curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm

Answer:

C , x>0

Step-by-step explanation:

anything times 0 is 0 and 3x has to be larger than 0

By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

The points of intersection between the two curves are (x, y) = (0, 0) and (x, y) = (-2, 4). The curve is f(x) = x² and upper curve is g(x) = -(x+2)² + 4. The area between the two curves is defined by this definite integral:

[tex]A = \int\limits^{0}_{-2} {f(x) - g(x)} \, dx[/tex]

[tex]A = \int\limits^{0}_{-2} {f(x)} \, dx - \int\limits^{0}_{-2} {g(x)} \, dx[/tex]

[tex]A = \int\limits^0_{-2} {[-(x+2)^{2}+4]} \, dx -\int\limits^0_{-2} {x^{2}} \, dx[/tex]

[tex]A = -\frac{(x+2)^{3}}{3}|_{-2}^{0} + 4\cdot x|_{-2}^{0}-\frac{x^{3}}{3}|_{-2}^{0}[/tex]

[tex]A = - \frac{2^{3}}{3} + 0 + 4\cdot [0 - (-2)] - 0 + \frac{(-2)^{3}}{3}[/tex]

[tex]A = -\frac{8}{3} + 8 -\frac{8}{3}[/tex]

A = 8

By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

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Answer:

8/3

Step-by-step explanation:

4 x 2 = 8, so (4 × 2)/2 = 8/3.

Answer:

0.462

Step-by-step explanation:

1km=1000m

so to get from metres to kilometres you divide by 1000

so 462÷1000=0.462

Considering the multiplication of mixed fractions, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

To multiply mixed fractions, it is necessary to transform these fractions into improper fractions. To do this, the whole part is multiplied by the denominator of the fraction that accompanies it. The result of the multiplication is added to the numerator of the fraction that accompanies it, and it will be the denominator of the new fraction, while the denominator remains the same.

After transforming the mixed fractions to be multiplied into improper fractions, they are multiplied. To do this, it is necessary to multiply the numerators of the two fractions, and the denominators of the fractions. If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.

On a day in winnipeg with 10[tex]\frac{1}{2}[/tex] h of daylight, it was sunny for [tex]\frac{1}{3}[/tex] of that time. This is:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex]

Solving:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex] = [tex]\frac{10x2+1}{2}[/tex] × [tex]\frac{1}{3}[/tex] =  [tex]\frac{21}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21x1}{2x3}[/tex]= [tex]\frac{21}{6}[/tex]= 3.5

Finally, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

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Answer:

-7 is -7 units away from zero. Its opposite is 7 from zero.

Step-by-step explanation: Count from 0 how many digits away it is

Answer:

• f(g(x)) =  [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65

Step-by-step explanation:

• f(g(x)) = f(x² + 1)

         = [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )

            = [tex](\sqrt{x } + 8)^{2}[/tex] + 1

            =  x + 16[tex]\sqrt{x}[/tex] + 64 + 1

            = 16[tex]\sqrt{x}[/tex] + x + 65

Answer:

i think the answe is. y=0x-6

Answer:

85%

Step-by-step explanation:

9+51 = 60

(51/3) ÷ (60/3) = 17/20

(17/20)% = 85%

Answer:

They are not parallel

Step-by-step explanation:

original equation

10x + 3y = -3

subtract 10x

3y = -10x - 3

divide by 3

y = -10/3x - 1

original equation

5x - 4y = -3

subtract 5x

-4y = -5x-3

divide by -4

y = 5/4x + 3/4

the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel

Answer:

12.5%

Step-by-step explanation:

1/8 × 100% = 12.5%

So 9f you multiply an eighth by one hundred percent and simplify accurately you'll get 12.5%

Answer:

x=1

Step-by-step explanation:

(2(x+4))/5=2

Multiply both sides by 5

2(x+4)=10

Divide both sides by 2

x+4=5

subtract 4 from both sides

x=1

Answer:

I think the best answer is 143

The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

Length of each scarf = Total length of scarf / Number of friends

= 39.9 ft / 7

= 5.7 ft

Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

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Answer:

ffhjjrhjzxuzdjzdjzsjezjdifi

The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.

The function is a type of relation, or rule, that maps one input to specific single output.

The following function represents the weekly weed growth:

f(x) = 86(1.08)x.

we'll represent the growth function by day g(x). If x is to represent days, then x/7 represents weeks.

We can write,

 g(x) = f(x/7) = 86·1.08^(x/7)

 g(x) = 86·(1.08^(1/7))^x

 g(x) = 86·1.011055^x

The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.

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The entry that it will pass on the accounting book based on the information about Galaxy Star Corporation is the credit sales.

It should be noted that credit sales are the sales where the amount that is owed will be paid at alter date.

From the information given, we were informed that the payment will be made after 20 days. Therefore, the appropriate entry will be in town credit sales.

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Answer: 5

Step-by-step explanation:

If [tex]\triangle LMN \cong \triangle FGH[/tex], this means that [tex]\overline{LM} \cong \overline{FG}[/tex] by CPCTC.

Using the distance formula,

[tex]FG=\sqrt{(-3-0)^{2}+(-4-0)^{2}}=5\\\\\therefore LM=\boxed{5}[/tex]

Answer:

B. 47 7/12

Step-by-step explanation:

=126 1/4 - 78 2/3

Change the two mix fraction to improper fractions.

= 505/4 - 236/3

= 1515-944/12

= 571/12

= 47 7/12

Answer:

449 units

Step-by-step explanation:

Perimeter of a rectangle = 2(a+b)

= 2(223+3/2)

=449 units

Answer:

the answer above the image

Answer:

a=-4/3, 14/3

Step-by-step explanation:

absolute value only makes the answer become positive whether the value inside is negative or positive.
so -3a+5=9 or -3a+5=-9 all works

-3a+5=9

-3a=4

a=-4/3

If -3a+5=-9

-3a=-14

a=14/3

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

[tex]\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

Now plug x = a - 5 = 30 - 5 = 25

[tex]\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

After solving:

[tex]\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}[/tex]

[tex]\rm y^2=\dfrac{6875}{36}[/tex]

y = ±13.819 ≈ ±13.82

Height cannot be negative

y = 13.82 feet

Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

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Answer: [tex]\sqrt{7}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]3^2 + b^2 = 4^2\\\\9+b^2 = 16\\\\b^2 = 7\\\\b=\boxed{\sqrt{7}}[/tex]

If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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Answer:

[tex](5+3\sqrt{2} )^{2} =43+30\sqrt{2}[/tex]  

≈85.43

Step-by-step explanation:

apply the binomial theorem to the square

[tex]=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}[/tex]

[tex]=25+30\sqrt{2} +18\\[/tex]

[tex]=43+30\sqrt{2}[/tex]

≈85.43

Hope this helps

Hello!

Here, we apply the algebraic identity :

[tex]\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}[/tex]

Let's solve!

⇒ (5 + 3√2)²

⇒ (5)² + 2(5)(3√2) + (3√2)²

⇒ 25 + 30√2 + 18

⇒ [tex]\boxed {43 + 30\sqrt{2}}[/tex]

∴ The final answer will be 43 + 30√2.

There are 10,080 different ways in which the friends can seat on the circular table.

There are 9 friends, such that two of them need to be separated by exactly two people.

Because the table is circular, we can consider the first position as the position where Bob is.

Now let's count the number of options for each of the other 8 positions. (counting to the left).

The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)

For the next seat, we could seat Anna or one of the remaining 5 friends.

Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.

The total number of combinations is given by the product between the numbers of options, so we have:

C = 7*6*5*4*3*2*1

But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.

C = 2*(7*6*5*4*3*2*1) = 10,080

There are 10,080 different ways in which the friends can seat on the circular table.

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Answer:

ok so it could be Careful because think about it 10000x 0.01...

Answer:10,000

Step-by-step explanation:

Answer:

sum of all sides

Step-by-step explanation:

x1y2 + x3y3 + x1y1

Answer:

average of the no. = sum of all no. / no. of terms

= 2 + 5 + 8 + 1 / 4

= 16/4

= 4

4 is the answer