===========================================================
Explanation:
For any two vectors defined as follows
u = <a,b>
v = <c,d>
the dot product is computed by
u dot v = a*c + b*d
If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.
-------------------
Let's find the dot product of these two given vectors
u = < 2, -4 >
v = < 6, 3 >
u dot v = 2*6 + (-4)*3
u dot v = 12 - 12
u dot v = 0
Therefore, these two vectors form a right angle and are orthogonal
-------------------
Extra info:
If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.
find The derivative of:(cosx/1+sinx)^3
Answer:
[tex]-\frac{3 \cdot cos^2x}{(1+sinx)^3}[/tex]
Step-by-step explanation:
[tex]y = (\frac{cosx}{1+sinx})^3\\\\\frac{dy}{dx} = 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{dy}{dx}(\frac{cosx}{1+sinx})[/tex] [tex][ y = x^n\ \ \ => \ \ \ \frac{dy}{dx} = b \cdot x^{n-1} \ ][/tex]
[tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{(1+sin x(-sinx) - cosx(cosx)}{(1+sinx)^2}\\\\[/tex] [tex][\ \frac{u}{v} = \frac{v \dcot u'- u \cdot v'}{v^2}\ ][/tex]
[tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-sin^2x- cos^2x}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x- (sin^2x+ cos^2x)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-1}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1 \cdot(sin x+1)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1}{(1+sinx)}\\\\[/tex]
[tex]= -3 \cdot \frac{cos^2x}{(1+sinx)^3}[/tex]
4. Dakota earned $30 in simple interest after 5 years. The interest rate was 4%
Answer:
The final balance is $36.5.
The total compound interest is $6.5.
Step-by-step explanation:
What is the length of u and v in this 30-60-90 triangle
Answer:
option 2
Step-by-step explanation:
Using trigonometric ratio:
[tex]Cos \ 60 = \frac{adjacent } {hypotenuse} \\\\\frac{1}{2} = \frac{4}{u}\\\\1 \times u = 2 \times 4 \\\\u = 8[/tex]
Now using Pythagoras theorem we will find v
[tex]8^2 = 4^2 + v^2\\\\64 = 16 + v^2\\\\v^2 = 64 - 16 \\\\v = \sqrt{48} = \sqrt{16 \times 3} = \sqrt{4^2 \times 3 } = 4\sqrt{3}[/tex]
By using trigonometric relations, we will see that v = 4*√3 and u = 8
How to get the missing lengths?
Here we have a right triangle, we can use trigonometric relations to find the missing sides.
We can see that v is the opposite cathetus of the 60° angle, then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing what we know, we get:
tan(60°) = v/4
4*tan(60°) = v = 4*√3
To get the value of u, we use:
cos(a) = (adjacent cathetus)/(hypotenuse).
cos(60°) = 4/u
u = 4/cos(60°) = 2*4 = 8
Then we have:
v = 4*√3
u = 8
If you want to learn more about triangles, you can read:
https://brainly.com/question/17972372
Identify the location of the point (0, -3).
Answer:
Point p
Step-by-step explanation
The first number in your point is on the x axis, but since it's 0 you don't move anywhere.
The second number in your point is on the y axis, it's -3, so you move down on the y axis 3 times.
When the x axis(first number) is negative you move left, and if the y axis(second number is negative you move down), and vise versa.
Which of the following correctly names a side of the triangle below?
A. ZC
B. B
С. АВ
D. AABC
Answer:
C. [tex]\frac{}{AB}[/tex]
Step-by-step explanation:
You can solve this in two ways, firstly by eliminating all the wrong answers, and secondly by just knowing that the horizontal line in [tex]_[/tex][tex]\frac{}{AB}[/tex] means that we are talking about a line.
This is how we solve this question by using the eliminating process.
(A. ∠C) is not the right answer because the ∠ sign lets us know that this answer represents an angle, not a line
(B. B) is not the right answer because it represent a point, not a line (in math we use a singular capital letter to represent points)
(D. ΔABC) is not the right answer because the Δ sign lets us know that the answer represents a triangle, not a line.
Therefore, the only option left is C. [tex]\frac{}{AB}[/tex]
Write the rule for the translation shown below.
WHAT IS THIS HELP- 20 points i think-
Answer:
(6,5)
Step-by-step explanation:
To keep the sides parallel, the y coordinate must be the same as the top point so y = 5
The distance between the bottom points is 1, so the distance between the top points must be 1
The point could be at 5-1 =4 or 5+1 = 6
(4,5) or (6,5)
Given the choices listed
Know how to rearrange formulae Question 1: Make y the subject of each of the following
(a) y + w = c
(b) y- p = m
C) m + y = s
(d) y - 2g = n
(e) 3y = c
(f) ay = w
(g) y/c =w
(h) y/a= 2c
(i) a = y + p
Someone please help me.
Answer:
y=c - w
y=m+p
y=n+2g
y=c/3
y=w/a
y=w×c
y=2c×a
y=a-p
Step-by-step explanation:
crossing the equality sign
- = +
+ = -
× = ÷
÷ = ×
hope this would help
PLEASE HELP MEEE!! AND DONT PUT THESE LIKE TINY.URL THINGS
=======================================================
Work Shown:
A = h*(b1+b2)/2 .... area of trapezoid formula
A = 4*(7+3)/2
A = 4*(10)/2
A = 40/2
A = 20 square units
-----------
notes:
The bases b1 and b2 are parallel to one another.b1 = 7 is the longer horizontal base at the bottom. It spans from x = 1 to x = 8, so it's 8-1 = 7 units long.b2 = 3 is the shorter horizontal base up top. It spans from x = 2 to x = 5, so it's a distance of 3 units.h = 4 is the height. We can count out 4 spaces when going one base to the other, or we can note that the y coordinates subtract to 4 (ie 5-1 = 4)The base and height are always perpendicular to one another.As an alternative way to solve, you can break the figure into 2 triangles and a rectangle in between. Find the area of each piece, and then add those areas up to get the final answer.I'm having trouble grasping this one
Answer:
- 50
Step-by-step explanation:
Given the equation :
2x³ - z
x = - 3 ; z = - 4
Substituting the values into the equation :
2(-3)³ - (-4)
-3³ = - 27
Hence,
2(-27) - (-4)
-54 + 4
= -50
2x³ - z at x = - 3 and z = - 4 is - 50
PLS I REALLY NEED HELP
Answer:
i dont know this sorry
Step-by-step explanation:
What is the image of N for a 288° counterclockwise rotation about the center of the regular pentagon?T A P E
9514 1404 393
Answer:
T
Step-by-step explanation:
The figure has 5-fold rotational symmetry, so each 72° of CCW rotation will bring point N to the next vertex in the CCW direction. Rotation of 288° will move point N 4 vertices CCW, equivalent to 1 vertex in the CW direction. Either way, that point is now occupied by point T.
N' ≅ T
Find the upper 20%of the weight?
Answer:
The upper 20% of the weighs are weights of at least X, which is [tex]X = 0.84\sigma + \mu[/tex], in which [tex]\sigma[/tex] is the standard deviation of all weights and [tex]\mu[/tex] is the mean.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Upper 20% of weights:
The upper 20% of the weighs are weighs of at least X, which is found when Z has a p-value of 0.8. So X when Z = 0.84. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - \mu}{\sigma}[/tex]
[tex]X = 0.84\sigma + \mu[/tex]
The upper 20% of the weighs are weights of at least X, which is [tex]X = 0.84\sigma + \mu[/tex], in which [tex]\sigma[/tex] is the standard deviation of all weights and [tex]\mu[/tex] is the mean.
como se obtiene el area de un polígono regular?
Answer:
Área de un polígono regular. El área o superficie de un polígono es igual al producto del perímetro por la apotema dividido por dos. El perímetro es la suma de todos los lados.
Step-by-step explanation:
Answer:
Step-by-step explanation:
El área de un polígono regular se calcula a partir de su perímetro y su apotema. Sea P el polígono regular con N lados, su área es:
Fórmula del área del polígono regular mediante su perímetro
A jogger travelled 52km in 4 days.what is the rate he travelled per day?
52km multiply by 4(days)=208
TTFN is the first one in secend and
Answer:
issue is the formula is still available
Step-by-step explanation:
what thw law do I have
PLS HELP ASAP ILL MARK BRAINLIEST Find the geometric probability of landing in the shaded area of the picture. The small circle has a diameter of 6 meters and the larger circle has a diameter of 54 meters. Show and explain all work.
Answer:
1/80
Step-by-step explanation:
(the area of the small circle)/(the area of the larger circle)
= (π× 3²)/(π× 27²)
(=> eliminate π)
= 3²/27² = (1/9)² = 1/81
since the shaded area is inside the larger circle,
the geometric probability =
1/(81-1) = 1/80
Which is the equation of the line that is parallel to the given line and has an X -intercept of -3
Answer:
Answer:Uh oh! It looks like your question is missing some crucial information.
Step-by-step explanation:
You didn't include the"given line"
The quotient of 9/10
Answer:
0.9 is the correct answer
How much would nick have over the span of 20 years if he put $1000 in his savings account with 10% of simple interest
Step-by-step explanation:
use the simple interest formula
Find the y- intercept and x-intercept of the line.
4x-y=8
Answer:
x-intercept is (2,0)
y-intercept is (0,-8)
Step-by-step explanation:
to find the 'x-intercept', substitute zero for 'y' and solve:
4x - 0 = 8
4x = 8
x = 2; x-intercept is (2,0)
4(0) - y = 8
0 - y = 8
y = -8; y-intercept is (0,-8)
x over 3 add 5 = 5
Pls help someone
Answer:
x=0
Step-by-step explanation:
0/3 = 0
0+5=5
The jackals howled loudly in the forest change in to interrogative
Answer:
did, the jackles howled loudly in the forest ?
please help me it this question
Answer:
4cm ×6cm(parallelogram)
Find the value of cos 28°cos 62°– sin 28°sin 62°
cos 28°cos 62°– sin 28°sin 62° = 0
Step-by-step explanation:From one of the trigonometric identities stated as follows;
cos(A+B) = cosAcosB - sinAsinB -----------------(i)
We can apply such identity to solve the given expression.
Given:
cos 28°cos 62°– sin 28°sin 62°
Comparing the given expression with the right hand side of equation (i), we see that;
A = 28°
B = 62°
∴ Substitute these values into equation (i) to have;
⇒ cos(28°+62°) = cos28°cos62° - sin28°sin62°
Solve the left hand side.
⇒ cos(90°) = cos28°cos62° - sin28°sin62°
⇒ 0 = cos28°cos62° - sin28°sin62° (since cos 90° = 0)
Therefore,
cos28°cos62° - sin28°sin62° = 0
Roman numeral for 67
Answer:
LXVII
Step-by-step explanation:
The roman numeral for 67 is LXVII
LX represents 60 and VII represents 7
which statement is true?
Answer:
The y-intercept of function A is less than the y- intercept of function B
hope it is helpful to you
need help with these table
What is the distance between -5 and 4
Answer:
9
Step-by-step explanation:
-5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4
-5 + 9 = 5
How many multiples of 9 are between 100,000 and 100,185?
Answer:
20
Step-by-step explanation:
After 99,999 is 100,008 So start from there
100,008 1
100,017 2
Ten 9's later...
100,107 12
Eight 9's later...
100.179
Ther are 20