Ask question

Ask question

All categories

2 years ago

6

in circle o, points a and b lie on the circle such that OA=5x-11 and OB=4(x-1) what represents the length of the circle' s diame

ter

1 answer:

AysviL [449]2 years ago

3 0

We know that
if <span>points a and b lie on the circle and O is the center
so
OA is the radius
OA=OB
5x-11=4(x-1)-----> 5x-11=4x-4----> 5x-4x=11-4-----> x=7
OA=5x-11-------> OA=5*7-11-----> OA=24 units

the diameter is (OA+OB)
2*OA------> 2*24------> 48 units</span>

You might be interested in

On a certain route, an airline carries 7000 passengers per month, each paying $30. A market survey indicates that for each $

KengaRu [80]

Answer:

The ticket price that maximizes revenue is $50.

The maximum monthly revenue is $250,000.

Step-by-step explanation:

We have to write a function that describes the revenue of the airline.

We know one point of this function: when the price is $30, the amount of passengers is 7000.

We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.

Then, we can write the revenue as the multiplication of price and passengers:

$R=p\cdot N=(30+x)(7000-x)$

where x is the variation in the price of the ticket.

Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.

$R(x)=(30+x)(7000-100x)=30\cdot7000-30\cdot100x+7000x-100x^2\\\\R(x)=-100x^2+(7000-3000)x+210000\\\\R(x)=-100x^2+4000x+210000\\\\\\\dfrac{dR}{dx}=100(-2x)+4000=0\\\\\\200x=4000\\\\x=4000/200=20$

We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:

$p=30+x=30+20=50$

The maximum monthly revenue is:

$R(x)=(30+x)(7000-100x)\\\\R(20)=(30+20)(7000-100\cdot20)\\\\R(20)=50\cdot5000\\\\R(20)=250000$

3 0

2 years ago

Find each product.<br> 1) (5n - 5)(4n - 4)

Paraphin [41]

Answer:

20n² - 40n + 20

Step-by-step explanation:

(5n - 5)(4n - 4)

= 5n(4n) + 5n(-4) - 5(4n) - 5(-4)

= 20n² - 20n - 20n + 20

= 20n² - 40n + 20

Another way to do this:

(5n - 5)(4n - 4)

= 5(n - 1) * 4(n - 1)

= 20(n - 1)(n - 1)

= 20(n - 1)²

= 20(n² - 2n + 1)

= 20n² - 40n + 20

6 0

2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of thr

Rina8888 [55]

Answer:

3 - (n - 1) = 1/2(3n - 4)

Step-by-step explanation:

We want to write three minus the difference of a number and one equals one-half of the difference of three times the same number and four as an equation.

Let the number be n.

The first part is: three minus the difference of a number and one:

3 - (n - 1)

The second part is: one-half of the difference of three times the same number and four:

1/2(3n - 4)

Now, let us equate the first and second parts:

3 - (n - 1) = 1/2(3n - 4)

PS: I really do not understand the options

9 0

1 year ago

Read 2 more answers

A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a funct

Agata [3.3K]

Answer:

$V(m) = (2 + 5m)^3$

Step-by-step explanation:

Given

Solid Shape = Cube

Edge = 2 feet

Increment = 5 feet per minute

Required

Determine volume as a function of minute

From the question, we have that the edge of the cube increases in a minute by 5 feet

<em>This implies that,the edge will increase by 5m feet in m minutes;</em>

Hence,

$New\ Edge = 2 + 5m$

Volume of a cube is calculated as thus;

$Volume = Edge^3$

Substitute 2 + 5m for Edge

$Volume = (2 + 5m)^3$

Represent Volume as a function of m

$V(m) = (2 + 5m)^3$

4 0

2 years ago