Answer:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
Step-by-step explanation:
For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.
If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.
Where;
cos α = [tex]\frac{a . i}{|a| . |i|}[/tex] ---------------------(i)
cos β = [tex]\frac{a.j}{|a||j|}[/tex] ---------------------(ii)
cos γ = [tex]\frac{a.k}{|a|.|k|}[/tex] ----------------------(iii)
And from these we can get the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
Now to the question:
Let the given vector be
a = 5i + j + 4k
a . i = (5i + j + 4k) . (i)
a . i = 5 [a.i is just the x component of the vector]
a . j = 1 [the y component of the vector]
a . k = 4 [the z component of the vector]
Also
|a|. |i| = |a|. |j| = |a|. |k| = |a| [since |i| = |j| = |k| = 1]
|a| = [tex]\sqrt{5^2 + 1^2 + 4^2}[/tex]
|a| = [tex]\sqrt{25 + 1 + 16}[/tex]
|a| = [tex]\sqrt{42}[/tex]
Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e
cos α = [tex]\frac{5}{\sqrt{42} }[/tex]
cos β = [tex]\frac{1}{\sqrt{42} }[/tex]
cos γ = [tex]\frac{4}{\sqrt{42} }[/tex]
From the value, now find the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
α = cos⁻¹ ( [tex]\frac{5}{\sqrt{42} }[/tex] )
α = cos⁻¹ ([tex]\frac{5}{6.481}[/tex] )
α = cos⁻¹ (0.7715)
α = 39.51
α = 40°
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{\sqrt{42} }[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{6.481 }[/tex] )
β = cos⁻¹ ( 0.1543 )
β = 81.12
β = 81°
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
γ = cos⁻¹ ([tex]\frac{4}{\sqrt{42} }[/tex])
γ = cos⁻¹ ([tex]\frac{4}{6.481}[/tex])
γ = cos⁻¹ (0.6172)
γ = 51.89
γ = 52°
Conclusion:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
Beverly has a backyard that is square. One of the sides is 10 feet long. What is the area of her back yard?
Answer:
100 ft sq.
Step-by-step explanation:
A square means all sides are equal.
Area = bxh
10 ft x 10 ft = 100 ft sq.
Answer:
The area is 100 ft^2
Step-by-step explanation:
A square has 4 equal sides so if one side is ten then all of the sides are 10
identify the perfect square that is closest . ex square 76 ; 81 ;8 ,9
Answer:
Perfect squares = 9 and 81
Step-by-step explanation:
[tex]\sqrt{76} = 2\sqrt{19} \\\sqrt{81} =9\\\sqrt{8} =2\sqrt{2} \\\sqrt{9} =3[/tex]
The Lions football team gained 20 yards after having lost 8 yearson the previous play. What was their net gain or loss for the two plays?
Answer:
Net gain = 12 years(point)
Step-by-step explanation:
The Lions football team gained 20 yards after having lost 8 yearson the previous play.
Years(point) gained= 20
Years(point) loss= 8
The net gain for the two plays
Net gain = gain - loss
Net gain = 20-8
Net gain = 12 years(point)
At a sale this week a suit is being sold for $323. This is a 32% discount from original price. What is the original price
Answer:
$475
Step-by-step explanation:
Make an algebraic expression
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. What is the probability that a carpet that is 8 feet by 14 feet contains no flaws
Answer:
Probabilty= 0.0015355
Step-by-step explanation:
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.
Probabilty= 1/270
Probabilty= 0.0037
carpet that is 8 feet by 14 feet
Area=8*14
Area=112 square feet
Probabilty= 0.0037*(112/270)
Probabilty= 0.0037*0.415
Probabilty= 0.0015355
Find the following Key Features of the Graph. Please submit a picture of your work or a
typed document with your work. Thank you..
1) Domain:
2) Range:
3) Positive Interval(s): I
4) Negative Interval(s):
5) Increasing Interval(s):
6) Decreasing Interval(s):
7) X-Intercept(s):
8) Y-Intercept(s);
Answer:
lo i just gto 100 %
Step-by-step explanation:
lets do dad i love you
You just bought a new car from a dealership that sells cars no older than 2015. Consider the relationship to be the same age." The relation is "same age and the set is cars made in 2015, 2016, 2017, 2018, 2019, and 2020.
(a) Prove that this relation is an equivalence relation.
(b) Describe the partition defined by the equivalence classes.
Answer:
dont list me i wont points
Step-by-step explanation:
duejcju4484574
if 10 students each own 10 pencils, which expression matches how many in total pencils they?
10×10=100
there is 100 pencils in total
Solve the problem
19-c=-10
Answer:
c=29
Step-by-step explanation:
19 - 29 = -10
Is 12 + 6 + 15= 12 +15+6 commutative property of addition
Answer:
yes
Step-by-step explanation:
answer above
A supermarket has 148 shrubs on their property, but they are having trouble mowing grass so they need to pay to have cut down shrubs each year until the property has less than 30 shrubs. If they can pay to have only three shrubs cut down this year, but six shrubs cut down every year after that, in how many years will they have less than 30 shrubs on their property?
Answer: 21 years
Step-by-step explanation: After the first year, it’s down by 3 so 145. For the next 20 years, you go down 6 shrubs a year. At year 20 it will be 31 shrubs so at year 21 it will be at 25 shrubs.
Answer:
21 years.
Step-by-step explanation:
All equations are written in bold so you can find them easier.The first thing we do is subtract the 3 shrubs from the first year from the total 148.
148 - 3 = 145
We then take 29 from 145, as the supermarket wants less than 30 shrubs on their property, so the maximum amount they want to keep is actually 29.
145 - 29 = 116
The supermarket can pay to have 6 shrubs cut down every year, excluding the first, so we need to do then is divide 116 by 6.
116 ÷ 6 = 19.333.
Because that equation leaves us with a decimal, we have to round up to get a whole number because the answer has to be in years, not years and months.
19.333 rounded up is 20.
So that's 20 years of paying for 6/per year. We have to add on the one year they only payed for 3 shrubs to be cut down, making the answer;
21 years.We can further confirm we have the right answer by doing;
6 × 20 = 120
145 - 120 = 25
Because we're going down in 6's, we know that 20 is the lowest amount of years it would take to get less than 30 shrubs, because 25 + 6 = 31.
Ju Chan solved the previous question by finding the expression 4(-15). Which addition problem would give the same result? Choose all that apply. A . 15 + 15 + 15 + 15
A . 15 + 15 + 15 +15 B . 4 + 4 + 4 + 4
C . (–1)(15 + 15 + 15 + 15)
D . (–15) + (–15) + (–15) + (–15)
Answer:
C. (-1)(15+15+15+15)
D. (-15)+(-15)+(-15)+(-15)
Step-by-step explanation:
The original expression: 4(-15)=-60
Let's try choice A: 15+15+15+15=60(not a negative number, so does not work)
Let's try choice B: 4+4+4+4=16(nowhere near -60)no
Let's try choice C: (-1)(15+15+15+15)=(-1)(60)=-60--yes
Let's try choice D: (-15)+(-15)+(-15)+(-15)=-60--yes
Only choices C and D work.
Answer:
c and d
Step-by-step explanation:
just did it
Plz help 7th grade math ASAP
Answer:
6
Step-by-step explanation: think of it this way. When you adding a positive to a negative, you simply taking the negative away from the positive. So in this case, you are subtracting 2 from 8 to get six. Or, its the difference between the positve and the negative!! Hope this helps!
Answer:
6
Step-by-step explanation:
Simplify: 8 + (-2) = 8 - 28 - 2 = 6I hope this helps!
solve for h
can someone please answer and explain thank you <33
Answer: [tex]h=\frac{2A}{(a+b)}[/tex]
Step-by-step explanation:
To solve for h, we want to get h alone. We need to use our algebraic properties.
[tex]A=\frac{1}{2} h(a+b)[/tex] [multiply both sides by 2]
[tex]2A=h(a+b)[/tex] [divide both sides by (a+b)]
[tex]h=\frac{2A}{(a+b)}[/tex]
Now that we have h alone, we know that [tex]h=\frac{2A}{(a+b)}[/tex].
If the perimeter of the
rectangle is 36 inches,
what is the value of x?
X-3
7x+5
Answer:
x = 2
Step-by-step explanation:
To find the value of x, we simply need to use the know values for the lengths, widths, and perimeter of the rectangle.
The formula for the perimeter of a rectangle is as follows:
P = 2L + 2W
Where P is the perimeter, L is the length, and W is the width.
Let L = 7x + 5 and W = x - 3
Now, we will simply plug our values into the formula and solve for x.
P = 2L + 2W
36 = 2 ( 7x + 5 ) + 2 ( x - 3 )
36 = 14x + 10 + 2x + -6
36 = 16x + 4
32 = 16x
2 = x
Thus, we have found the value of x to be 2.
Cheers.
In how many distinct ways can the letters of the word DALLAS be arranged?
Answer:
720ways
Step-by-step explanation:
DALLAS = 6!
6x 5 x 4 x 3 x 2 x 1
720 ways
The letters of the word DALLAS can be arranged in 720 distinct ways.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbdistinctn event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
A word has n letters. then there are m repeating letters, each of them repeating r0, r1, r2.. times
So the number of distincts ways the letters DALLAS can be arranged are:
DALLAS = 6!
= 6x 5 x 4 x 3 x 2 x 1
= 720 ways
The letters of the word DALLAS can be arranged in 720 distinct ways.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ2
solve for x if 10/4x-3 = 2
Answer:
We need to solve this equation:
[tex]\frac{10}{4x}-3=2[/tex]
We pass -3 to the right summing:
[tex]\frac{10}{4x} = 2 + 3[/tex]
[tex]\frac{10}{4x}=5[/tex]
We pass the 4x that is dividing to the right multiplying:
[tex]10 = 5*4x[/tex]
[tex]10=20x[/tex]
We pass the 20 of the right to the left dividing:
[tex]\frac{10}{20}=x[/tex]
[tex]x=\frac{1}{2}[/tex]
Now, we know [tex]x=\frac{1}{2}[/tex], so we can verify:
[tex]\frac{10}{4*\frac{1}{2}}-3 = 2[/tex]
[tex]\frac{10}{2}-3=2[/tex]
[tex]5 - 3 = 2[/tex] TRUE
Answer:
Kindly see attached picture
hope it helped you:)
Which expression shows
8 less than the product of
4 times 7?
A: 7 + 7 - 8
C:4x7 - 8
B:8-4x7
D: 4X 7 + 8
Answer:
8 less than the product of 4 times 7 is....
8-4×7.
Answer:
i think b cuz it shows 8 less means minus than product of 4 × 7 so it shows the answer b
1. 25p=100 2. 35=-2x-15
• Answer:
p = 4
x = - 25
• Step-by-step explanation:
25p = 100
p = 100÷25
p = 4
35 = - 2x - 15
2x = - 35 - 15
2x = - 50
x = - 25
Answer:
1) P= 4 2) x = -25
Step-by-step explanation:
25p = 100
divide both sides by 25
p = 4
35 = -2x - 15
add 15 to both sides
50 = -2x
divide both sides by -2
x = -25
Hope this helps!
PLS HELP BEST ANSWER GETS BRAINLIEST Find the height of the triangle whose base is 1/4 inch and its area is 7/8 square inches?
Answer:
7
Step-by-step explanation:
Half the base (.25) times x = 7/8
.25x = 7/8
7/8 divided by .125 = 7
how'd I do?
I hope I got it correct
Find the equation of a line containing the given points (4,3) and (8,1). Write the equation in slope-intercept form.
Answer:
y= -1/2x +5
Step-by-step explanation:
Find the distance. V(X2-X.)2+(2-Y.)?
(1,2)(5,4) (-3,5)(2,3)
Answer: If you divide a trinomial by a monomial the result is a bionomial
A. True
B. False
Step-by-step explanation: tell me the correct answer and I'll tell you
Answer:
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
Example
Find the distance between (-1, 1) and (3, 4).
This problem is solved simply by plugging our x- and y-values into the distance formula:
Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.
If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates: HOPES THIS HELPS
Step-by-step explanation:
what doesIf 7! = 7x6x5x4x3x2x1 then 5! =
Answer:
Step-by-step explanation:
5!=5*4*3*2*1=20*6=120
Answer:
Hey!
5! Is equal to 5×4×3×2×1
So your answer is 120!
Step-by-step explanation:
7! Is 5040!
HOPE THIS HELPS!
What details can you determine about the dive from the coordinates of the point (5, −8)?
Answer:
(See explanation below for further details)
Step-by-step explanation:
A. What details can you determine about the dive from the coordinates of the point (5, -8)?
First component corresponds to time and second component to depth with respect to sea level. The diver is 8 feet below sea level at 5 seconds.
B. What is the average speed of the diver in the water? How can you tell from the graph?
The average speed of the diver ([tex]\bar v[/tex]), measured in feet per second, can be calculated by the following expression:
[tex]\bar v = \frac{x_{f}-x_{o}}{t_{f}-t_{o}}[/tex]
Where:
[tex]x_{o}[/tex], [tex]x_{f}[/tex] - Initial and final depth of diver, measured in feet.
[tex]t_{o}[/tex], [tex]t_{f}[/tex] - Initial and final instant, measured in seconds.
There are three different average speeds: (i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex]), (ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex]), (iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
(i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = -8\,ft[/tex]
[tex]\bar v_{i} = \frac{-8\,ft-0\,ft}{5\,s-1\,s}[/tex]
[tex]\bar v_{i} = -2\,\frac{ft}{s}[/tex]
(ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = -8\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{ii} = \frac{0\,ft-(-8\,ft)}{9\,s-5\,s}[/tex]
[tex]\bar v_{ii} = 2\,\frac{ft}{s}[/tex]
(iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{iii} = \frac{0\,ft-0\,ft}{9\,s-1\,s}[/tex]
[tex]\bar v_{iii} = 0\,\frac{ft}{s}[/tex]
C. Which point on the graph shows the starting location of the diver?
The initial location is when [tex]t = 0\,s[/tex], which corresponds to the intercept of the line on y-axis.
if X = a^1/3 - a^-1/3 , show that x^3 + 3x = a - 1/a
Answer:
Step-by-step explanation:
Hello,
[tex](a^{1/3}-a^{-1/3})^3=a-3a^{1/3}+3a^{-1/3}-\dfrac{1}{a}=-3x+a-\dfrac{1}{a}\\\\<=> x^3+3x=a-\dfrac{1}{a}[/tex]
Thanks
x^2+y^2=25 Y= 2x - 5
What are the x coordinates
Answer:
(0, -5) and (4, 3)
Step-by-step explanation:
I assume you're looking for the coordinates of the intersections, if any.
Solve by substitution:
x² + (2x − 5)² = 25
x² + 4x² − 20x + 25 = 25
5x² − 20x = 0
5x (x − 4) = 0
x = 0 or 4
So the coordinates are (0, -5) and (4, 3).
Use scientific notation to find the product of 20.5 × 10^7 and 0.000036.
73.8 × 10 2
7.38 × 10 2
5.69 × 10 12
7.38 × 10 3
In the figure above, the radius of the inscribed circle is inches (in.). What is the perimeter of square CABD?
Answer:
perimeter of the square is 32 inches
which agrees with the last answer in your list of options.
Step-by-step explanation:
Notice that the radius of the circle is exactly half of the side of the square, therefore, each side of the square must be 8 inches long.
Then, the perimeter of the square (addition of its four sides) is :
4 x 8 inches = 32 inches
Answer:
Step-by-step explanation:
32
The distance around a figure is called _____
The distance around a figure is the perimeter, although around a circle is the perimeter is actually called the circumference.
Answer:
PerimeterStep-by-step explanation:
A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg was 35 with a standard deviation of 8.6. The correlation coefficient between city mpg and highway mpg is 0.95. Although a scatterplot is not show, it has been determined that a linear equation is appropriate for the data. Determine the correct value of the slope for the linear model that predicts highway mpg based on city mpg and interpret it in context.
Answer:
0.89
Step-by-step explanation:
Nunber of samples = 100
City mpg :
Mean = 28
Standard deviation =9.2
Highway mpg:
Mean = 35
Standard deviation = 8.6
correlation Coefficient (r) between city mpg and highway mpg = 0.95.
The value of the slope of the regression line that predicts highway mpg based on city mpg can be obtained by:
(Standard deviation of highway mgp / standard deviation of city mpg) × correlation Coefficient
Slope = (8.6 / 9.2) × 0.95
Slope = (0.934782 × 0.95) = 0.8880
Slope = 0.89 ( two decimal place)