The line segment between the points (8,-7) and (4,5) is the diameter of the circle. Find the equation of this circle

ANSWER ASAP!! chris collected a total of t coins from 8 people. if each person contribute the same amount of coins, write an exp

Alja [10]

T/8=c

C: coins per person

3 0

2 years ago

Explain what is meant by balance stretching

ArbitrLikvidat [17]

Answer:

you balance your stretching

Step-by-step explanation:

7 0

3 years ago

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You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

Mike compared the y-intercept of the graph of the function

aleksklad [387]

Answer:

-4

Step-by-step explanation:

<u>Given function</u>

f(x) = 5x + 12

From the table we get the function g(x), use pairs (1, 10) and (3, 14)

<u>The slope:</u>

m = (14 - 10)/(3 - 1) = 4/2 = 2

<u>The y-intercept:</u>

10 = 2(1) + b
b = 10 - 2
b = 8

<u>The function g(x) is found as:</u>

g(x) = 2x + 8

<u>The y- intercept of f (x) is subtracted from the y-intercept of g (x):</u>

8 - 12 = -4

4 0

3 years ago

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If f(x) = 7 + 4x and g(x)=1/2x, what is the value of (f/g)(5)?

Romashka [77]

<h2>Answer:</h2>

$d. \ \boxed{270}$

<h2>Step-by-step explanation:</h2>

In this exercise we need to make a division and evaluate the new function at $x=5$ . so we have two functions, namely:

$f(x)=7+4x \ and \\ \\ g(x)=\frac{1}{2x}$

Therefore:

$f(5)=7+4(5)=27 \\ \\ g(5)=\frac{1}{2\times 5}=\frac{1}{10}$

So:

$(f/g)(5)=\frac{27}{\frac{1}{10}}=270$

3 0

3 years ago

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