Model 3: Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and . A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart. 8. Algebraically determine the x -value of where the beam should be placed. (15 points) 9. Explain where to place the beam. (10 points)

Answers

Answer 1

Answer:

The beam should be placed 8 feet from the center.

Step-by-step explanation:

According to the Question,

Given That, Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region.Again, using the center of the half-circle as the origin, the struts are modeled by the equations y=x+8 and y=x-4. A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart. Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.

The struts are y = √(x + 8) and y = √(x − 4).  The struts are 2 feet apart at the location of the beam:

thus, √(x + 8) − √(x − 4) = 2  

on Solving we get,

√(x + 8) = 2 + √(x − 4)

x + 8 = 4 + 4√(x − 4) + x − 4

8 = 4√(x − 4)

2 = √(x − 4)

x − 4 = 4

x = 8


Related Questions

Math a challenging subject, sigh...

Answers

1340+160=1500
1500-300=1200
100x7=700
1200-700=500
he has $500 left to pay.

i don’t understand this at all

Answers

Answer:

use the pythagorean theorem

Step-by-step explanation:

a²+b²=c²

okay so a triangle has 3 sides. right now you’re given the lengths of 2 of them. to find the 3rd length you have to put it into an equation which is a2+b2=c2. side C is the hypotenuse (the longest side on a triangle). since, you only have side A and C you need to use c2-a2=b2. in your case it would be 12^2-6^2=c2. 144-36=108. to find the actual length of the side you need to find the square root of 108 which is 6/3 (/ is the square root symbol).

if you need a deeper explanation or more help just message me :))

please help! urgently

Answers

Answer:

sinC = [tex]\frac{4\sqrt{41} }{41}[/tex]

Step-by-step explanation:

We require to find the side DE before finding sinC

Using Pythagoras' identity in the right triangle

DE² + CE² = CD²

DE² + 5² = ([tex]\sqrt{41}[/tex] )²

DE² + 25 = 41 ( subtract 25 from both sides )

DE² = 16 ( take the square root of both sides )

DE = [tex]\sqrt{16}[/tex] = 4 , then

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{DE}{CD}[/tex] = [tex]\frac{4}{\sqrt{41} }[/tex] , rationalise the denominator

sinC = [tex]\frac{4}{\sqrt{41} }[/tex] × [tex]\frac{\sqrt{41} }{\sqrt{41} }[/tex] = [tex]\frac{4\sqrt{41} }{41}[/tex]

What is the nth term rule of 7,9,11,13,15

Answers

The answer is twenty three

Answer:

[tex]a_{n}[/tex] = 2n + 5

Step-by-step explanation:

There is a common difference between consecutive terms, that is

9 - 7 = 11 - 9 = 13 - 11 = 15 - 13 = 2

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 7 and d = 2 , then

[tex]a_{n}[/tex] = 7 + 2(n - 1) = 7 + 2n - 2 = 2n + 5

Given the general form of the sinusoidal function, y = AsinB(x - C) + D, match the following items.

Answers

Answer:

[tex]\Delta y = A[/tex] (Amplitude) (Correct answer: 1)

[tex]\omega = B[/tex] (Angular frequency) (Correct answer: 2)

[tex]x_{o} = C[/tex] (Phase shift) (Correct answer: 3)

[tex]y_{o} = D[/tex] (Vertical shift) (Correct answer: 4)

[tex]\frac{2\pi}{\omega} = \frac{2\pi}{B}[/tex] (Period) (Correct answer: 5)

Step-by-step explanation:

The general form of a sinusoidal function is represented by the following characteristics:

[tex]y = \Delta y \cdot \sin \omega\cdot (x- x_{o}) + y_{o}[/tex] (1)

Where:

[tex]\Delta y[/tex] - Amplitude.

[tex]\omega[/tex] - Angular frequency.

[tex]x_{o}[/tex] - Phase shift.

[tex]y_{o}[/tex] - Vertical shift.

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

In addition, we know that the period associated with the sinusoidal function ([tex]T[/tex]) is:

[tex]T = \frac{2\pi}{\omega}[/tex]

By direct comparison, we get the following conclusions:

[tex]\Delta y = A[/tex] (Amplitude) (Correct answer: 1)

[tex]\omega = B[/tex] (Angular frequency) (Correct answer: 2)

[tex]x_{o} = C[/tex] (Phase shift) (Correct answer: 3)

[tex]y_{o} = D[/tex] (Vertical shift) (Correct answer: 4)

[tex]\frac{2\pi}{\omega} = \frac{2\pi}{B}[/tex] (Period) (Correct answer: 5)

The following equation 3(2x - 1) = 6(1 + 1) has infinite solutions True False​

Answers

Answer:

False

Step-by-step explanation:

3(2x - 1) = 6(1 + 1)

Distribute

6x -3 = 6(2)

6x -3 = 12

Add 3 to each side

6x  =15

x = 15/6

There is one solution

Answer:

False.

Step-by-step explanation:

3(2x - 1) = 6 (1+1)

3*2x - 3*1 = 6*2

6x - 3 = 12

Add 3 to both side

6x = 12+ 3

6x = 15

Divide both sides by 6

x = 15/6

x = 2.5

This equation has one solution

pls help due in 10 mins

Answers

Answer:

Area = 97.4 cm²

Step-by-step explanation:

a = 15 cm

        [tex]Area = \frac{ \sqrt 3}{4} a^2\\[/tex]

                 [tex]=\frac{\sqrt 3}{ 4 } \times 15^2\\\\=\frac{\sqrt 3}{ 4 } \times 225\\\\= 97.4 \ cm^2[/tex]

-x+2y=11 on a graph plz help

Answers

Answer:

Hope this helps.

help me find the size of the rhombus :)

Answers

Answer:

Step-by-step explanation:

The diagonals of a rhombus divides it into four congruent right triangles.  Each triangle is a mirror image of the adjacent.

Therefore angle 2 is the alternate interior angle of 57°, and angle 3 is the mirror image, so also 57°.

Angles 1 is the complement of angle 3, and angle 4 is equal to the complement of angle 2 , so both equal 90-57 = 33°.

To summarize,

angle 1 = 33°

angle 2 = 57°

angle 3 = 57°

angle 4 = 33°

What is the following sum?
4.5+2V5
O 6.10
O 8/10
O ENG
O ONE

Answers

Answer:

[tex]6 \sqrt{5} [/tex]

Step-by-step explanation:

Take out Square root 5 as common and then add numbers

[tex]4 \sqrt{5} + 2 \sqrt{5} \\ 6 \sqrt{5} [/tex]


Which term best describes a major arc of a circle that has the same starting
and ending point?
A. Diameter
B. Chord
O
C. Radius
D. Circumference

Answers

Answer:

Circumference! it's the major arc whose starting and ending point coincide.

PLEASE HELP BRAINLIEST!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Simplify and leave in radical form.

Answers

Answer:

[tex] { ({x}^{2}. {y}^{6} )}^{ \frac{1}{8} } \\ {x}^{2 \times \frac{1}{8} } . {y}^{6 \times \frac{1}{8} } \\ = {x}^{ \frac{2}{8} } . {y}^{ \frac{6}{8} } \\ = {x}^{ \frac{1}{4} } . {y}^{ \frac{3}{4} } [/tex]

Please help me
How many solutions does the equation
1-(6x - 4) = 3(1 – x) have?

Answers

Answer: one solution

this is all i know

Answer:

D

Step-by-step explanation:

Given

1 - [tex]\frac{1}{2}[/tex] (6x - 4) = 3(1 - x) ← distribute parenthesis on both sides

1 - 3x + 2 = 3 - 3x

3 - 3x = 3 - 3x

Since both sides of the equation are the same , then

This indicates the equation has infinitely many solutions.

A grocery store sells a bag of 4 oranges for $2.84. If arianna spent &3.55 on oranges, how many did she buy?

Answers

Answer:

5 dollors i just tookthe test 4

Step-by-step explanation:

Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.

To find out how many oranges Arianna bought, we can use the given price of a bag of 4 oranges and the total amount she spent on oranges.

Let's set up a proportion:

Price of a bag of 4 oranges = $2.84

Amount Arianna spent on oranges = $3.55

Let "x" be the number of bags of oranges Arianna bought.

Since each bag contains 4 oranges, the total number of oranges she bought is 4 times the number of bags (4x).

Now, we can set up the proportion:

(Price of a bag of 4 oranges) / (Amount spent on oranges) = (Number of bags bought) / 4x

$2.84 / $3.55 = 1 / 4x

To solve for "x," cross-multiply:

$2.84 * 4x = $3.55 * 1

11.36x = 3.55

Now, solve for "x":

x = 3.55 / 11.36

x ≈ 0.3125

Since we can't buy a fraction of a bag, we round the value of "x" to the nearest whole number:

x ≈ 0 (rounded to the nearest whole number)

So, Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.

To know more about oranges:

https://brainly.com/question/28969541

#SPJ3

Please help I don’t know how to do this

Answers

Step-by-step explanation:

I cannot see all the answer options.

square garden, side length x.

area = x² (or x×x)

new area r = (x-p)(x+q) = x² - px + qx - pq =

= x² + (q - p)x - pq

3D printer. costs p in general.

makes x figurines.

material per figurine costs q.

costs per figurine r = q + p/x

as the printer costs themselves need to be distributed equally across all produced figurines.

investment account. q% pretty year.

p dollars starting balance.

letting it sit for x years.

a0 = p

a1 = a0 + a0×q/100 = a0 × (1 + q/100)

a2 = a1 + a1×q/100 = a1×(1 + q/100) = a0×(1 + q/100)²

a3 = a2 + a2×q/100 = a2×(1 + q/100) = a0×(1 + q/100)³

...

ax = a0×(1 + q/100) to the power of x =

= p × (1 + q/100) to the power of x

account without interest. p dollars are already in it.

adding q dollars every month for x months.

balance after these x months

r = x×q + p = q×x + p

100 students are interviewed to see which of biology, chemistry or physics they prefer.
57 of the students are girls. 34 of the girls like biology best.
27 of the boys prefer physics.
20 out of the 28 who prefer chemistry are girls.
What percentage of the students prefer biology?

Answers

Step-by-step explanation:

everything can be found in the picture

For the equation 3(7 + 2) = 3x + k, what value of k will create an equation with infinitely many solutions?
A)7

B)21

C)10

D)3​

Answers

Answer:

ygftyhhhhgffyujhhgyjjjhhguj

This would be C.


Mark me brainlest if this work!!

what is the width of a rectangle if the length is 5cm

Answers

Answer:

it's can be anything from 1 to infinite.

If the length is 5 cm longer than the width, then l = w + 5. The width of this rectangle is 7.5 cm.

what is 3.78 × 10 ²=

Answers

Answer:

3.78 × [tex]10^{2}[/tex] = 378

Step-by-step explanation:

Find the sum of the first terms of the sequence

Answers

Answer:

-4+8+-16+32+-64+128 = 84

Step-by-step explanation:

The fifth and sixth terms are -64 and 128

84 for sum of first 6terms

When an electron is removed the atom gets a ( ) Charge .

Answers

Answer:

positive charge...............

Order the list of numbers from least to greatest.

Answers

Answer:

0, 0.5, 8/3, root 5, 3.1

help i need this asap

Answers

Answer:

The minimum is -4

Step-by-step explanation:

The minimum is the lowest point on the parabola

It is at (-3,-4)

The y value is the minimum of the function

The minimum is -4

what number is not a perfect square

Answers

Answer:

1 -1

2-4

3-9

4-16

5-25

6-36

7-49

8-64

9-81

10-100

11-121

12-144

Those are the first 12

Step-by-step explanation:

In your English class you are given a list of 12 books you want to choose three books to read over the summer how many groups of three books are available from the list of 12

Answers

Answer:

4

Step-by-step explanation:

A pair of fair dice each numbered 1 to 6 is tossed . Find the probability of a score of :
i. two odd numbers.
ii. a sum of 8 or a sum of 12.
ii. both prime or both odd numbers.

Answers

Answer:

i)

Odd numbers:

1, 3, 5 - 3 options of 6

P(odd and odd) = 3/6*3/6 = 1/4

ii)

Total outcomes:

6*6 = 36

Sum of 8:

2 + 6, 3 + 5, 4 +4, 5 + 3, 6 + 2 - 5 options

Sum of 12:

6 + 6 = 12 - 1 option

P(8 or 12) = 5/36 + 1/36 = 6/36 = 1/6

iii)

Prime numbers:

2, 3, 5 - 3 options of 6

Odd numbers:

1, 3, 5 - 3 options of 6

P(prime or odd) = 3/6*3/6 + 3/6*3/6 = 1/4 + 1/4 = 1/2

Jackie burns 250 calories per hour doing aerobics. She has to burn 3500 calories
to lose one pound. How long will Jackie have to work out to lose 5 pounds?

Answers

Answer:

70

Step-by-step explanation:

she burns 250 calories per hour .to burn 3500 calories and shed 1 pound she has to work 14 hours and to shed 5 pounds she has to work 14×5=70 hours

Which numbers are a distance of 6 units from 2 on the number line? Select the location on the number line to plot each point.
-5 -4 -3 -2 -1 0 +EEE 4 5 6 7 8 9 10 1 2 3​

Answers

Answer:

We reach at 8.

Step-by-step explanation:

The starting point is 2 .

Jump at the six places, the final point reaches at 8, so the point is 8.

help please asap!!! working too please not just the answers!!​

Answers

Answer:

Area = 4600m

explanation: I worked it out in the image attached if that helps let me know if you need a more in depth explanation step by step

Answer:

244280

Step-by-step explanation:

you divide it into three rectangles so you have three diffenet products of 6480+57800+180000 to get 244280

3 vertices of a parallelogram ABCD are shown in the applet. What are the coordinates of point D?
Need ASAP

Answers

Answer:

D   (0, 3)

Step-by-step explanation:

To go from B (8, 3) to C (3, 8)

subtract 5 from x, add 5 to y

A (5, -2)

subtract 5 from x,   x = 0

add 5 to y,   y = 3

D (0, 3)

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