The measure of an angle is 49Â°. what is the measure of a complementary angle?

What is the best approximation of the projection of (5,-1) onto (2,6)?

Hatshy [7]

Answer:

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .

Step-by-step explanation:

We have given two points $(5, -1)$ and $(2, 6)$ .

Let, $\vec a=5\hat {i}-\hat {j}$ and $\vec b= 2\hat {i}+6\hat{j}$ .

and we have calculate the projection of $\vec a$ onto $\vec b$ .

Now,

For the calculation of projection, first we need to calculate the dot product of $\vec a$ and $\vec b$ .

$\vec a.\vec b=(5\hat {i}-\hat{j}).(2\hat{i}+6\hat{j})$

$=10-6$

$=4$

then, we have to calculate the magnitude of $\vec b$ .

$\mid {\vec {b}}\mid$ = $\sqrt{2^{2}+6^{2} }$ = $\sqrt{40}$ = $2\sqrt{10}$ .

Now, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\vec a.\vec b}{\mid b\mid}$

= $\frac{4}{2\sqrt{10} }$ $\frac{2}{\sqrt{10} } \times\frac{\sqrt{10} }{\sqrt{10} } =\frac{2\sqrt{10} }{10} = \frac{\sqrt{10} }{5}$

and the vector projection of $\vec a$ onto $\vec b$ = $\frac{\vec a. \vec b}{\mid\vec b \mid^{2} } . \vec b$

= $\frac{4}{40} . (2\hat i+ 6\hat j)$

= $\frac{1}{5} \hat i+\frac{3}{5} \hat j$

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .

6 0

4 years ago

A circle has an area of 40 square meters. Which answer is closest to the measure of its diameter?

fomenos

D. 7.1
A circle has an area of 40 square meters. Which answer is closest to the measure of its diameter?

7 0

3 years ago

Read 2 more answers

1. Based on data collected over several sessions, a statistically minded trainer of office typists modeled the linzoom in

ipn [44]

Answer:

Statement D is correct.

Step-by-step explanation:

Solution:

Data Given:

Linear Regression Relationship = Speed = 10.3 + 5.4 (hour)

Linear Regression Relationship = y = mx + c

Here,

m = slope = 5.4

c = 10.3 = y - intercept

The correct Answer is D)

Because:

As, the residual value is positive, it means the typist attained faster speed than the model predicted. As we know, residuals is the result of difference between predicted values of the model and data values. On the contrary, if residual would be negative then we would say that typist speed is slower than the model predicted.

Hence, Statement D is correct.

6 0

3 years ago

How to simplify and expression

Ahat [919]

Answer:

Find something the parts of the equation (which are separated by a sign (+, -, x, or /)) and sort of un-distribute a common number out.

Step-by-step explanation:

Example: 5x + 10

Step One: Find what number they have in common. (5)

Step Two: Divide it from both parts of the equation and put it outside parentheses.

Step Three (result): 5(x+2)

3 0

3 years ago

Approximate the data using the line y = 0.25x + 3. Find the data point that has the residual with the greatest absolute value. G

ohaa [14]

Solution: We are given data points and associated residuals:

Data Point Residual Absolute value(Residual)

(20,6) -2.00 2.00

(15,5) 6.75 6.75

(5,3) -1.25 1.25

(10,10) 4.50 4.50

From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.

Therefore, the data point and its associated residual is:

(15,5) and 6.75

5 0

3 years ago

Read 2 more answers