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tia_tia [17]
2 years ago
13

Suppose cos(O) = 5/13, Quadrant I. Find sin(O). A:13/12 B:12/13 C:13/5 D:5/12

Mathematics
1 answer:
Ne4ueva [31]2 years ago
8 0

Answer:

B. 12/13.

Step-by-step explanation:

Using the identity sin^2 O + cos^2 O = 1:

sin^2 O = 1 - cos^2 O

sin^2 O = 1 - (5/13)^2

= 1 - 25/169

= 169/169 - 25/169

= 144/169

So sin O = √(144/169)

= 12/13.

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3 0
3 years ago
compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.
Nina [5.8K]

\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})

We have been given two vectors $\vec{a}$ and $\vec{b}$, we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of$\vec{b}$onto $\vec{a}$means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

#SPJ4

3 0
1 year ago
The radius of a circle is 9 feet. What is the circumference?
Vlad1618 [11]

Answer: 18\pi

Step-by-step explanation:

The circumference formula is C= 2\pir

r being the radius, so you can just plug in.

C= 2\pi(9) = 18\pi

7 0
3 years ago
What is the seventh term of a sequence whose first term is 1 and whose common ratio is 3?
ikadub [295]
\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=1\\
r=3\\
n=7
\end{cases}
\\\\\\
a_7=1\cdot 3^{7-1}\implies a_7=1\cdot 3^6\implies a_7=1\cdot 729\implies a_7=729
7 0
3 years ago
Four times the sum of a number and ter is the same as one-hundred added to eight
AfilCa [17]

Answer:

GIVE BRAINLIEST PLZ

I DONT NEED THNX

x = -15

Step-by-step explanation:

1) Four times sum of a number and 10

4(x + 10)

2) is equal to 100 added to 8 times the number

4(x+10) = 8x + 100

x + 10 = 2x + 25

-15 = x

7 0
3 years ago
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