MATHEMATICS COLLEGE

Given the function and the graph below, please answer the following:

Answers

Answer 1

Answer:

The given quadratic function is

$f(x)=(-x-1)^2+3$

It represented graphically by an upward parabola

Since the parabola is upward, then it has a minimum vertex

From the graph, the minimum vertex is (-1, 3)

Then let us answer the questions

Maximum point: None

Minimum point: (-1, 3)

To find f(-5), substitute x by 5 in the function above

$\begin{gathered} f(-5)=(--5-1)^2+3 \n f(-5)=(5-1)^2+3 \n f(-5)=(4)^2+3 \n f(-5)=16+3 \n f(-5)=19 \end{gathered}$

To find f(6), substitute x by 6 in the function above

$\begin{gathered} f(6)=(-6-1)^2+3 \n f(6)=(-7)^2+3 \n f(6)=49+3 \n f(6)=52 \end{gathered}$

The answers:

f(-5) = 19

f(6) = 52

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- 5 + 7k = -19Help pwease
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.

Find the length of the curve. R(t) = 2 i + t2 j + t3 k, 0 ≤ t ≤ 1

Answers

Length of a curve is the length of its plot its curve. The length of the given curve for given range of t is: L = 1.44 units approx.

How to find the length of a curve?

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

$L = \int_a^b ||p'(x)||dx\n$ units.

For the given case, we have:

Position vector = $R(t) = 2\hat i + t^2 \hat j + t^3 \hat k$

Its differentiation gives:

$R'(t) = 2t\hat j + 3t^2\hat k$

Its non negative magnitude is: ||R'(t)|| = $√((2t)^2 + (3t^2)^2) = t√(4+9t^2)$

Thus, as t ranges from a = 0 to b = 1, thus, length of the curve is:

$L = \int_0^1 (t√(4+9t^2))dt\n\n\text{Let v = 4+9}t^2, \text{then dv = 18tdt}\nand\nt=0\implies v = 4\nt=1 \implies v = 13\nThus,\nL = \int_4^(13)((√(v))/(18))dv = (1)/(18) [(2(v)^(3/2))/(3)]^(13)_4 \approx (38.87)/(27) \approx 1.44 \: \rm units$

Thus,

The length of the given curve for given range of t is: L = 1.44 units approx.

Learn more about length of the curve here:

brainly.com/question/4464059

curve equation is

$\n \vec{R}\left ( t \right ) = 2\hat{i}+t^(2)\hat{j} + t^(3)\hat{k}$ ,0≤ t≤ 1

now taking the differentiation

$\n{R}'t = 2t\hat{i} + 3t^(2)\hat{j}$

now taking the modulus

$\left \| {R}'(t) \right \|=$ $\sqrt{4t^(2) +9t^(4)}$

= $\sqrt{4 + 9 t^(2) } .t$

now taking the integration

length of the curve = $\n\int t\sqrt{4 + 9 t^(2)} dt\n$

now put the value v= 4 + 9t²

dv= 18 tdt

now put this value in the above equation

we get

length of the curve = $\n(1)/(18)\int √(v)dv\n$

now taking integation we get and put the value of the v

we get

= $(1)/(18)$ × $(2)/(3)$ × $(4 + 9t^(2) )^{(3)/(2) }$

= $(1)/(27) ( 4 + 9 t^(2) )^{(3)/(2) }$

now find out the length of the curve in the interval from 0 to 1.

length of the curve $= (1)/(27) (13^{(3)/(2)} -4^{(3)/(2)} )\n=(1)/(27) (13√(13) -8)$

Hence proved

LET'S GOOOOOOOOO!!!!!!!!!!!

Answers

Answer: YAYYYY

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Solve the equation. -3x + 1 + 10x = x + 4

Answers

Answer:

$x=[tex](1)/(2)$ [/tex]

Step-by-step explanation:

Solving the equation mean finding the value of x

Equation given is:

$-3x+1+10x=x+4$

Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.

$-3x+10x-x=4-1$

Now simplify values with x and the numbers.

$6x=3$

$x=[tex](1)/(2)$ [/tex]

Therefore $x=[tex](1)/(2)$ [/tex]

x = $(1)/(2)$

simplify the left side by collecting like terms

7x + 1 = x + 4 ( subtract x from both sides )

6x + 1 = 4 ( subtract 1 from both sides )

6x = 3 ( divide both sides by 6 )

x = $(3)/(6)$ = $(1)/(2)$

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.62.(a) What is the probability of more than one death in a corps in a year?

(b) What is the probability of no deaths in a corps over 7 years?

Round your answers to four decimal places (e.g. 98.7654).

Answers

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

$P(X=x)=(e^(-\lambda)\lambda^(x))/(x!);\ x=0,1,2,...$

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-(e^(-0.62)(0.62)^(0))/(0!)-(e^(-0.62)(0.62)^(1))/(1!)\n=1-0.54335-0.33144\n=0.12521\n\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7*0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=(e^(-4.34)(4.34)^(0))/(0!)=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

Sally's bank account had a balance of 230 at the beginning of the month. She had two deposits of 50 and 420 and just one withdrawal of 190. Her balance at the end of the month was $______ ?

Answers

Answer:

510

Step-by-step explanation:

Sally bank account had a beginning balance of 230

She made two deposits of 50 and 420

50+420

= 470

She made a withdrawal of 190

Therefore her balance at the end of the month can be calculated as follows

470+230

= 700

= 700-190

= 510

Hence the balance at the end of the month is 510

A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)452.16 cm3

840.54 cm3

1,055.04 cm3

1,456.96 cm3

Answers

Given:
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³

Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³

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