Find the arc length, x, when
r = 1 and 0 = 5 radians.
п
9
5л
9
1
X
X =
?TT

Answer:

y = [tex]\frac{24}{\sqrt{x} }[/tex]

Step-by-step explanation:

given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is

y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation

to find k use the condition y = 8 when x = 9 , then

8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

24 = k

y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation

Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

The volume of the grain storage building is 3770. 4 m³

From the given question, it can be deduced that the grain storage is a combination of a cylinder and a cone

The volume of the grain storage = volume of the cone + the volume of the cone

The formula for finding the volume of a cylinder is given as;

Volume of cylinder = πr²h

But we know that radius is the diameter divided by 2

radius = 20/2

radius = 10 meters

height = 10 meters

Substitute the values in the formula

Volume of cylinder = 3. 142 × 10 × 10 × 10

Volume = 3. 142 × 1000

Volume = 3142 m³

The formula for finding the volume of a cone is given as;

Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]

If the cone has the same diameter, then the radius is 10 meters and the height is 6 meters

Substitute the values into the formula

Volume of the cone = 3. 142 × 10 × 10 × 6/ 3

Volume = 3. 142 × 100 × 2

Volume = 628. 4 m³

The volume of the grain storage building = 3142 + 628. 4

The volume of the grain storage building = 3770. 4 m³

Thus, the volume of the grain storage building is 3770. 4 m³

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Answer:

3770. 4 m³

Step-by-step explanation:

i took the test

The count of numbers in the list a, a+1, a+2.... b is b - a + 1

The list of numbers is given as:

a, a+1, a+2.... b

From the above list, we can see that the numbers are consecutive numbers.

This means that, the count of numbers in the list is

Count = Highest - Least + 1

Where

Highest = b

Least = a

Substitute the known values in the above equation

Count = b - a + 1

Hence, the count of numbers in the list a, a+1, a+2.... b is b - a + 1

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Answer:

B = - 23

Step-by-step explanation:

5(B + 4) = 3(B - 1) + B ← distribute parenthesis on both sides

5B + 20 = 3B - 3 + B

5B + 20 = 4B - 3 ( subtract 4B from both sides )

B + 20 = - 3 ( subtract 20 from both sides )

B = - 23

The total cost of the truck is $16,000

We know that first, we have a down payment of $4000.

And then we have a monthly payment of $250 for 4 years. In each year there are 12 months, then in 4 years there are:

4*12 = 48 months.

Then the student needs to pay $250 48 times, this is:

$250*48 = $12,000

Then the total cost is:

$12,000 + $4,000 = $16,000

The total cost of the truck is $16,000

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Answer:

eight and thirty-seven fiftyths

Step-by-step explanation:

6 and 4/100 + 2 and 5/10

6 and 1/25 + 2 and 1/2

156 / 25 + 5 / 2

312 / 50 + 125 / 50

437 / 50

400 / 50 = 8

8 and 37 / 50

Answer:

Step-by-step explanation:

The probability and the parameter

Step-by-step explanation:

The formula for probability  in a binomial distribution is where p is the probability of success (ticket with popcorn coupon), n is the number of trials (tickets bought) and x the number of successes desired. In this case p=0.629 (probability of buying a movie ticket with coupon), n=29,  and x=17,18,19, ...29.

The probability of more than 16 is equal to the sum of the probability of x=17, 17,18,19, ...29.

Answer:

13, 21, 29

Step-by-step explanation:

You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.

The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.

Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars [tex]c_1,c_2,c_3[/tex] (not all zero) such that

[tex]c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)[/tex]

which leads to the system of linear equations,

[tex]\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}[/tex]

From the third equation, we have [tex]c_1=-c_2[/tex], and substituting this into the second equation gives

[tex]-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3[/tex]

and in turn, [tex]c_1=c_3[/tex]. Substituting these into the first equation gives

[tex]2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0[/tex]

which tells us that any value of [tex]c_3[/tex] will work. If [tex]c_3 = t[/tex], then [tex]c_1=t[/tex] and [tex]c_2 = -t[/tex]. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.

Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.

Answer:

  a. no

  b. yes

  c. yes

  d. no

Step-by-step explanation:

To test a solution, put the values where the variables are, and simplify to the point where you can tell whether the statement is true.

Each ordered pair is (x, y), so the first value gets substituted for x; the second value gets substituted for y.

  11 < 13 -2 = 11 . . . . no

  8 ≤ 16 -3 = 13 . . . . yes

  20 > 18 -4 = 14 . . . . yes

  9 ≥ 15 -5 = 10 . . . . no

Answer: A

Step-by-step explanation:

The points are (-5, 8) and (4, 6).

The distance is [tex]\sqrt{(-5-4)^2 + (8-6)^2}=\sqrt{85}[/tex]

Answer:

-20

Step-by-step explanation:

Use the distributive property to get [tex]2xy-14[/tex] (you multiply both xy and -7 by 2.) Now plug in the x and y values to get: [tex]2(-1)(3)-14[/tex]. This gets you [tex]-6-14[/tex] which is [tex]-20[/tex].

Step-by-step explanation:

there is a nice formula for the height in a right-angled triangle :

h = sqrt(p×q)

h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.

so, in our case

x = sqrt(25×144) = 5×12 = 60

Answer:

The equation of the line passing through point __0___ and point __1___ plotted below in point-slope form is y+3 =-(x-4

Considering the asymptotes of the function, the equation that represents the graph is:

[tex]y = \frac{1}{x + 2} + 3[/tex]

This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:[tex]y = \frac{1}{x + 2} + 3[/tex]

x + 2, as x + 2 = 0 -> x = -2.

The horizontal asymptote is of y = 3, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]

Which means that the function is described by the following rule:

[tex]y = \frac{1}{x + 2} + 3[/tex]

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Answer:

250 - 6 - 3n

Step-by-step explanation:

Let n equal the number of students.

Answer:

false

Step-by-step explanation:

The converse of the statement is

This is false by definition.

Answer:

Step-by-step explanation:

3.5805

Answer:

x = 6

Step-by-step explanation:

the tangent- tangent angle UVW is half the difference of the intercepted arcs, that is

∠ UVW = [tex]\frac{1}{2}[/tex] (UW - WU ) , then

5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - (23x - 5) ) ← multiply both sides by 2

10x + 34 = 37x + 5 - 23x + 5

10x + 34 = 14x + 10 ( subtract 14x from both sides )

- 4x + 34 = 10 ( subtract 34 from both sides )

- 4x = - 24 ( divide both sides by - 4 )

x = 6

Step-by-step explanation:

"congruent" for lines simply means they are equally long.

15. yes. AB = EF = 3

16. yes. BD = DF = 8

17. no. AC = 5, CD = 6

18. yes. AC = DE = 5

19. no. BE = 13, CF = 14

20. no. CD = 6, DF = 8

The time at which the break started is 10 : 30 am.

The first step is to convert the time between  10:00 a.m. - 11:15 a.m. to minutes.

The time  between  10:00 a.m. - 11:15 a.m. is 1 hour 15 minutes

In order to convert hours to minutes, multiply hour by 60

1 x 60 = 60 minutes

60 minutes +  15 minutes =  75 minutes

The second step is to subtract the time from the break from the duration of the golf lesson

75 minutes -  15 minutes = 60 minutes

The third step is to divide 60 minutes into equal halves by dividing 60 by 2

60 / 2 = 30 minutes

The last step is to add 30 minutes to the time the lesson started : 10 : 00 am + 30 minutes = 10 : 30 am

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Answer:

c subtract 5 from both sides

Answer:

Step-by-step explanation:

A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.

The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.

The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.

__

Additional comment

The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.

We know the x^2 coefficient is the opposite of the sum of the zeros:

  -(7 +(-2) +3) = -8 . . . . x^2 coefficient

And we know the constant is the opposite of the product of the zeros:

  -(7)(-2)(3) = 42 . . . . . constant

These checks lend further confidence that the zeros are those given.

(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)

The number of different groups of cookies he can choose from the 12 cookies is 220

The given parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

The number of different groups of cookies he can choose from the 12 cookies is calculated as:

Numbers = 12C3

The combination formula is represented as:

nCr = n!/(n - r)!r!

Substitute the known values in the above equation

Numbers = 12!/(12 - 3)!3!

Evaluate the difference in the above equation

Numbers = 12!/9!3!

Expand the above equation

Numbers = 12*11*10*9!/9!3!

Evaluate the quotient

Numbers = 12*11*10/3!

Expand the above equation

Numbers = 12*11*10/3*2*1

Evaluate the products

Numbers = 1320/6

Evaluate the quotients

Numbers = 220

Hence, the number of different groups of cookies he can choose from the 12 cookies is 220

So, the complete parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

Number of selection = 220

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In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.

About the Central Angle:

An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.

Since BD is the diameter of the circle,

∠BAC + CAD = 180°

It is given that ∠BAC = 100°

⇒ ∠CAD = 180° - 100°

⇒ ∠CAD = 80°

About Major Arc:

The arc which subtends an angle greater than 180° at the center, is called a major arc.

Angle subtended by arc BEC = 360° - m(arc CD)

= 360° - 80°

= 280° > 180°

∴ Arc BEC is the major arc

About Minor Arc:

The arc which subtends an angle less than 180° at the center, is called a minor arc.

⇒ Arc CD is the minor arc.

Calculating arc BEC and arc BC:

Let us assume the radius of the circle is r.

Then, the formula of the measure of an arc is given by,

θ × (π/180) × r

Here, θ is the angle ( in degrees) subtended by the arc at the center.

Arc BEC = 260 × (π/180)r  ......... [Put π = 3.14]

= 2.27r

Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]

= 0.87r

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Answer:

hey can you show me the pic because the question doesn't make any sense

When [tex]n=1[/tex],

[tex]10^{2\cdot1 - 1} + 1 = 10^1 + 1 = 11[/tex]

which is of course divisible by 11.

Assume this holds for [tex]n=k[/tex], that

[tex]11 \mid 10^{2k - 1} + 1[/tex]

In other words,

[tex]10^{2k - 1} + 1 = 11\ell[/tex]

for some integer [tex]\ell[/tex].

Use this to show the claim is true for [tex]n=k+1[/tex].

[tex]10^{2(k+1) - 1} + 1 = 10^{2k + 1} + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k+1} + \left(10^{2k-1} + 10^{2k-1}\right) + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = \left(10^{2k+1} - 10^{2k-1}\right) + \left(10^{2k-1} + 1\right) \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k-1} \left(10^2 - 1\right) + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 99\times10^{2k-1} + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 11\left(9\times10^{2k-1} + \ell\right)[/tex]

which is indeed divisible by 11. QED

On the off-chance you meant [tex]10^{2^n-1}+1[/tex], notice that [tex]2n-1[/tex] is odd for any integer [tex]n[/tex]. Similarly [tex]2^n-1[/tex] is odd for all [tex]n[/tex], so the above proof actually proves this automatically.

The cross-section perpendicular to the base of a right rectangular prism is a rectangle.

A shape or a solid that has three dimensions that is length, width and height is called a 3D shape. 3D shapes have faces, edges, and vertices. Examples are cylinder, cone, prism, pyramid.

A shape that has two dimensions is called a 2D shape. 2D shapes have breadth and length.

The cross-section perpendicular to the base of a right rectangular prism is a rectangle.

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Answer: W

Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .