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nika2105 [10]
2 years ago
6

^2-2ab cosC" align="absmiddle" class="latex-formula">
This is one form of the Law of?
Mathematics
1 answer:
Ad libitum [116K]2 years ago
8 0
\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\ \quad \\

\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C
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Help me asap! I will give you marks
Law Incorporation [45]

Recall the binomial theorem.

(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k

1. The binomial expansion of \left(1+\frac x3\right)^7 is

\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}

Observe that

k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x

k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2

When we multiply these by 8-9x,

• 8 and \frac73 x^2 combine to make \frac{56}3 x^2

• -9x and \frac73 x combine to make -\frac{63}3 x^2 = -21x^2

and the sum of these terms is

\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}

2. The binomial expansion is

\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k

We get the a^6b^2 term when k=2 :

k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2

6 0
1 year ago
Find the value of x. Round the length to the nearest tenth.
Virty [35]

Answer:

5.1

Step-by-step explanation:

tan \ 25 = \frac{opposite \ side}{adjacen \ side}\\\\tan \ 25 =\frac{x}{11}\\\\0.4663 =\frac{x}{11}

0.4663 * 11 = x

x = 5.1293

x = 5.1

7 0
3 years ago
4. Jonathan takes his dog to be groomed. The fee to groom the dog is $80 plus 6.75% tax.
frutty [35]

Step-by-step explanation:

Tax charge

80 × 6.75/100 = 5.4

Cost + tax charge

80 + 5.4 = 85.4

Tip (15% of cost and tax)

85.4 × 15/100 = 12.81

(Cost + tax charge + tip)

85.40 + 12.81 = 98.21

therefore, $95 is not enough.

3 0
3 years ago
Solve for x in the parallelogram.<br><br><br><br> The solution is x= <br> units.
natka813 [3]

\textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=13\\ A=104\\ h=x \end{cases}\implies 104=(13)(x)\implies \cfrac{104}{13}=x\implies 8=x

5 0
2 years ago
A human hair is approximately 40 microns (um) wide. If 1 um is equal to 10
Natasha2012 [34]

Answer:

D 40,000nm

Step-by-step explanation: 1nm/10^-9m * 10^-6/1um = 10^3 nm/um

Therefore in 40 microns there are:

40um * 10^3 nm/um = 40 * 10^3 nm = 40,000 nm

5 0
2 years ago
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