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3 years ago

Which is the intersection of the sets {2,3,5,7} and {2,5,11,13}?

Mathematics

1 answer:

pishuonlain [190]3 years ago

4 0

ANSWER

The set of the intersection of { $2,3,5,7$ } and { $2,5,11,13$ } is

{ $2,5$ }

EXPLANATION

Let $A=$ { $2,3,5,7$ }

and

$B=$ { $2,5,11,13$ }.

The intersection of the two sets are the elements that are in both set A and set B.

The elements that are common to both sets are 2 and 5. So, we write;

$A \cap B=$ { $2,5$ }

Therefore the correct answer is C

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10 months ago

Find the components of the vertical force Bold Upper Fequalsleft angle 0 comma negative 8 right anglein the directions parallel

nydimaria [60]

Answer with Step-by-step explanation:

We are given that

F=<0,-8>=0i-8j=-8j

$\theta=\frac{\pi}{3}$

The component of force is divided into two direction

1.Along the plane

2.Perpendicular to the plane

1.The vector parallel to the plane will be= $r=cos\frac{\pi}{3}i-sin\frac{\pi}{3}j=\frac{1}{2}i-\frac{\sqrt 3}{2}j$

By using $cos\frac{\pi}{3}=\frac{1}{2},sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Force along the plane will be= $\mid F_x\mid=F\cdot r$

Force along the plane will be = $\mid F_x\mid=F\cdot (\frac{1}{2}i-\frac{\sqrt 3}{2}j)=-8j\cdot(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=8\times \frac{\sqrt 3}{2}=4\sqrt 3$ N

By using $i\cdot i=j\cdoty j=k\cdot k=1,i\cdot j=j\cdot k=k\cdot i=j\cdot i=k\cdot j=i\cdot k=0$

Therefore, force along the plane= $\mid F_x\mid(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)$

2.The vector perpendicular to the plane= $r=-sin\frac{\pi}{3}-cos\frac{\pi}{3}=-\frac{\sqrt 3}{2}i-\frac{1}{2}j$

The force perpendicular to the plane= $\mid F_y\mid=F\cdot r=-8j(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

The force perpendicular to the plane= $4$ N

Therefore, $F_y=4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $F_x+F_y=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)+4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $2\sqrt 3i-6j-2\sqrt3 i-2j=-8j$

Hence,sum of two component of forces=Total force.

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2 years ago

When evaluating (6.28x10^12)/(3.14x10^4) what will be the exponent of 10 in the quotient?

alexdok [17]

2*10^8
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hope this helps!

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2 years ago

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If the sales tax is 7% on all purchases, how much should you set aside for $300. Show your work.

trasher [3.6K]

Answer:

$21

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3 years ago

A pressure of a gas at 22°C is 600 mmHg when it occupies 2.5 L. If the gas is compressed to 1.8 L and the pressure changes to 76

zhuklara [117]

APPLICATION OF COMBINED GAS LAW

Combined gas law is a combination of Boyle's, Charles', and Gay-Lussac's Laws that expresses the relationship between pressure, temperature, and volume in a constant amount of gas (moles).

<u>Note:</u>

In solving any problems related to Gas Law, it is important to remember that the standard unit measure for the temperature is always expressed in Kelvin (K). To do so, whatever the given temperature is (either °C or °F) you should convert them first so computation will be efficient.
If the given is in °C, then use the formula $\sf{K = °C + 273.15}$
And if °F, $\sf K = \frac{5}{9} (°F - 32) + 273.15$

So to answer your question, what is the new temperature in K, the new temperature is T2 = 269.176 K or 269.18 K

(Please see attached image for the solution).

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1 year ago