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2 years ago

Which expression is equivalent to

Mathematics

2 answers:

hram777 [196]2 years ago

8 0

Answer:

Step-by-step explanation:

subtract : 3x - x = 2x

Add : 10 + 12 = 22

Answer: 2x + 22

elena-14-01-66 [18.8K]2 years ago

4 0

Answer:

2x + 22

Step-by-step explanation:

3x - (1)x = 2x

10 + 12 = 22

therefore 2x + 22 is your answer

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Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

3 years ago

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

tatyana61 [14]

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB = 753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

Learn more about trigonometry here:

brainly.com/question/26719838

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2 years ago

A certain calling card gives you the following rate to call Malaysia. There is a connection fee of $0.39 which allows you to con

Paha777 [63]

F(x<40)= 0.39+(x*0.24) This formula will quantify what you have written out above.

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3 years ago

A school uniform for boys consists of black or gray slacks, a short-sleeve or long-sleeve white button-down shirt, and a red, bl

sdas [7]

If I am right the answer would be 6

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3 years ago

Absolute Bagels makes bagels using two different recipes, one recipe for regular bagels

shutvik [7]

Answer:

At its most basic, traditional bagel dough contains wheat flour (without germ or bran), salt, water, and yeast leavening. Bread flour or other high gluten flours are preferred to create the firm, dense but spongy bagel shape and chewy texture.

Step-by-step explanation:

A bagel (Yiddish: בײגל, romanized: beygl; Polish: bajgiel; also historically spelled beigel)[1] is a bread product originating in the Jewish communities of Poland. It is traditionally shaped by hand into the form of a ring from yeasted wheat dough, roughly hand-sized, that is first boiled for a short time in water and then baked. The result is a dense, chewy, doughy interior with a browned and sometimes crisp exterior. Bagels are often topped with seeds baked on the outer crust, with the traditional ones being poppy and sesame seeds. Some may have salt sprinkled on their surface, and there are different dough types, such as whole-grain and rye.

The earliest known mention of a boiled-then-baked ring-shaped bread can be found in a 13th-century Arabic cookbook, where they are referred to as ka'ak.[4] Today, bagels are widely associated with Ashkenazi Jews from the 17th century; it was first mentioned in 1610 in Jewish community ordinances in Kraków, Poland.Bagel-like bread known as obwarzanek was common earlier in Poland as seen in royal family accounts from 1394.

Bagels are now a popular bread product in North America and Poland, especially in cities with a large Jewish population, many with alternative ways of making them. Bagels are also sold (fresh or frozen, often in many flavors) in supermarkets.

The basic roll-with-a-hole design is hundreds of years old and has other practical advantages besides providing more even cooking and baking of the dough: The hole could be used to thread string or dowels through groups of bagels, allowing easier handling and transportation and more appealing seller displays.

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2 years ago