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3 years ago

How is shading a grid to show 1 tenth different from shading a grid to show 1 hundreth?

1 answer:

8 0

Shading a grid to show 1 tenth means that for every shaded square there are 9 unshaded squares. To show 1 hundreth, for every shaded square there should be 99 unshaded squares. Example: Suppose a grid has 100 squares total. For 1 tenth, you would shade 10 squares, leaving 90 squares unshaded - maintaining the ratio of one shaded square per nine unshaded square. On the same grid, 1 hundreth would require 1 shaded square with the remaining 99 squares unshaded.

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Six identical squares are cut from the corners and edges of an 80 cm by 50 cm cardboard rectangle. the remaining piece is folded

Anna11 [10]

Check the picture.

let the length of a side of each of the squares removed be x.

The box formed will have dimensions: 80-2x, 50-2x, x(the height)

So the volume can be expressed as a function of x as follows:

f(x)=(80-2x)(50-2x)x= $[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x$

so $f(x)=4 x^{3}-260x^{2}+4000x$

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

$f'(x)=12x^{2}-520 x +4000=0$

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions

x=10 and x=33.333

plug in f(x) these values to see which greater:

$f(10)=(80-20)(50-20)10=60*30*10=18000$ cm cubed

$f(33.333)=(80-66.666)(50-66.666)33.333=$ which is negative because (50-66.666)<0

Answer: 18000 cm cubed

5 0

2 years ago

Read 2 more answers

How can you calculate the area of the circle if you know the circle's circumference?

Jobisdone [24]

Answer with step-by-step explanation:

We know that the formula for area of a circle is given by:

Area of a circle = $\pi r ^ 2$

So to find the area of circle, we basically need to know the radius of the circle.

If we know the circumference of the circle, we can calculate the area of the circle too.

Formula for the circumference of the circle is given by:

$2\pi r$

So if we know the circle's circumference, we can find the value of radius and then find the area of circle with it.

5 0

2 years ago

Read 2 more answers

To raise money, the Boy Scouts bought 190 kg of taffy for $723.90. They sold the tafty in 400 g bags

babunello [35]

They made profit of $\$834.10$ by selling 190 kg of taffy in 400 g bags at rate of $\$3.28$ each.

Solution: 

Given that

To raise money, the Boy Scouts bought 190 kg of taffy for $\$723.90$ .

They sold the tafty in 400 g bags for $\$3.28\text{ each }$

Need to calculate the profit the made.

Cost price of 190 kg of taffy = $\$723.90$

As 1 kg = 1000 gram,

So 190 kg of taffy = $190\times 1000 = 190000\text{ grams of taffy }$

So cost price of 190000 gram of taffy = $\$723.90$

Now let us calculate number of 400 grams bags which can be made from 190000 grams of taffy

Number of 400 grams bags = $\frac{190000}{400}=475 \text { bags }$

Amount generated from 1 bag of 400 gram taffy = 3.28

So amount generated from 475 bags of taffy = $475\times3.28 = \$1558$

Selling price of 190000 grams of taffy = amount generated from 475 bags of taffy = $\$1558$

$\text{ Profit }= \text{ selling price }-\text{ cost price }= 1558-723.90 = \$834.10$

Hence they made profit of $\$834.10$ by selling 190 kg of taffy in 400 g bags at rate of $\$3.28$

6 0

3 years ago

M^3-8n^3 factor the sum and difference

Keith_Richards [23]

Factor: (M-2n)(M^2+2Mn+4n^2)

7 0

2 years ago

Suzanne has a rectangular garden which is 18 feet long and 11 feet wide. She has 168 square foot of paving stones, and she wants

VikaD [51]

Answer:

width = 2.5 feet

Step-by-step explanation:

Suzanne has a rectangular garden which is 18 feet long and 11 feet wide.

Area of the garden = length times width = 18 times 11= 198 square foot

Let 'w' be the width of the border

Length of the garden with border = 18+2w

Width of the garden with border = 11+2w

Area of the garden with border = $(18+2w)(11+2w)=4w^2+58w+198$

Area of the border = $4w^2+58w+198-198=4w^2+58w$

She has 168 square foot of paving stones,

$4w^2+58w=168$

Solve for w

apply quadratic formula

a= 4, b= 58 and c=-168

$\quad x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$w=\frac{-58+-\sqrt{58^2-4\cdot \:4\left(-168\right)}}{2\cdot \:4}$

$w=\frac{-58+-\sqrt{6052}}{8}$

we get two values for w

$w=\frac{-58+\sqrt{6052}}{8}=2.47$

$w=\frac{-58-\sqrt{6052}}{8}=-16.97$

5 0

3 years ago