Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
We need to find the expressions whose simplified form is a rational number.
Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.
For example: 0,2, 4.3 etc.
Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.
First expression is
![2\sqrt{9}\cdot \sqrt{4}=2(3)\cdot (2)\Rightarrow 6\cdot 2=12](https://tex.z-dn.net/?f=2%5Csqrt%7B9%7D%5Ccdot%20%5Csqrt%7B4%7D%3D2%283%29%5Ccdot%20%282%29%5CRightarrow%206%5Ccdot%202%3D12)
12 is a rational number.
Second expression is
![\sqrt{3}\cdot \sqrt{16}=\sqrt{3}\cdot 4\Rightarrow 4\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%5Ccdot%20%5Csqrt%7B16%7D%3D%5Csqrt%7B3%7D%5Ccdot%204%5CRightarrow%204%5Csqrt%7B3%7D)
is an irrational number.
Third expression is
![7\sqrt{3}\cdot \sqrt{3}\Rightarrow 7\cdot 3=21](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%5Ccdot%20%5Csqrt%7B3%7D%5CRightarrow%207%5Ccdot%203%3D21)
21 is a rational number.
Fourth expression is
![\sqrt{5}\cdot \sqrt{5}=5](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%5Ccdot%20%5Csqrt%7B5%7D%3D5)
5 is a rational number.
Therefore, the correct options are 1, 3 and 4.
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
21/25, 4.37, 5, 5.844, 117/20
Answer:
533.6cm²
Step-by-step explanation:
Hello!
I'm here to answer your question!
<u>Area of each triangular base:</u>
![\frac{1}{2}(12)(10)=60](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2812%29%2810%29%3D60)
<u />
<u>Area of the rectangular faces:</u>
![12\times 11 =132](https://tex.z-dn.net/?f=12%5Ctimes%2011%20%3D132)
![15.6\times 11=171.6](https://tex.z-dn.net/?f=15.6%5Ctimes%2011%3D171.6)
![10\times 11=110](https://tex.z-dn.net/?f=10%5Ctimes%2011%3D110)
<u>Add to find the surface area:</u>
![60+60+132+171.6+110=533.6](https://tex.z-dn.net/?f=60%2B60%2B132%2B171.6%2B110%3D533.6)
Thus, the surface area of the triangular prism is = 533.6 yd²
Hope this helps you!
Hugs from,
Josh
You are inversing for subtraction which is addition so D