in how many ways can 7 people line if A needs to be first or last and B needs to be in the middle

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Answer:

14

Step-by-step explanation:

10000 = 5000[tex](1.05)^{t}[/tex]

2 =  [tex](1.05)^{t}[/tex]

ln(2) = t ln(1.05)

t = ln(2)/ln(1.05)

[tex]\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots[/tex]

For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.

If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,

then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

For $5000 invested at 5% p.a. compound interest with yearly

rests to double in value, we need to find the time.

So,

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

[tex]10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21[/tex]

Hence, The time will be 14 years. So, option D is correct.

Learn more about compound interest here:

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Answer:

Have you gotten the answer. if yes Hmu... Aihs I sit beside you

Step-by-step explanation:

502.5 = -502.5

Now

x = -502.5

= -5025/10

= -1005/2 feet

Answered by Gauthmath must click thanks and mark brainliest

Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

Answer:

cột số 2

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

you multiply through by 3y^2

3y^4 - 18y^2 =30y^2

Collect like terms

3y^4=48y^2

divide through by y^2

3y^2=48

divide through by 3

y^2=16

take the square root of both sides

y=4

Answer:

A.

[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]

Answer:

1. 90-68= 22

2. 90-80= 10

3. 90-3= 87

Step-by-step explanation:

A complement angle is found by their sum being 90 degrees. So, you are looking for the angle that would add to the given angle to = 90.

Answer:

.63

Step-by-step explanation:

bc the first three numbers are less then 0 so add the three probabilities and boom magic.

Answer:

Option c is correct

Step-by-step explanation:

From the screenshot I attached.

sinA/a=SinC/c

a/c=SinA/SinC

Thus a=cSinA/SinC

Answer: 33 tulips bloomed / 66 tulips did not bloom

Step-by-step explanation:

Total number of tulips = 99

Total number of tulips bloomed = 3/9 of total

Step One: Find the number of tulips that bloomed

99 × (3/9) = 99 × (1/3) = 33 tulips

Step Two: Find the number of tulips that did not bloom

99 - 33 = 66 tulips

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4x² - 8x - 60

Step-by-step explanation:

Given :-

Simplify ,

Trinomial expression :-

The polynomial function [tex](2x-10)(2x+6)[/tex] expressed as a trinomial is [tex]4x^2 - 8x - 60[/tex].

Given data:

The polynomial function is represented as A.

Now, the value of [tex]A=(2x-10)(2x+6)[/tex].

On simplifying the equation:

From distributive property to multiply the terms:

[tex]A=2x * 2x + 2x * 6 - 10 * 2x - 10 * 6[/tex]

[tex]A=4x^2 + 12x - 20x - 60[/tex]

On simplifying the equation:

[tex]A=4x^2 - 8x - 60[/tex]

Hence, the trinomial is [tex]4x^2 - 8x - 60[/tex].

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Answer: x= 2/5 or x= 3

how?

Step 1: Subtract 17x from both sides

5x² + 6 -17x = 0

*PUT THEM IN ORDER* --> 5x² -17x + 6= 0

Step 2: Factor left side of equation:

(5x-2) (x-3) = 0

Step 3: Set factors equal to 0.

5x−2=0 or x−3=0

which gives us an answer of x= 2/5 or x=3

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{5x^2 + 6 =17x}\\\\\large\textsf{SUBTRACT 17x to BOTH SIDES}\\\\\mathsf{5x^2 + 6 - 17x = 17x - 17x}\\\\\mathsf{5x^2 - 17x + 6 = 0}\\\\\large\textsf{SET the LEFT SIDE to equal 0}\\\\\mathsf{(5x -2)(x -3)=0}\\\\\large\textsf{SET the FACTORS to EQUAL to 0}\\\\\mathsf{5x - 2 = 0\ or\ x - 3 = 0}\\\\\large\textsf{SIMPLIFY ABOVE AND YOU HAVE YOUR RESULT}\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf x = \dfrac{2}{3}\ or\ x = 3}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

9514 1404 393

Answer:

  a) 30.7 million

  b) 1.5% per year

  c) 42.0 million

  d) 2017

Step-by-step explanation:

a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.

__

b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.

The population is growing by 1.5% per year.

__

c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.

  P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0

The population in Canada in 2021 is predicted to be 42.0 million.

__

d) For this we need to solve for t when P(t) = 40.

  40 = 30.7·1.015^t

  40/30.7 = 1.015^t

Taking logarithms gives ...

  log(40/30.7) = t·log(1.015)

  t = log(40/30.7)/log(1.015) ≈ 17.773

In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.

_____

Additional comment

The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.

Answer:

4.5, - 27, 162, - 972, 5832

Step-by-step explanation:

Using the recursive rule and a₁ = 4.5 , then

a₂ = - 6a₁ = - 6 × 4.5 = - 27

a₃ = - 6a₂ = - 6 × - 27 = 162

a₄ = - 6a₃ = - 6 × 162 = - 972

a₅ = - 6a₄ = - 6 × - 972 = 5832

The first 5 terms are 4.5, - 27, 162, - 972, 5832

Answer:

[tex]m\angle WVT=40^{\circ}[/tex]

Step-by-step explanation:

When two secants or a secant and a tangent of a circle intersect outside the circle, the measure of the acute angle formed is equal to half of the positive difference of smaller and larger arc formed.

Therefore, we have the equation:

[tex]m\angle WVT=\frac{1}{2}(\widehat{TW}-\widehat{UW}),\\3x+4=\frac{1}{2}(14x+7-(7x+11))[/tex]

Distribute:

[tex]3x+4=\frac{1}{2}(14x+7-7x-11),\\\\3x+4=\frac{1}{2}(7x-4),\\\\3x+4=3.5x-2[/tex]

Add 2 to both sides and subtract [tex]3x[/tex] from both sides:

[tex]6=0.5x[/tex]

Divide both sides by 1/2:

[tex]x=\frac{6}{\frac{1}{2}}=6\cdot 2=12[/tex]

Now substitute [tex]x=12[/tex] into [tex]3x+4[/tex]:

[tex]m\angle WVT=3(12)+4,\\m\angle WVT=36+4,\\m\angle WVT=\boxed{40^{\circ}}[/tex]

Answer:

∠4 = ∠8

Step-by-step explanation:

the lines are parallel if a pair of corresponding angles are congruent

Answer:

B

Step-by-step explanation:

Using the identities

sec x = [tex]\frac{1}{cosx}[/tex] , csc x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex] , then

sec²x cot²x

= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cos^2x}{sin^2x}[/tex] ( cancel out cos²x )

= [tex]\frac{1}{sin^2x}[/tex]

= csc²x → B

# Sin θ = 9/15.

# Cos θ = 12/15.

# Cosec θ = 15/9.

# Sec θ = 5/4

Step-by-step explanation:

[tex]by \: using \: pythagorian \: triplets[/tex]

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {9}^{2} + {12}^{2} = {c}^{2} [/tex]

[tex]81 + 144 = {c}^{2} [/tex]

[tex]225 = {c}^{2} [/tex]

[tex]c = 15.[/tex]

[tex] \sin θ = \frac{9}{15} [/tex]

[tex] \cos θ = \frac{12}{15} = \frac{4}{5} [/tex]

[tex] \csc θ = \frac{15}{9} [/tex]

[tex] \secθ = \frac{5}{4} [/tex]

Answer:

4

Step-by-step explanation:

Hi there!

Range = largest number from data given - smallest number from data given

From the given data, 58, 59, 57, 59, 55,

59 is the largest number and 55 is the smallest number

So the range = 59 - 55 = 4

Step-by-step explanation:

hope this helps you thank you

[tex]\boxed{ \sf{Answer}} [/tex]

[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]

Use the algebraic identities ⟶

Squaring on both the sides

[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]

[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]

[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

The area of D is 36 times bigger than C

Step-by-step explanation:

The scale factor is 1:6

We know the ratio of the areas is the ratio of the scale factor squared

1^2 : 6^2

1:36

The area of D is 36 times bigger than C

Answer:

None.

Step-by-step explanation:

There is no expression for the square root of negative numbers. In other words it is undefined.

Answer:

4√5

Step-by-step explanation:

Answer:

[tex]{ \tt{ \frac{dy}{dx} ( {x}^{2}) = \frac{dy}{dx} ( \frac{x + y}{x - y}) }} \\ { \tt{2x = \frac{(x - y) \frac{dy}{dx} + (x + y) \frac{dy}{dx} }{ {(x - y)}^{2} } }} \\ { \tt{ \frac{dy}{dx}(2x) = 2x {(x - y)}^{2} }} \\ { \tt{ \frac{dy}{dx} = {(x - y)}^{2} }}[/tex]

Answer:

Benito llega en segundo lugar.

Eladio llega en sexto lugar

Hermes llega en noveno lugar.

Step-by-step explanation:

Tenemos 3 amigos:

Benito

Hermes

Eladio

Hay 3 posiciones:

segundo

sexto

noveno.

Sabemos que:

Benito llegó antes que Hermes.

Cuando Eladio estaba llegando a la meta, solo Benito estaba descansando.

Es decir, cuando Eladio llego a la meta, Hermes aún no había llegado.

Eladio llegó a la meta antes que Hermes, pero después que Benito.

Entonces el primero en llegar es Benito, el segundo es Eladio y el tercero será Hermes.

Con la data inicial podemos decir que:

Benito llega en segundo lugar.

Eladio llega en sexto lugar

Hermes llega en noveno lugar.

Hello!

-9y > 9 <=>

<=> -9y ÷ (-9) > 9 ÷ (-9) <=>

<=> y < -1 <=>

<=> y ∈ { -∞; -1 }

Good luck! :)

Answer:

f(x) = -3(x+3)(x-1)

Step-by-step explanation:

x = -3 & 1; f(x) = 9

f(x) = a(x-r1)(x-r2)

f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)

9 = a(3)(-1); 9 = a(-3)

a = -3

f(x) = -3(x+3)(x-1)

Answer:

f(x) = -3x^2 - 6x + 9.

Step-by-step explanation:

As the x intercepts are - 3 and 1 we can write it as:

f(x) = a(x - 1)(x + 3)    where a is a constant to be found.

As the - intercept is at (0, 9),  x =0 when f(x) = 9 so we can also write:

a( 0 - 1)(0 + 3) = 9

(-1)(3)a = 9

a = 9 / -3

= -3.

So the equation is f(x) = -3(x - 1)(x + 3)

In expanded form it is

-3(x^2 + 2x - 3)

= -3x^2 - 6x + 9.

Answer:

[tex]\angle 72=BC-86/2[/tex]

[tex]144+86=BC[/tex]

[tex]BC=230[/tex]

[tex]BC=230/2[/tex]

[tex]\angle BAC= 115[/tex]°

~OAmalOHopeO