Mathematics College

Noelle stands at the edge of a cliff and drops a rock. The height of the rock, in meters, is given by the function f(x)=−4.9x2+17 , where x is the number of seconds after Noelle releases her rock.

Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock, in meters, is given by the function g(x)=−4.9x2+13x , where x is the number of seconds after he releases his rock.

There is a moment when the rocks are at the same height.

What is this height?

Answers

Answer 1
For this case what we must do is to equal both functions at the moment in which it is to find the result.
 We have then:
 f (x) = g (x)
 -4.9x2 + 17 = -4.9x2 + 13x
 Clearing x we have:
 17 = 13x
 x = 17/13
 x = 1.31 s
 Then, to find the height, with respect to the floor we have:
 g (1.31) = - 4.9 * (1.31) ^ 2 + 13 * (1.31)
 g (1.31) = 8.62
 Answer:
 The height with respect to the ground is:
 8.62 m
Answer 2

Answer: 8.62 meters

Step-by-step explanation:

Given: The height of the rock, in meters, is given by the function [tex]f(x)=-4.9x^2+17[/tex] , where x is the number of seconds after Noelle releases her rock.

The height of Cesar’s rock, in meters, is given by the function [tex]g(x)=-4.9x^2+13x[/tex] , where x is the number of seconds after he releases his rock.

The moment when the rocks are at the same height  then f(x)= g(x)

[tex]\Rightarrow-4.9x^2+17=-4.9x^2+13x\\\\\text{Add }-4.9x^2\text{ ion both sides, we get}\\\\\Rightarrow\ 17=13x\\\\\Rightarrow\ x=\frac{17}{13}\\\\\Rightarrow\ x=1.3076[/tex]

To calculate height put x in first equation, we get

[tex]-4.9(1.3076)^2+17=8.62189\approx8.62[/tex]

Hence, the height = 8.62 meters

Related Questions

Using synthetic division, find the quotient Q(x) and the remainder R if the polynomial P(x) = x3 − 2x2 − 3x + 18 is divided by (x + 2).

Answers

Answer:

quotient: x^2 - 4x + 5
remainder: 8

Explanation:

1) Given

p(x) = x^3 - 2x^2 - 3x + 18
divisor: x + 2

2) Write the coefficients of p(x) in order:

1       -2        -3      18

3) dividing by x + 2 => run the division  for x = - 2

4) division

     | 1     -2     -3     +18
     |
 -2 |       -2     +8     - 10
-----------------------------------
      1     -4     +5      +8

The last digit is the remainder, the others are the coefficients of the quotient:

=>

quotient = x^2 - 4x + 5
remainder = 8

The quotient Q(x) is found to be x² - 4x - 11 and the remainder R is 4.

The question involves using synthetic division to find the quotient Q(x) and the remainder R when the polynomial P(x) = x³ − 2x² − 3x + 18 is divided by (x + 2).

To perform synthetic division, we first write down the coefficients of P(x): 1, -2, -3, and 18. The divisor is (x + 2), so we use -2 for the synthetic division.

Write the coefficients of P(x): 1, -2, -3, 18.

Write the root of the divisor (x + 2) = -2 on the left side of the synthetic division setup.

Bring down the first coefficient (1).

Multiply -2 by 1, place the result (-2) under the second coefficient (-2), and add the two numbers yielding -4.

Repeat the multiplication and addition process for the rest of the coefficients.

The results of the synthetic division process give us the coefficients of the quotient Q(x) and the remainder R.

In performing the synthetic division, we find that the quotient Q(x) is x² - 4x - 11 and the remainder is R = 4.

simplify the complex fraction

Answers

pl see the attachment
the final answer is (y+z)/(y-z)

A geometric sequence is shown below : 2/3,2,6,18.. write the explicit formula

Answers

so we know this is a geometric sequence, meaning it has a multiplier, or a "common ratio".

now, we get the next term's value by simply multiplying the current term's value by the common ratio, so if we just divide any of the terms by the term before it, the quotient will just be the common ratio.

18/6 is just 3, so there you have it, and we know the first term is 2/3.

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=3\\ a_1=\frac{2}{3} \end{cases}\implies a_n=\cfrac{2}{3}\cdot 3^{n-1}[/tex]

3^2•3^n simplifies to 3^20 what is the value of the exponent n?

Answers

Given that:
[tex]3^2 \times 3^n = 3^20 [/tex]
Solving for n.
Divide both sides by 3²
[tex] \frac{3^2 \times 3^n}{3^2} = \frac{3^{20}}{3^2} [/tex]
Simplify
[tex]3^n= 3^{20-2} \\ 3^n=3^{18} \\[/tex]
[tex]if \ a^{f(x)}=a^{g(x)} , \ then \ f(x)=g(x)[/tex]
So, n=18

Answer: n=18

Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = <1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =

Answers

Answers: 

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t> 
- parametric equations:   
      x = 1 + 6t
      y = -1 + 7t
      z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
   = (7,6,1) - (1,-1,7)
v  = (6, 7, -6)

The vector equation of the line is given by

[tex]r(t) = v_0 + tv[/tex]

Where

[tex]v_0[/tex] = a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by

[tex]r(t) = v_0 + tv \\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle \\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle \\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }[/tex]

In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by 

[tex]r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle[/tex]

The parametric equations of the line are given by:

[tex]x(t) = 1 + 6t \\y(t) = 1 + 7t \\z(t) = 7 - 6t[/tex]


Final answer:

The vector equation for the line segment joining the points p(1, -1, 7) and q(7, 6, 1) is r(t) = <1+6t, -1+7t, 7-6t> and the corresponding parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.

Explanation:

To find the vector and parametric equations for the line segment joining two points p(1, -1, 7) and q(7, 6, 1), we first need to understand that the vector equation for a line segment in space is given by r(t) = p + t (q - p), where 0 ≤ t ≤ 1, and p and q are the coordinates of the points. The parametric equations are obtained by expressing the x, y, and z coordinates of r(t) as individual functions of t.

Substituting the given points into the vector equation we get: r(t) = <1+6t, -1+7t, 7-6t>. Then, the corresponding parametric equations will be x(t) = 1 + 6t, y(t) = -1 + 7t, and z(t) = 7 - 6t.

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The region r is bounded by the parabola y = x2 and the line y = 4. set up definite integrals to find the moment mx of r about the x-axis and the area a of the region r. then find (x, y )

Answers

Consider this option:
Volume is 256π/5, area is 32/3.
Details are in the attachment.
P.S. intersection points are (-2;4) and (2;4).

Shelly has a photo that is 7 1/3 inches tall. she wants to shrink it down to fit in a picture frame that is only 5 1/3 inches tall. the photo shop can only reduce photos by certin fractions. they can reduce it to 2/3 the original size, 3/4 the original size, or 5/9 the original size. which reduction should she use so the picture fills as much of the frame as possible, without being too large?

Answers

we know that 

the photo is 7 1/3 inches tall-----> 7 1/3=(7*3+1)/3=22/3 in ----- > (7.33 in)
the picture frame  is 5 1/3 inches tall--> 5 1/3=(5*3+1)/3=16/3 in----> (5.33 in)

a) case A reduce 2/3 the original size------> (22/3)*(2/3)=44/9 in-----> (4.89 in)

b) case B reduce 3/4 the original size---> (22/3)*(3/4)=66/12 in-----> (5.5 in)
this is not solution because 66/12 (5.5 ) in >16/3 (5.33) in ( picture frame)

c) case C reduce 5/9 the original size---> (22/3)*(5/9)=110/27 in-----> (4.07 in)

the answer is the case A reduce 2/3 the original size----> 44/9 in  (4.89 in)

A slice is made perpendicular to the base of a right rectangular prism as shown.
What is the area of the resulting two-dimensional cross section?
Drag and drop the answer into the box.

mm²
48
28
84
144
16

Answers

Answer:

The correct option is 1. The area of cross section area is 48 mm².

Step-by-step explanation:

From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.

The area of a rectangle is the product of its dimensions.

[tex]A=l\times w[/tex]

Where, l is length of the rectangle and w is width of the rectangle.

The area of cross section is

[tex]A=4\times 12[/tex]

[tex]A=48[/tex]

Therefore the area of cross section area is 48 mm². Option 1 is correct.

A math test took 50 minutes to complete. The test ended at 3:55. What time did the test begin?

Answers

The test started at 3:05 if it ended 50 minutes later at 3:55

A math test ended at 3:55 and it took 50 minutes to complete. What time did the math test start?

The math test started at 3:05.

If we know that the math test ended at 3:55 and lasted 50 minutes, we can subtract 50 minutes from 3:55 and we will get an answer of 3:05.

Therefore, the math test started at 3:05.

A cookie recipe states for every 3 cups of flour, 1 1/2 teaspoons of vanilla are needed. How many teaspoons are needed for 5 cups of flour?

Answers

3 / 1½ = 2 cups of flour per teaspoon

2x = 5
divide both sides by 2 to isolate x

x = 2.5

You need 2.5 teaspoons of vanilla for 5 cups of flour.

Why do clouds tend to form around 3:00 pm and 6:00 am

Answers

During daytime, the sun heats the land and warms the air that rises. That lowers the pressure, causing a gradient force to bring air from the colder sea. The wind is then onshore. Small cumulus clouds form over the land, often following the coastline very closely 

Alicia buys a 5 pound bag of rocks for fish tank. She uses 1 1/8 pounds for a small fish bowl. How much is left

Answers

Hello,

Here is your answer:

The proper answer to this question is "4".

Here is how:

First convert the mix number into a fraction:

1 1/8=9/8

5*8=40
1*8=8
-
9*1=9
8*1=8

40-8=32

32/8=4
8/8=1

Which means your answer is 4/1 or 4!

If you need anymore help feel free to ask me!

Hope this helps!

Please help me with this question

Answers

Try this option:
1. S=12²-10²=44 sq. ft.
2. S=10*12-6*8=120-48=72 sq. ft.

answers: 1-C; 2-C.

6 Bands were going to play at a concert. How many ways can the concert manager send them on stage?

Answers

Try this option:
there are two ways to resolve this task:
1. the 1st in this sequence is for 6 bands, the 2d in this sequence is for 5 rest bands, the 3d in this sequence is for 4 rest bands, the 4th in this sequence is for rest 3 bands, the 5th in this sequence is for rest 2 bands and the 6th in this sequence is for the last 1 band. Using the logical rule 'AND': A=6*5*4*3*2*1=720.
2. According to arrangement rules it is the formula: A=n!, where n - number of bands.
A=6!=720.

answer: 720.

 and  are similar. Find the value of x. A. 5 B. 15 C. 60 D. 240

Answers

Dude we need to actualy see the question all we see is find the value of x but we don't know our other value?

EXPERTS/ACE/GENIUSES

Answers

the answer would be D

find the product 3012 and 4

Answers

product is multiplying, so it is 3012*4 which equals 12048
753. Its hard to show long division with out a paper, but if you remember divide, multiply and subtract, bring it all down and bring it all back, you'll be good. There is a really good video online to help remember it, but with this specific problem, 4 ends up going into 3012, 753 times.

Can somebody please help me out ?

Answers

The area of a triangle is:
 A = (1/2) * b * h
 Where
 b: base
 h: height.
 For the lower triangle we have:
 A = (1/2) * (10) * (root ((8) ^ 2- (5) ^ 2))
 A = 31 in ^ 2
 We add this area with the area of the upper triangle:
 31 in ^ 2 + 17 in ^ 2 = 48 in ^ 2
 Answer:
 The quadrilateral area will be:
 48 in ^ 2 (option 3)

Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?

Answers

If the ratio from Kala to Rose is 4:1, then for the 48 words Rose typed Kala typed 192 words. 48*4=192
Then Lita types twice as fast so 192*2=384.
It should be 384 words.

plz help ill give u branlist

Answers

Remember complementary sum is 90
so...
48 + 7(x + 1) = 90
7(x + 1) = 42
x + 1 = 6
x = 5

how to do this 24:96 = 5:?

Answers

Um... I think you meant 24:96 = 5:x

In that case, x=20


A square playground has an area of 175 m2. What is the approximate length of each side of the playground? Round your answer to the nearest meter

Answers

We know that the area of a square = side &sup2;

Therefore, for a known area A, the side length is
side = &radic; (area)
= &radic; (175) 
= 13.2288  (to 4 places of decimals).

If the area of a square playground is 175 [tex]m^{2}[/tex] then the approximate length is 13 meters.

What is square?

A square is a two dimensional figure having four vertices, four edges, four angles and all the sides are equal to each other. The perimeter is equal is equal to 4*side and the area is side*side.

How to find side of square?

We have been given the area of the square playground equal to 175 meter square. We know that the area of a square is side*side means [tex]side^{2}[/tex].

Put the value of 175 equal to side square and we will get the value of slide.

Area =[tex]side^{2}[/tex]

175=[tex]side^{2}[/tex]

side=[tex]\sqrt{175}[/tex]

Side=13.22m

If we round to nearest meter then it will be equal to 13m.

Hence if the area of a square playground is 175 meter square then the side will be equal to 13m.

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At noon, ship a is 60 km west of ship
b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?

Answers

dA/dt=15 km/h and dB/dt=5 km/h
base of our triangle if drawn is 60 km
to find dD/dt when t=4 hours we shall have:

(A+B)²+60²=D²
d/dt[(A+B)²+60²]=d/dt(D²)
[d(A+B)]/dt*2(A+B)(2)=dD/dt*2D
B=5km/h*4hr=20km
A=15km/hr*4=60km
20²+60²=D²
D=√4000

(15+5)*(2)*80*(2)=2*√4000*dD/dt
dD/dt=6400/√4000=101.192 km/hr

The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.

Therefore, from the below triangle, we have

[tex]\frac{dx}{dt} = 20 \text{  km/hr}[/tex]

Let the distance between the ships is y. On applying Pythagorous theorem, we have

[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]

On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]

[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]

Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have

[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]

On substituting the value in above, we get

[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]

[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]

Therefore,  the distance between the ships changing at a rate of 16 km/hr at 4:00 pm

The Bureau of Justice Statistics reports that the number of Americans on probation increased 76% from 1980 to 1995 and that 3.09 million Americans were on probation in 1995. If the rate of increase continues in the same way for the next 15-year period, what might be the number of Americans on probation in 2010?

Answers

For this case, what we are going to do is first define variables.
 x: current number of Americans.
 y: number of Americans after the next 15 years.
 We now write the expression to model the problem, assuming:
 "the rate of increase continues in the same way for the next 15-year period".
 We have then:
 y = 1.76 * x
 y = 1.76 * (3.09)
 y = 5.44 million Americans
 Answer:
 the number of Americans on probation in 2010 might be:
 y = 5.44 million Americans

how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% compounded quarterly

Answers

To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula: [tex]A=P(1+rt)[/tex]
  where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment 
  [tex]r[/tex] is the interest rate in decimal form 
  [tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex], so lets replace those values in our simple interest formula to find [tex]A[/tex]:
[tex]A=5000(1+(0.04)(5))[/tex]
[tex]A=5000(1.2)[/tex]
[tex]A=6000[/tex]

Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
  where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment 
  [tex]r[/tex] is the interest rate in decimal form
  [tex]n[/tex] is the number of times the interest is compounded per year
  [tex]t[/tex] is the time in years 
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex]. Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded [tex] \frac{12months}{4months} =3[/tex] times per year, so [tex]n=3[/tex]. Now that we have all the vales, lets replace them in our formula:
[tex]A=5000(1+ \frac{0.04}{3} )^{(3)(5)} [/tex]
[tex]A=5000(1+ \frac{0.04}{3} )^{15} [/tex]
[tex]A=6098.95[/tex]

now that we know the final amounts of our investments, lets find how much difference is between them: 
[tex]6098.95-6000=98.95[/tex]

We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.

The prism is completely filled with 1750 cubes that have edge length of 1/5 feet. What is the volume of the prism,

Answers

we know that
the volume one cube=(1/5)*(1/5)*(1/5)=(1/125) ft³
the volume of prism=1750*(1/125)=14 ft³

the answer is 14 ft³

What is 3^2/3 equal to? A.3√9 B.2√9 C.3√27 D.2√27

Answers

[tex] a^{\frac{m}{n}} = \sqrt[n] {a^m} [/tex]

[tex] 3^{\frac{2}{3}} = \sqrt[3] {3^2} = \sqrt[3] {9} [/tex]

53b−7b−6b+1 if b=25
Please help me with this problem! And what is the simplified expression?

Answers

Answer: 1001

B/c i said so

can someone please help me with this equation? thank you.

Answers

I found it simplest to start with the given line in standard form. That is
.. x +2y = 3 . . . . . . . . divide the given equation by 3

Now, the perpendicular line is easily written as
.. 2(x -(-4)) -(y -2) = 0 . . . . . swap x, y coefficients, negate one. Translate to the given point

Simplifying, we have
.. 2x -y +10 = 0
Solving for y gives
.. y = 2x +10 . . . . . . . . . . . . corresponds to selection B

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answers

The direction and magnitude can be found by summing the x- and y-components of each force.
It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65

Force  angle     x-component          y-component
25       30         25cos(30)=21.65    25sin(30)=12.5
30       100       30cos(100)=-5.21   30sin(100)=29.54
Total                Fx=16.44                 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 &deg;
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds
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