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2 years ago

By selling a radio with 12% profit , the profit

Mathematics

1 answer:

Setler79 [48]2 years ago

5 0

Answer:

the Radio was 52.8%

Step-by-step explanation:

60-12%=52.8

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What is the product of 5/10 x 4/5 in lower terms (simplified)?*

xenn [34]

If I’m not wrong 2/5

6 0

2 years ago

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Can anyone help me integrate :

worty [1.4K]

Rewrite the second factor in the numerator as

$2x^2+6x+1=2(x+2)^2-2(x+2)-3$

Then in the entire integrand, set $x+2=\sqrt3\sec t$ , so that $\mathrm dx=\sqrt3\sec t\tan t\,\mathrm dt$ . The integral is then equivalent to

$\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt$
$=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\sec^2t-1}}\,\mathrm dt$
$=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\tan^2t}}\,\mathrm dt$
$=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{|\tan t|}\,\mathrm dt$

Note that by letting $x+2=\sqrt3\sec t$ , we are enforcing an invertible substitution which would make it so that $t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}$ requires $0\le t$ or $\dfrac\pi2$ . However, $\tan t$ is positive over this first interval and negative over the second, so we can't ignore the absolute value.

So let's just assume the integral is being taken over a domain on which $\tan t>0$ so that $|\tan t|=\tan t$ . This allows us to write

$=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt$
$=\displaystyle\int(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\csc t\,\mathrm dt$

We can show pretty easily that

$\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C$
$\displaystyle\int\sec t\csc t\,\mathrm dt=-\ln|\csc2t+\cot2t|+C$
$\displaystyle\int\sec^2t\csc t\,\mathrm dt=\sec t-\ln|\csc t+\cot t|+C$
$\displaystyle\int\sec^3t\csc t\,\mathrm dt=\frac12\sec^2t+\ln|\tan t|+C$

which means the integral above becomes

$=3\sqrt3\sec^2t+6\sqrt3\ln|\tan t|-18\sec t+18\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|-6\ln|\csc t+\cot t|+C$
$=3\sqrt3\sec^2t-18\sec t+6\sqrt3\ln|\tan t|+12\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|+C$

Back-substituting to get this in terms of $x$ is a bit of a nightmare, but you'll find that, since $t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}$ , we get

$\sec t=\dfrac{x+2}{\sqrt3}$
$\sec^2t=\dfrac{(x+2)^2}3$
$\tan t=\sqrt{\dfrac{x^2+4x+1}3}$
$\cot t=\sqrt{\dfrac3{x^2+4x+1}}$
$\csc t=\dfrac{x+2}{\sqrt{x^2+4x+1}}$
$\csc2t=\dfrac{(x+2)^2}{2\sqrt3\sqrt{x^2+4x+1}}$

etc.

3 0

2 years ago

Almonds cost $3.49 per pound a bag of almonds cost $6.95 to the nearest whole pound about how many pounds of almonds are in the

Kryger [21]

Answer:

The hint in this problem is the word "about" or approximately how many pounds. So we could find the solution by estimation through rounding off. We know that almonds cost about 3.50 per pound and a bag costs about $7.00. Dividing 7 by 3.50 per pound, will give us $7 ÷ $3.50 = 2 pounds.

The answer is 2 pounds.

5 0

2 years ago

A triangle has side lengths of 11 cm and 7 cm. Which could be the value of the third side, 19 cm or 17 cm ?

9966 [12]

Answer:

By the triangle side length theorem, the sum of the two shorter sides has to be equal to or larger than the third side. Thus, we can write the following inequation.

≥

, where a and b are the shorter sides and c the longest.

11, 9 and 15 satisfies this inequality while 11, 9 and 20 doesn't.

Justification:

The reason for this rule is simple; it's because if the longest side is longer than the sum of the two shorter sides, this means that the shorter sides aren't long enough to connect with the longest side, thus rendering the shape a collection of lines and disqualifying the possibility of having a triangle, which was our objective.

Practice exercises:

Which of the following triangles is possible?

a) 4,6 and 14

b) 5,11 and 16

c) 1,3,6

D). 12,19 and 26

Find the smallest possible value of a to make the following an actual triangle :

Hopefully this helps:

Step-by-step explanation:

8 0

3 years ago

I don’t know how to simplify this equation

yanalaym [24]

Answer:

$7^5$

Step-by-step explanation:

According to the Product Rule for Exponents, $\frac{a^m}{a^n} = a^{m-n}$

a = 7

m = 9

n = 4

So,

$\frac{7^9}{7^4} = 7^{9-4} = 7^5$

So, the answer is $7^5$ .

Hope this helps!!!

Please mark me as brainliest!!!

7 0

1 year ago

Read 2 more answers