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2 years ago

4000

Mathematics

1 answer:

Airida [17]2 years ago

5 0

Answer:

$1000 ; 500 ; 1000 ; y = 500x + 1000

Step-by-step explanation:

From the graph, the initial deposit which started the savings account is $1000 ; this is the value on the y - intercept, the value in the account at time or period = 0.

The slope :

x1 = 0 ; y1 = 1000

x2 = 6 ; y2 = 4000

Slope = Rise / Run

Rise = y2 - y1 = 4000 - 1000 = 3000

Run = x2 - x1 = 6 - 0 = 6

Hence,

Slope = 3000 / 6

Slope = 500

y - intercept = 1000 (from. Graph)

Equation in slope intercept form:

General form : y = mx + c

m = slope ; c = intercept

Equation is written as ;

y = 500x + 1000

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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

Use the drop-down menus to identify the GCF of each pair of numbers.

horrorfan [7]

Answer:

4, 15, 6, 18.

Step-by-step explanation:

12 = 1, 2, 3, 4, 6, 12 16 = 1, 2, 4, 8, 16 The GCF of 12 and 16 is 4 because when you compare the numbers that go into 12 and 16, 4 is the highest number that they both are multiples of.

Try the others by yourself and if you have any questions ask me in the comments

4 0

2 years ago

Simplify square root 58 over square root 2

pantera1 [17]

Answer:

5.38516482 or 5.4 or 5

Step-by-step explanation:

The square root of 58 is 7.61577311 and the square root of 2 is 1.41421356.

Divide those 2 numbers and you get 5.38516482 or 5.4 or 5

6 0

3 years ago

What are the first 9 nonzero multipes of 7?

Marrrta [24]

7, 14, 21, 28, 35, 42, 49, 56, 63

5 0

3 years ago

Read 2 more answers

Mr. Dexter sells subscriptions to a magazine for $18 each. For each subscription he sells, he earns $8. One month, he sold $900

TiliK225 [7]

Answer:

$400

Step-by-step explanation:

Dexter's earnings can be found using the proportion ...

earnings/sales = $8/$18 = ??/$900

Multiplying by $900, we find ...

?? = $900(8/18) = $400

Dexter's earned $400 on the sales for the month.

6 0

2 years ago