please help quickly !

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

4a+2b+c = 72 ...2

49a+7b+c = 27 ...3

Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

-9 + b = 9

b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

-3+18+c = 63

15+c = 63

c = 48

a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

ii) If the height of the cliff is modelled by the equation  s(t)=at²+bt+c

The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

t² - 6t - 16 =0

t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

Answer:

9 recipientes

Step-by-step explanation:

Para empezar, tenemos que encontrar a cuánto equivalen 3/4 partes de 6 litros.

Para poder hacer esto, multiplicamos:

[tex](6)(\frac{3}{4})= \frac{18}{4} =\frac{9}{2}=4\frac{1}{2}[/tex]

Por lo tanto, el garrafón tiene 4.5 litros de agua.

Ahora, vamos a dividir esta agua en recipientes de 0.5 litros, por lo tanto, vamos a hacer una división:

4.5 ÷ 0.5 = 9

Por lo tanto, se van a poder llenar 9 recipientes.

Answer:

xy and bc is parallel

70 degrees

Step-by-step explanation:

a) it's a rule

b) since angle xbc is 55 degrees, angle xcb must also be 55 degrees as it's a isoceles triangle. then you would take 180 degrees to subtract the sum of angle xcb and xbc which would give you 70 degrees

Answer:

1.) 5 cm

2.) 4 cm

3.) 5 cm

Step-by-step explanation:

1.) LxWxH=V

8(W)(2)=80

16W=80

W=5 cm

2.)4(3)(H)=48 cm

12H=48cm

H=4cm

3.)L(5)(5)=125

25L=125

L=5 cm

Answer:

1. Width of 5

2. Height is 4

3. Length is 5

Step-by-step explanation:

1. LxWxH

8x2 = 16

16x5 = 80

2. LxWxH

4x3 = 12

12x4 = 48

3. LxWxH

5x5 = 25

25x5 = 125

Answer:

have no idea lol im terrible at math

Answer:

74

Step-by-step explanation:

21, 22, 20, 74, 25, 22, 29, 26, 26, 22, 21, 22

An outlier is a piece of data that is significantly different from the other pieces of data

All of the data is in the twenties except 74.  It is significantly different

It is an outlier

Hello!

[tex]\boxed{ \bf The~outlier~in~the~data~set~is~74.}[/tex]

__________________________________________________

An outlier is basically a number that is much greater or smaller than the rest of the numbers in the data set. In this case, all of the numbers are twenty-something, except for 74. There is a huge difference between 74 and these numbers.

Answer:

B. This because the power 7 will be multiplied to the powers of 3 and 5

Answer:

x=3.8

Step-by-step explanation:

Divide 5 by 9 to get the ratio in which the figure was reduced, then multiply this by 7 to get the value of x. In other words, 5/9x7= x

Answer:

p=-2

Step-by-step explanation:

4p + 19 + 13p = –17 − p

4p+13p=17p

17p + 19 = -17 - p

18p=-36

p=-2

So the value of p is -2.

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

x = 256

Step-by-step explanation:

-5/8x = -160

Multiply each side by -8/5 to isolate x

-8/5*-5/8x = -160*-8/5

x = 256

Answer:

Step-by-step explanation:

There are 3 blue cubes, 8 ref cubes and 4 yellow cubes, which gives a total of 15 cubes.

Now, if you pick 360 times from the bag, the chances to get a blue cube is 100%, because there's only 15 cubes in total. For trial number 16, you wouldn't have any more cubes.

Therefore, after 360 attempts, there's a 100% probability of picking a blue cube.

Answer:idk

Step-by-step explanation:

Answer:

2 committees

Step-by-step explanation:

9/4=2 with a remainder of 1

this means that only two full committees are possible

Answer: 3 && 5 are correct

Step-by-step explanation:

On edge

Answer:

C and E

Step-by-step explanation:

The conditional relative frequency that someone is in high school, given that the person prefers to study without music, is about 0.56.

If someone prefers to study with music, the probability the person is in HS is about 44%.

Answer:

3^-x= 3^ 3x + 6

Step-by-step explanation:

match bases

remeber if a^b=a^c where a=a then b=c

remember

(x^m)^n=x^(mn)

1/(x^m)=x^-m

base of 3

(1/3)^x=(3^-1)^x=3^(-x)

27^(x+2)=(3^3)^(x+2)=3^(3x+6)

3^(-x)=3^(3x+6)

-x=3x+6

0=4x+6

-6=4x

-3/2=x

Answer:

x~-0.59179865 or -3/2=x

Step-by-step explanation: I don't wanna type anymore.

Answer:

1) You divide x measure by a2 and y measure by b^2 to equal 1 whole.

2) Using the vertices 0,0 we look for the negative (x-h^2)/ a2   and (y-k)^2/b^2

Which means distance from center to a vertices is 'a ' and means (hk)

3) So the parabola is a conic section (a section of a cone). Equations. x-squared is a parabola. The simplest equation for a parabola is y = x2.   Most renowned is the given y = ax2 + bx + c

For graphs the difference from the given x2 equation is we keep double 'x' x2 to y and multiply h to 4p;  we see (x - h)2 = 4p (y - k) usually focusing upright g k and p. Note below this focus changes from y to x if rotated on transversal.

Real life objects ;

Ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.

Hyperbola;

Satellites, lenses radios, monitors Graphing a hyperbola shows this immediately: when the x-value is small, the y-value is large, and vice versa. Many real-life situations can be described by the hyperbola, including the relationship between the pressure and volume of a gas.

Parabolas; Are also used in satellite dishes to help reflect signals that then go to a receiver.From the paths of thrown baseballs, to fountains, this geometric shape is prevalent, and even functions to help focus light and radio waves.

Using Parabolic Reflectors to Focus Light

Flat surfaces scattered light too much to be useful to mariners. Spherical reflectors increased brightness, but could not give a powerful beam. But using a parabola-shaped reflector helped focus light into a beam that could be seen for long distances.

The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope.

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve.

Where the focus–directrix property of the parabola and other conic sections is due to Pappus of Alexandria. (c. 340) an encyclopedist where 8 volumes survived.

Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.

Step-by-step explanation:

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.

The standard for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Answer:

The answer is a parebola

Step-by-step explanation:

1) You divide x measure by a2 and y measure by b^2 to equal 1 whole.

2) Using the vertices 0,0 we look for the negative (x-h^2)/ a2   and (y-k)^2/b^2

Which means distance from center to a vertices is 'a ' and means (hk)

3) So the parabola is a conic section (a section of a cone). Equations. x-squared is a parabola. The simplest equation for a parabola is y = x2.   Most renowned is the given y = ax2 + bx + c

For graphs the difference from the given x2 equation is we keep double 'x' x2 to y and multiply h to 4p;  we see (x - h)2 = 4p (y - k) usually focusing upright g k and p. Note below this focus changes from y to x if rotated on transversal.

Real life objects ;

Ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.

Hyperbola;

Satellites, lenses radios, monitors Graphing a hyperbola shows this immediately: when the x-value is small, the y-value is large, and vice versa. Many real-life situations can be described by the hyperbola, including the relationship between the pressure and volume of a gas.

Parabolas; Are also used in satellite dishes to help reflect signals that then go to a receiver.From the paths of thrown baseballs, to fountains, this geometric shape is prevalent, and even functions to help focus light and radio waves.

Using Parabolic Reflectors to Focus Light

Flat surfaces scattered light too much to be useful to mariners. Spherical reflectors increased brightness, but could not give a powerful beam. But using a parabola-shaped reflector helped focus light into a beam that could be seen for long distances.

The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope.

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve.

Where the focus–directrix property of the parabola and other conic sections is due to Pappus of Alexandria. (c. 340) an encyclopedist where 8 volumes survived.

Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.

Step-by-step explanation:

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.

The standard for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Answer:

D

Step-by-step explanation:

In this question, we are to select which of the options represents the the amount earned working per hour last weekend by Samuel.

To get this, all we need to do is to divide the amount of money earned by the total

number of hours worked.

mathematically that is 18.9/2.25

Kindly note that 2 1/4 is same as 2.25

Dividing the above, we have 8.4

Hence , Samuel earned 8.40 per hour working last weekend

The option that best describes this is 18.90 = 2.25e

Answer:

(0.4, -57.9)

Step-by-step explanation:

y = 3x³ + 12x² - 10x - 56

dy/dx = 9x² + 24x - 10 = 0

x = [-24 +/- sqrt(24² - 4(9)(-10))]/(2×9)

x = -3.033006505, 0.3663398379

d²y/dx² = 18x + 24

For minima, d²y/dx² > 0 which is at x = 0.3663398379

y = 3(0.3663398379)³ + 12(0.3663398379)² - 10(0.3663398379) - 56

y = -57.90544608

Answer:

I'm glad you asked!

Step-by-step explanation:

5/18 pounds per person.

he problem already says what to do, we need to divide because that's what Karen is doing, she is spliting or dividing the pounds of candy for 3 people. So, we just need to divide 5/6 by 3,

[tex]\frac{5}{6} \div 3 = \frac{5}{6} \times \frac{1}{3} =\frac{5}{18}[/tex]

Answer:

( x + 4 )^2 + ( y - 15 )^2 = 1; Option A

Step-by-step explanation:

~ Let us apply the standard circle equation ( x - a )^2 + ( y - b )^2 = r^2, provided r ⇒ radius when centered at point ( a, b ) ~

1. If the center is provided to be ( -4, 15 ) we could substitute this value into the circle equation with variables x and y remaining such:

( x - ( - 4 ) )^2 + ( y - 15)^2 = r^2

2. Simplifying this equation, we have: ( x + 4)^2 + ( y - 15 )^2 = r^2

3. Now by point on the circle, it would be a point on the circumference, to be clear in more mathematical terms. So far we have eliminated two options, with two remain - and each of them has either a radius of 1 or 2. If the point on the circle is ( -4, 16 ) that would mean 1 more than 15, which means that with a radius of 1 ⇒ this point will be on the circle.

Answer: ( x + 4 )^2 + ( y - 15 )^2 = 1

Answer:

The answer is "5051".

Step-by-step explanation:

Given equation:

[tex]\bold{E(x)= 2(x+3)^2-3(x-1)(x+3)+(x-2)^2-31}\\\\[/tex]

put the 1, 2, 3, ........2019, 20202:

When E(1),

[tex]E(1) =2(1+3)^2-3(1-1)(1+3)+(1-2)^2-31\\\\[/tex]

        [tex]=2(4)^2-3(0)(4)+(-1)^2-31\\\\=2(16)-0+1-31\\\\=32+1-31\\\\=2[/tex]

When E(2),

[tex]E(2) =2(2+3)^2-3(2-1)(2+3)+(2-2)^2-31\\\\[/tex]

        [tex]=2(5)^2-3(1)(5)+(0)^2-31\\\\=2(25)-15+0-31\\\\=50-15-31\\\\=4[/tex]

When E(3),

[tex]E(3) =2(3+3)^2-3(3-1)(3+3)+(3-2)^2-31\\[/tex]

        [tex]=2(6)^2-3(2)(6)+(1)^2-31\\\\=2(36)-36+1-31\\\\=72-66\\\\=6[/tex]

When E(2019),

[tex]E(2019) =2(2019+3)^2-3(2019-1)(2019+3)+(2019-2)^2-31\\[/tex]

        [tex]=2(2022)^2-3(2018)(2022)+(2017)^2-31\\\\=8,176,968-12,241,188+4,068,289-31 \\\\= 4038[/tex]

When E(2020),

[tex]E(2020) =2(2020+3)^2-3(2020-1)(2020+3)+(2020-2)^2-31\\\\[/tex]

             [tex]=2(2023)^2-3(2019)(2023)+(2018)^2-31\\\\=8,185,058-12,253,311+4,072,324-31\\\\=4040\\[/tex]

[tex]\ Calculate: \\\\ \bold{A= E(1)-E(2)+E(3)-E(4).....+E(2019)-E(2020)}\\\\A= 2-4+6-8.....+4038-4040[/tex]

[tex]A= (2+6....+4038)-(4+ 8+12...4040)\\[/tex]

Formula:

[tex]t_n= a+(n-1)d\\\\\ When \\ \\ T_n =4040 \\ a= 4 \\ d= 4\\4040= 4+(n-1)4\\4040=4+4n-4\\4n=4040\\n= \frac{4040}{4}\\n= 1010\\\\When \\\\T_n =4038 \\ a= 2 \\ d= 4\\4038= 2+(n-1)4\\4038=2+4n-4\\4038=-2+4n\\4036=4n \\ n= \frac{4036}{4}\\n= 1009\\\\[/tex]

Formula for sum:

[tex]When, n= 1010\\ a=4 \\ l=4040\\ \\ S= \frac{n}{2}(2a+l)\\\\S= \frac{1010}{2} (2\times 4+4040)\\\\S= 505(8+4040)\\\\S_1= 2044240 \\\\\\[/tex]

[tex]When, n= 1009\\ a=2 \\ l=4038\\ \\ S= \frac{n}{2}(2a+l)\\\\S= \frac{1009}{2} (2\times 2+4038)\\\\S= 504.5(4+4038)\\\\S_2= 2039189 \\\\\\[/tex]

[tex]S= S_1-S_2\\\\S= 2044240 -2039189\\\\S= 5051[/tex]

The absolute value is = 5051

Answer: It sounds as if you worded it correctly the first time, though for a math assignment, I probably wouldn't use the term "doubled" (though it is technically correct)

Step-by-step explanation:

G = 2B is "The total number of girls is two times the number of boys"

B = 2G is "The total number of boys is two times the number of girls"

Answer:

The first time you pick a three the probability is [tex]\frac{1}{4}[/tex]  but if you already pick a three then the probability of you picking a 3 again is 0 because you only have one 3.

Answer:

f(x)= (X+5)^2

Answer:

[tex]\frac{3}{14}[/tex]

Hope this is right :)

Step-by-step explanation:

Hopefully the question is asking probability.

There is a [tex]\frac{1}{2}[/tex] chance of wearing a blue shirt on Monday.

Then if you get a blue shirt on Monday, you have to wash that one.

There are now 3 blue shirts and 4 green shirts.

There is now a [tex]\frac{3}{7}[/tex] chance of getting a blue shirt.

[tex]\frac{1}{2} *\frac{3}{7} = \frac{3}{14}[/tex]

Answer:

population mean

Step-by-step explanation:

This price is a population mean, and symbol used to denote it is μ = ΣX/N.

A mean in maths is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mathematically,

Mean = Sum of the observations/number of observations

Now it is given that,

average price of the paintings = $350

Number of paintings = 20

Now since the average is calculated by adding the prices of all the paintings and divides this number by 20.

Thus, it is a population mean denoted by the summation of X divided by the number of values in population which is denoted by Ν

⇒ μ = ΣX/N

Thus, this price is a population mean, and symbol used to denote it is μ = ΣX/N.

To learn more about population mean :

https://brainly.com/question/20597891

#SPJ2

Answer:

$ 4,425.69

Step-by-step explanation:

A = $ 4,425.69

A = P + I where

P (principal) = $ 4,253.00

I (interest) = $ 172.69

Omi calculator will help u

Answer:

it will cost $205.99 dollars

Step-by-step explanation: