If V = 12R / (r + R) , then R =

Answers

Answer 1

Answer: $V=(12R)/(r+R)\n\nV(r+R)=12R\n\nVr+VR=12R\n\nVR-12R=-Vr\n\n(V-12)R=-Vr\ \ \ \ /:(V-12)\neq0\n\nR=(-Vr)/(V-12)\n\nR=(Vr)/(12-V)$

Answer 2

Answer: vr+vR=12R
vr=12R-vR
vr=R(12-v)
R=vr/12-v

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To solve 493x = 3432x+1, write each side of the equation in terms of base
- 18 < - 3x + 9 < 12

What is -4x+8=48 what is x

Answers

Subtract 8 from each side:

-4x = 40

Divide each side by -4 :

x = -10

X= -10

-4x+8=48

Subtract 8 on both sides so it would be -8

Then rewrite the equation and it should be

-4x/-4 = 40/-4

Which equals -10

Solve the following equation. Then place the correct number in the box provided.-7z - 7 ≤ -5z + 5

Answers

Your answer should be z≥−6

The answer is:

z ≥ − 6

What is perpendicular to y= 3x -9 and passes through the point (3,1)

Answers

$(3,1) , \ \ y= 3x -9 \n \n The \ slope \ is :m _(1) =3 \n \n If \ m_(1) \ and \ m _(2) \ are \ the \ gradients \ of \ two \ perpendicular \n \n lines \ we \ have \ m _(1) \cdot m _(2) = -1 \n \n3\cdot m_(2)=-1 \ \ /:3\n \n m_(2)=-(1)/(3)$

$\Now \ your \ equation \ of \ line \ passing \ through \ (3,1) would \ be: \n \n y=m_(2)x+b \n \n1=-(1)/( 3) \cdot3 + b$

$1=-1+b\n \n b=1+1\n \nb=2 \n \n y =- (1)/(3)x+2$

One of the Great Pyramids in Egypt has the shape of a square pyramid with the base length of 20 feet, and the height of 150 feet tall. If the stones that were used to build the pyramid had a volume of 40 cubic feet each, how many stones did the Egyptians need to build the pyramid?

Answers

Answer:

500

Step-by-step explanation:

Given that:

Shape of one of the Great Pyramids in Egypt is a square pyramid.

Base of pyramid is of square shape with length = 20 feet

Height of pyramid = 150 feet

Volume of each stone used for the construction of the pyramid = 40 cubic feet

To find:

Number of stones used for the construction of the pyramid.

Solution:

First, we need to find the volume of the square pyramid and then we need to divide the volume of pyramid with the volume of one stone used for the construction.

It will give us the number of stones used for the construction of pyramid.

Volume of a pyramid is given as:

$V = (1)/(3)* \text{Area of base}* Height$

Here, base is a square, so area of base = $(Side)^2$

$V = (1)/(3)* 20^2* 150 = 400* 50 ft^3$

Number of stones of 40 cubic feet each, required = $(400* 50)/(40)$ = 500

The product of three and a squared number is twice the sum of the number and four

Answers

From the text of the task we can write the equation:

$3 x^(2) =2(x+4)\n \n 3x^2=2x+8\n \n 3x^2-2x-8=0\n \n \Delta=(-2)^2-4.3.(-8)=4+96=100\n \n x=(2 \pm√(100))/(2.3)=(2 \pm10)/(6)\n \n x_1=(2-10)/(6)=-(8)/(6)=-(4)/(3)\n \n x_2=(2+10)/(2.3)=(12)/(6)=2$

$3x^2=2(x+4)\n 3x^2=2x+8\n 3x^2-2x-8=0\n 3x^2-6x+4x-8=0\n 3x(x-2)+4(x-2)=0\n (3x+4)(x-2)=0\n x=-(4)/(3) \vee x=2$

Which formula can be used to find the nth term of the geometric sequence below? 1/6,1,6,36

Answers

ratio = 1÷1/6 = 6÷1 = 36÷6 = 6

nth term

$a_(n) = a r^(n-1)$ (where a is the first term)

$a_(n) = (1)/(6) 6^(n-1)$

Answer:

(6^(n-1))/6

Step-by-step explanation:

The nth term of a geometric series is a function of the number n, the common ratio between each successive number in the series r and the first term a. This may be expressed mathematically as

= a(r)^n-1

Given the series,

a = 1/6,

r = T2/T1 = 1/1/6 = 6

The nth term

= (1/6)(6)^n-1

= (6^(n-1))/6

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A rectangle has an area of 40 square units. The length is 6 units greater than the width.

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