |

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     |                               |_____________________|                                            |                              |

     |                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

     |                               |                                              |____________________|                              |

     |                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

140|                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

120|                               |                                              |                                            |                              |

     |                               |                                              |                                            |                              |

     |______________|_____________________|____________________|______________|

  80            100                                                      120                                       140                        160

Therefore, the number of crates is 0.

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Answer:

200 times

Step-by-step explanation:

6 * 10^-6= 0.000006

3*10^-8= 0.00000003

0.000006/0.00000003= 200

Answer:

your dad is never coming back

Step-by-step explanation:                                                
$3 milk                                                      |
x= distance                                               |
                                                                  |
                                                   _______|________________
y= time                                                     o                                   |
                                                             home                    grocery store
f(x)= | 3/x |        
lim
x ➔ o
 f (x)               now thats your answer bye give credits >:)                                                

The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t

Number of chocolate violet eats each night = 4

Number of chocolate originally in the box = 24

Number of chocolate remaining = C

Number of days after violet birthday = t

Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)

C = 24 - (4 × t)

C = 24 - 4t

In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t

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Answer:

105

Step-by-step explanation:

You need to find the unit rate which is 10.50$. Then you would multiply it by 10.

Answer:

35.5 pounds or less

Step-by-step explanation:

99.7% is a z score of 2.75

(x - 30)/2 = 2.75

x - 30 = 5.5

x = 35.5

Answer:

yeah it is bcoz if x is -1 then x+1 will be

-1+1 which is 0 and ur whole equation will say

now thats a lot of damage

Answer:

7i

Step-by-step explanation:

√-49= √-1*7²= 7√-1= 7i

Answer:

7i

Step-by-step explanation: