Use the laplace transform to solve the given initial-value problem. y'' − 6y' 13y = 0, y(0) = 0, y'(0) = −5

The surface area of the cone exists as πr² + πrl

= (3.14)(6)² + (3.14)(6)(3)

= 169.56 cm²

Therefore, the surface area of the cone exists at 169.56 cm².

The surface of the cone consists of the lateral surface and the base area. So,

1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.

2. the base area exists πr² (since the base exists a circle with radius r).

Then the surface area exists SA = πrs + πr²

The surface area of the cone exists as πr² + πrl

where "r" exists the radius, "l" exists the slant height

The radius of the cone exists at 6 cm

The slant height of the cone exists at 3 cm

To find the surface area of a cone

The surface area of a cone = πr² + πrl

= (3.14)(6)² + (3.14)(6)(3)

= 169.56 cm²

Therefore, the surface area of the cone exists at 169.56 cm².

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∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.

Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².

∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find

[tex]\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm[/tex]

where [tex]h[/tex] is the length of the altitude originating from vertex O, and so

[tex]\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm[/tex]

where [tex]b[/tex] is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².

So, the total area of the shaded region is

(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²

The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

For given question,

We need to find the critical values for a 2-tailed sign test for 13-coin flips.

We have been given an alpha level of 0.05 that is 5%

⇒ α = 0.05

We know that in hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

These are the points on the distribution which have the same probability as your test statistic, equal to the significance level α.

The critical values are assumed to be at least as extreme at those critical values.

Now we find 1 - α

⇒ 1 - α = 1 - 0.05

⇒ 1 - α = 0.95

Because it is a two-tailed test, we are going to divide 0.95 by 2.

⇒ 0.95/2 = 0.475

Now we look in the z-table to find out cutoff points.

For the area of 0.475, the critical values is ± 1.96 .

Therefore, the critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

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Answer:

y = 8x+7

Step-by-step explanation:

firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....

Secondly, identify the common difference: 8
we now know that the answer must contain 8x

Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y

Answer:

y = 8x + 7

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table

m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8

the ordered pair (0, 7 ) indicates c = 7

y = 8x + 7 ← equation of linear function

Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

Let the mass of the object exists at 60 N and the height exists at 3m then work

exists in 1764.

What is work?

The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.

Work can be estimated by multiplying Force and Distance in the direction of force as follows.

W = F × d. Unit.

Given data:

m = mass of the object = 60 N

h = height = 3 m

Work = Fh = mgh

g = gravity = 9.8 m/s²

work = Fh = mgh

[tex]= 60*3*9.8[/tex]

= 1764

Therefore, the work exists in 1764.

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Answer:0.0625

Step-by-step explanation:

Answer:

1/16.

Step-by-step explanation:

4 ^-2 = 1 / 4^2

= 1/16.

Answer:

roots (1,0) (3,) the vertical intercept is (0,-12)

Step-by-step explanation:

The number of terms, 'n' is 8

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

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x[x²-25] - [x³+8] = 17

x³- 25x - x³- 8 = 17

-25x = 17 + 8

-25x = 25

x = -1

Answer:

6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on

Step-by-step explanation:

PLEASE GIVE BRAINLIEST OR 5 ⭐

Answer:

7/5

Step-by-step explanation:

Answer:

x = -6, y = -8

Step-by-step explanation:

8x - 5y = -8

-7x - 5y = 82

minus them

15x = -90

x = -90 / 15

x = -6

8(-6) - 5y = -8

-48 - 5y = -8

-5y = -8 + 48

-5y = 40

5y = -40

y = -40 / 5

y = -8

Fraction of cake each children's  get 1/12.

fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

Cake  available for Sharing = 1/6

The cake future divide into 1/2:

so,

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

= 1/12

fraction of cake each children's  get 1/12.

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Answer:

he didn't mistake step 2

Hi :)

To find the tan of a number, just type the number into your calculator and press [tex]\boxed{\tan}[/tex].

[tex]\tan 24=0.45[/tex], Rounded to the nearest hundredth, or 2 numbers after the decimal point, just like you asked

[tex]\textit{\textbf{Learn\;More;Work\;Harder}}[/tex]

:)

Answer:

  130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

  7n ≤ 1000

  n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

  77n ≤ 1000

  n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

  142 -12 = 130 integers divisible by 7, but not 11.

The value of function f(x) at x = 7 is f(7) = 28

For given question,

we have been given the value of function f(x) at x = 5.

f(5) = 12

We have been given that f'(x) is continuous on 5 and 7

Also, [tex]\int\limits^7_5 {f(x)} \, dx =16[/tex]

We need to find the value of f(7)

Since ∀x, f'(x) = f'(x), f is a primitive function of f' .

And f ' is continuous

[tex]\Rightarrow \int\limits^7_5 {f(x)} \, dx =16\\\\\Rightarrow [f(x)]_5^7=16[/tex]

⇒  [f(7) - f(5)] = 16

⇒ f(7) - 12 = 16

⇒ f(7) = 16 + 12

⇒ f(7) = 28

Therefore, the value of function f(x) at x = 7 is f(7) = 28

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Answer:

a) -6/2

b) -9/2

Step-by-step explanation:

a) rearrange by making y the subject as y = mx+c

y = -6/2x-9/2

the gradient = -6/2

b) c is the y-intercept as it touch the y-axis, therefore -9/2 is where the line crosses the y-axis

The missing value in the table is 12.4

From the question, we are to determine the missing value in the table

From the given information,

The chart shows conversion between kilometers and miles

The given table is

Kilometers           Miles

2                            1.2

7                            4.2

20                          ?

30                          18

NOTE: 1 kilometer ≈ 0.62 miles

Then, 20 kilometer ≈ 20×0.62 miles

20 kilometer ≈ 12.4 miles

Hence, the missing value in the table is 12.4

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Answer:

Let's go part by part:

14 raised to 2 = 196

-9+7x2=-9+14 = 5

196/5= 39,2 (final result)

Answer:

-3.2

Step-by-step explanation:

14 SQUARED is 196

196 - 34 = 5.7647

- 9 + 7.2 = - 1.8

5.7647 / -1.8 = -3.2

-3.2 would be your answer.

concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.

These numbers go from 1 to 10.

5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.

This means that if the card that we turn up is smaller than 6, we discard it.

If the card has the value 6 or larger, we keep it.

In this case, the probability of losing is if one of the other cards has a value larger than 6.

The probability that a random card has a value larger than 6 is:

p = (number of cards with a value larger than 6)/(total number of cards)

p = (16/39)

(The quotient is 39 instead of 40, because we already know one of the cards)

This means that if keep the 6, the probability of winning is:

1 - 16/39 = 0.59

If instead, we got a 7, obviously we keep it, in that case the probability of winning is:

1 - 12/39 = 0.69

And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

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Answer: 380 ft and 780 ft

Step-by-step explanation:

We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.

The formula for the perimeter of a rectangle is [tex]2(l+w)[/tex]. Let's plug in the values we know.

[tex]P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380[/tex]

We know that the length is 400 more than the width, so let's find the length.

[tex]l=w+400\\l=380+400=780[/tex]

Hence, the flag's width is 380 ft and the length is 780 ft.

Answer:Answer:

12 (D)

Step-by-step explanation:

The first one is 2:1.2 so i did x10 on it to get 20:12.

Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award

The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

According to the question,

The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)²  = r².

        (x-0)² + (y-0)²  = -(√41)². This is not possible.

Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

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Answer:

x = 5, y =2

Step-by-step explanation:

I guess the question is saying x+y = 7 and 3x-2y = 11?

then there are multiple ways but

I will multiply the first one by 2 so 2x+2y = 14

you add the equations to get 5x = 25 so x = 5 plug x into the first equation you get y = 2

if that isn't what the question means just comment and I'll change it

Solving a system of equations, we conclude that the value of x is 28.

Here we have the quadratic number pattern:

6, 15, x, 45, ...

First, we have that:

15 - 6 = 9

So 9 is the first difference.

Then we will have:

x = 15 + 9 + a

(where a is the second difference, constant of the sequence).

And:

45 = x + 9 + a + a

Then we have a system of equations:

x = 15 + 9 + a

45 = x + 9 + a + a

We can isolate a on the first equation:

a = x - 24

We can replace that in the other equation:

45 = x + 9 + 2a

45 = x + 9 + 2*(x - 24)

Now we can solve that for x:

45 - 9 = x + 2*(x - 24)

36 = 3x - 48

36 + 48 = 3x

84 = 3x

84/3 = x = 28

The value of x is 28.

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Step-by-step explanation:

-3(x+8)=-21

open the bracket

-3x-24=-21

-3x=-21+24

-3x=3

x=-3/3

x=-1

Length of the line

= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]

= [tex]\sqrt{36+64}[/tex]

=[tex]\sqrt{100}[/tex]

= 10