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3 years ago

In a sale, normal prices are reduced by 10%.

1 answer:

4 0

You do 54/x = 90%/100. As prices are reduced by 10%, 54 is 90% of the original number. After cross multiplying you get 5400=0.9x. Which turns into 6000. Adding the decimal point back on you get £60.00.

So the original price of the shoes is £60.00.

Checking: all you have to do is take 10% of 60, which is 6 and subtract 6 from 60 to get 54. Thus, 60 is your answer.

Hope this helps!

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Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find

Anastasy [175]

Required area of shaded portion

= Area of square ABCD - 4 × area of one quadrant

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3 0

3 years ago

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3 years ago

A country will produce 3000 missiles this year. Each of the short-range missiles cost $200000 to produce. Each of the medium-ran

Lynna [10]

Answer:

$350,000

Step-by-step explanation:

Let's define:

s: amount of short-range missiles produced

m: amount of medium-range missiles produced

l: amount of long-range missiles produced

From the total production and the ratios we can write the following equations:

s + m + l = 3000

s/m = 3/3 = 1 = m/s

s/l = 3/4 or l/s = 4/3

Dividing the first equation by s, we get:

s/s + m/s + l/s = 3000/s

1 + 1 + 4/3 = 3000/s

10/3 = 3000/s

s = 3000*3/10 = 900

m = 900

l = 4/3*900 = 1200

From the money that the countries plans to use and each missile cost, we can write the following equation:

200,000*s + 300,000*m + cost*l = 870,000,000

Replacing with previous result:

200,000*900 + 300,000*900 + cost*1200 = 870,000,000

cost = (870,000,000 - 200,000*900 - 300,000*900)/1200 = 350,000

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3 years ago

Which graph represents the solution to the inequality?1/3(9x+27)>x+33

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Answer:

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Step-by-step explanation:

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3 years ago

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Alenkasestr [34]

Answer:

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

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If we plug in x = 0, the limit evaluates to 0/0. So using L'Hopital's rule:

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lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

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Again, the limit evaluates to 0/0. So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

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-π/2 (-2)

8 0

3 years ago