Answer:
40%
Step-by-step explanation:
[tex]\frac{8}{20} X 100%[/tex][tex]=40%[/tex]%
Express each vector as a product of its length and direction.
16–√i−16–√j−16–√k
Question:
Express each vector as a product of its length and direction.
[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Step-by-step explanation:
A vector v can be expressed as a product of its length and direction as follows;
v = |v| u
Where;
|v| = length/magnitude of v
u = unit vector in the direction of v
---------------------------------------------------------------------------------------
Let the given vector be v, i.e
[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
(i) The length/magnitude |v| of vector v is therefore,
|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]
|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]
|v| = [tex]\sqrt{(\frac{3}{6})[/tex]
|v| = [tex]\sqrt{(\frac{1}{2})[/tex]
|v| = [tex]\frac{1}{\sqrt{2}}[/tex]
(ii) The unit vector u in the direction of vector v, is therefore,
u = [tex]\frac{v}{|v|}[/tex]
[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]
[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Therefore, the vector can be expressed as a product of its length and direction as:
|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Subtract. Fill in the missing numbers. 11-4=? 4=3+1 So, 11-4=
Answer:
7
Step-by-step explanation:
C is the midpoint of segment AB. Find the value of m+k.
A(-3,m)
B (4, -1)
C (k, 2)
Answer:
The value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].
Step-by-step explanation:
We are given that C is the midpoint of segment AB where A(-3,m) , B (4, -1) , and C (k, 2).
As we know that the mid-point formula states that;
Mid-point = [tex]\frac{a+b}{2}[/tex]
This means that;
Mid-point of AB = [tex]\frac{A+B}{2}[/tex]
C(k, 2) = [tex](\frac{-3+4}{2}, \frac{m+(-1)}{2} )[/tex]
C(k, 2) = [tex](\frac{1}{2}, \frac{m-1}{2} )[/tex]
This means that;
[tex]k = \frac{1}{2}[/tex] and [tex]2=\frac{m-1}{2}[/tex]
[tex]k = \frac{1}{2}[/tex] and [tex]m-1=4[/tex]
[tex]k = \frac{1}{2}[/tex] and [tex]m = 4+1 = 5[/tex]
So, the value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].
please help me out with this
Answer:
up is equal to 5/ 6
left side is equal to 3/4
Step-by-step explanation:
1/6 + 1/6+ 1/6+ 1/6+ 1/6= 5/6
1/4 + 1/4 + 1/4= 3/4
What percent is equivalent to 2/3?
A.) 66 1/3% B.) 66 3/5% C.) 66 2/3% D.) 66 7/10%
Answer:
C
Step-by-step explanation:
2/3=66 therefore it also equals 2/3%
Answer: C
Step-by-step explanation:
First find the decimal of 2/3
Divide it 2/3 = 0.6666666
Now multiply it by 100 to convert it to a percent
You get 66.66..% which is the same as 66 2/3%
E Solve for x 6(x - 1) = 9(x + 2) x = -8 x= 3 x = 8
Answer:
x = -8
Step-by-step explanation:
[tex]6(x - 1) = 9(x + 2)[/tex]
Expand :
[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]
[tex]6x - 6 = 9x + 18[/tex]
Collect like terms and simplify
[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]
Divide both sides of the equation by -3
[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]
Answer:
Step-by-step explanation:
6x - 6 = 9x + 18
-3x - 6 = 18
-3x = 24
x = -8 is the solution
What is the slope of the line on the graph?
We can use the points (-4, 0) and (0, 2) to solve.
Slope formula: y2-y1/x2-x1
2-0/0-(-4)
2/4
1/2
Best of Luck!
I need help with this please
Answer:
C
Step-by-step explanation:
Please help 4+(-10)-(-9)
Answer:
-15
Step-by-step explanation:
-10+-9=-19+4=-15
(-17) (0) what does this equal
Answer:
-17 × 0 = 0
every number multiplied by 0 is equal to 0
determine if the interval is increasing or decreasing
What is the greatest common factor of 28, 34, and 42?
Answer:
28 (0,2,4,14,28)
34 (0,2,17,34)
42 (0,2,6,7,21,42)
the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42
please help Spotting Axis Intercepts
Answer:
Coordinate A ins not intercepting any axis.
Step-by-step explanation:
For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]
Since in (3, 6), none of the components are 0, it is not intercepting any axes.
What is the value of 30-2(7+2)-1?
O 11
0 14
017
019
What is the common ratio of the Fibonacci sequence called
Answer:
1.618
The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.
Step-by-step explanation:
Plz Mark me as brainliest
[tex]\Large \boxed{\sf golden \ ratio}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
For the points P1(-2,3,2) and P2(1,2,0) , find the direction of P1P2 and the midpoint of line segment P1P2.
Given :
Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .
To Find :
The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .
Solution :
Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :
[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]
Now , mid point is given by :
[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]
Hence , this is the required solution .
Select the measurement scale in the right column that best matches the description in the left column. Note that each scale (nominal scale, ordinal scale, interval scale, and ratio scale) will be used exactly once. 1. Values measured on this scale can be compared such that you can say, for example, one value is twice as big as another value. 2. The values of data measured on this scale can be rank ordered and have meaningful differences between scale points.3. The values of data measured on this scale can be a number or a name, but they cannot be rank ordered. 4. The values of data measured on this scale can be rank ordered.
Answer:
1. RATIO SCALE
2. INTERVAL SCALE
3. NOMINAL SCALE
4. ORDINAL SCALE
Step-by-step explanation:
The scales are:
- Nominal Scale
- Ordinal Scale
- Interval Scale
- Ratio Scale
Rule: Each scale will be used exactly once.
For number 1, the description is that of a Ratio Scale because size comparisons can be made between values on the scale, such as the example given - that one value is twice as big as another value.
For number 2, the description is that of an Interval Scale because the values of data measured on the scale can be ranked e.g. Yes ranks as 1, No ranks as 2, Indifferent ranks as 3 and there is meaningful difference (not numerical difference) between scale points.
For number 3, the description is that of a Nominal Scale, because it says obviously that the values of data measured on this scale can be in form of names (watch out for keywords like this when reading through) and cannot be rank ordered! A good example is the following data set:
- Yellow, Brown, Purple, Cream, Fustian Pink
For number 4, the description is that of an Ordinal Scale. A keyword "rank" is to be given attention here, even as the statement is straightforward and gives just a simple information.
Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.
Answer:
The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].
Step-by-step explanation:
The equation of a sphere of radius r, with center (a,b,c) is given by
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.
Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]
Then,
[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
This is the equation of the sphere with center (-3, 2 , 5) and radius 4,
Now, for the intersection of this sphere with the yz- plane,
The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]
Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes
[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]
This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]
This is the part of the sphere that intersects with the yz-plane.
Match the expression on the left when it’s simplified form on the right answer options on the right may be used.more than once
Here are the expressions on the left matched with the simplifed form on the right:
-(-9) = 9|-9| = 9 -|9| = -9|9| = 9 -|-9| = -9How can the expressions be simplied?Here are some mathematical rules:
a negative sign multiplied by a negative sign is equal to a postive sign a postive sign multiplied by a negative sign is equal to a negative sign.a positive sign multiplied by a postive sign is equal to a postive sign.Also, this sign | | indicates that the number is postive.
To learn more about addition, please check: https://brainly.com/question/349488
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Please hurry! Which expression is equivalent to 2 (5) Superscript 4? 2 times 5 times 4, 2 times 5 times 5 times 5 times 5, 2 times 4 times 4 times 4 times 4 times 4 ,10 times 10 times 10 times 10
Answer:
10 x 10 x 10 x 10.
Step-by-step explanation:
2(5)^4
10^4
Expanded form; 10*10*10*10.
Answer:
10 x 10 x 10 x 10
Step-by-step explanation:
P(t) = 520/1+5e^-0.2t
Find the initial population size
PLS HELP! 10 POINTD ILL MARK BRAINLIEST
l=3w
3w(4)=48
12w=48
w=4
l=12
hope it helps
comment if u have any questions
Answer:
Length is 18; width is 6.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:
[tex]l=3w[/tex]
So, substitute this for l and 48 for P. Thus:
[tex]48=2(3w)+2w[/tex]
Distribute:
[tex]48=6w+2w[/tex]
Combine like terms:
[tex]48=8w[/tex]
Divide both sides by 8:
[tex]w=6[/tex]
So, the width is 6.
The length as we know is 3 times the width, so the length is 3(6) is 18.
And we are done!
r+4r-1=24
Be quick please :)
Step-by-step explanation:
r+4r=24+1
5r=25
r=25/5
r=5
Answer:
r = 5
Step-by-step explanation:
r + 4r - 1 = 24
r + 4r = 25
5r = 25
r = 5
Which answer describes the type of numbers that are dense? whole numbers and integers whole numbers but not integers rational numbers and irrational numbers rational numbers but not irrational numbers
Answer:
rational numbers and irrational numbers
Step-by-step explanation:
Help I am stuck on this.
Answer:
i think is the second one
Step-by-step explanation:
Match the vocabulary to the correct operation
Answer:
Step-by-step explanation:
Product—Multiplication
Sum— Addition
Difference—Subtraction
Quotient—Division
Quantity— Parenthesis
bfnskalalalallsmsmsm help
Answer:
x>18
Step-by-step explanation:
salesperson receives 16.7% commission. If her total sales for the month are $4900, what is her commission?
Answer:
$818,3
Step-by-step explanation:
16.7% in decimal is 0.167
= 0.167 x $4900
= $818,3
Find the modulus of the following |9+40i|
Answer:
modulus of |9+40i| is 41
Step-by-step explanation:
Let z = 9+40i
then
|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]
= [tex]\sqrt{81+1600}[/tex]
= [tex]\sqrt{1681}[/tex]
= 41
|z| = 41
Answer:
Step-by-step explanation:
1. |9+40i| = 41
2. |-10+24i| = 26
When three professors are seated in a restaurant, the hostess asks them: "Does everyone want coffee?" The first professor says: "I do not know." The second professor then says: "I do not know." Finally, the third professor says: "No, not everyone wants coffee."
The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?
the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.