Find the first five terms of the sequence below <br> a1=3<br> An=an-1+6

A 152 cm tall barrel has a circumference of 56.52.

kirill [66]

Answer:

V = 38659.68 cm^3

Step-by-step explanation:

If we pretend A barrel is a cylinder we use V=πr^2h for the volume. We know h, but we need to find r

The question tells us the circumference, well how do we find circumference? C = 2πr, so we can use this to find r.

C = 2πr

56.52 = 2 * 3.14 * r Here divide both sides by 2*3.14

56.52/(2*3.14) = r

9 cm = r

Now we can just plug into the volume.

V=πr^2h

V = 3.14 * 9^2 * 152

V = 38659.68 cm^3

I feel I should mention this is all true if the circumference is in centimeters, since the question didn't specify.

6 0

2 years ago

Find the area of the shaded region.

mihalych1998 [28]

Answer:

351π cm^2.

Step-by-step explanation:

Area of shaded part = area of the large circle - area os small circle

= π * (13+7)^2 - π * 7^2

= 400π - 49π

= 351π.

8 0

2 years ago

Richard, Henry and Gavin share some sweets in the ratio 4:1:3. Richard gets 7 more sweets than Gavin. How many sweets does Henry

N76 [4]

Answer:

7 sweets for Henry

Step-by-step explanation:

Let their respective shares be 4x,x,and 3x for Richard,Henry and Gavin

If Richard gets 7 more sweets than Gavin then the difference between their shares is 7 that is

4x-3x=7

x=7

To find Henry's share,

x=7

3 0

2 years ago

2x2 – 5x + 67 = 0<br> What would be your first step in completing the square for the equation above?

7nadin3 [17]

Answer:

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

The solutions to the quadratic equation $2x^2\:-\:5x\:+\:67\:=\:0$ are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Step-by-step explanation:

Considering the equation

$2x^2\:-\:5x\:+\:67\:=\:0$

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

so

$\frac{2x^2-5x}{2}=\frac{-67}{2}$

$x^2-\frac{5x}{2}=-\frac{67}{2}$

Lets now solve the equation by completeing the remaining steps

Write equation in the form: $x^2+2ax+a^2=\left(x+a\right)^2$

Solving for $a$ ,

$2ax=-\frac{5}{2}x$

$a=-\frac{5}{4}$

$\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}$

Completing the square

$\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}$

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For $f^2\left(x\right)=a$ the solution are $f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

Solving

$x-\frac{5}{4}=\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}$

$x-\frac{5}{4}=i\sqrt{\frac{511}{16}}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}$

$-\frac{5}{4}=i\frac{\sqrt{511}}{4}$

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4}$

Similarly, solving

$x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Therefore, the solutions to the quadratic equation are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

4 0

2 years ago

Differentiation y=x^-5 ?

OLga [1]

Answer:

the differentiation d/dx will be ..... -5x^-6

5 0

3 years ago

Find the first five terms of the sequence below a1=3 An=an-1+6