Answer:
Step-by-step explanation:
Given:
u = 1, 0, -4
In unit vector notation,
u = i + 0j - 4k
Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.
If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then
u. v = 0 [substitute for the values of u and v]
=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k) = 0 [simplify]
=> v₁ + 0 - 4v₃ = 0
=> v₁ = 4v₃
Plug in the value of v₁ = 4v₃ into vector v as follows
v = 4v₃ i + v₂ j + v₃ k -------------(i)
Equation (i) is the generalized form of all vectors that will be orthogonal to vector u
Now,
Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e
[tex]\frac{v}{|v|}[/tex]
Where;
|v| = [tex]\sqrt{(4v_3)^2 + (v_2)^2 + (v_3)^2}[/tex]
|v| = [tex]\sqrt{17(v_3)^2 + (v_2)^2}[/tex]
[tex]\frac{v}{|v|}[/tex] = [tex]\frac{4v_3i + v_2j + v_3k}{\sqrt{17(v_3)^2 + (v_2)^2}}[/tex]
This is the general form of all unit vectors that are orthogonal to vector u
where v₂ and v₃ are non-zero arbitrary real numbers.
[tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
A vector is a quantity that has both magnitude and direction.
Two vectors are said to be orthogonal if they are perpendicular to each other.
Unit vectors orthogonal to [tex]u=\left ( a,b,c \right )[/tex] are given by [tex]\left ( \frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}},\frac{c}{\sqrt{a^2+b^2+c^2}} \right )[/tex]
So, vectors orthogonal to [tex]u=\left ( 1,0,-4\right )[/tex] are [tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )[/tex]
[tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )=\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
So, unit vector orthogonal to [tex]u[/tex] is [tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
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If f is a differentiable function such that f′(x)≥6, find the largest value of ???? so that f(4)≥???? whenever f(2)=10. (Use decimal notation. Give your answer as exact number.)
Answer:
12
Step-by-step explanation:
If the slope of the function were exactly 6 on the interval between 2 and 4, then the increase on that interval from f(2) = 10 would be (4-2)·6 = 12. Since the slope is at least 6, the increase is at least 12, so ???? = 10+12 = 22.
Geometry and Trigonometry
Answer:
a. 227 cm
b. 495 cm
Step-by-step explanation:
a. Radius of arc = sin(½θ) = 2.10/r
θ = (360-225)/2 = 67.5
Radius of arc = sin(67.5) = 2.10/r
r = 2.10/sin(67.5) = 2.273 m = 227 cm (nearest cm)
b. Length of arc = θ/360*2πr
Take π as 3.14
r = 210 cm
θ = 360 - 225 = 135°
Length of arc = [tex] \frac{135}{360}*2*3.14*210 = 495 cm [/tex] (to nearest cm)
Rena decides to go to a technical college for 18 months to get a degree in computer networking. There are 6 school quarters in the program with a tuition of $600 each. Books for the entire program cost $2,800. How much will it cost Rena to get his degree?
Answer:
Total Cost 6400
Step-by-step explanation:
Each quarter is 600 dollars
There are 6 quarters. 6 * 600 = 3600
Books 2800
Total 6400
Answer:
6400
Step-by-step explanation:
600*6=3600
3600+2800=6400
25x + 11(2+2) when X = 6 a.234 b.83 c.194 d.150
Answer:
194
Step-by-step explanation:
Charlie has—$19 in his bank account. This is $28 more then Steve’s bank account. How much money does Steve have in his bank account?
Answer:
may be incorrect but probably not -9
Step-by-step explanation:
19 - 28 = -9
Which list shows all the factors of 18?
1, 2, 3, 4, 6, 9, 18
1, 2, 3, 6, 9, 18
2, 3, 4, 6,9
2, 3, 6, 9
[tex]:\implies\sf\:18=1\times 18[/tex]
[tex]:\implies\sf\:18=2\times 9[/tex]
[tex]:\implies\sf\:18=3\times 6[/tex]
Hence, All the factors of 18 are
[tex]\boxed{\bf{\orange{(1,2,3,6,9,18)}}}[/tex]
Answer:
1, 2, 3, 6, 9, 18 is the answer
Step-by-step explanation:
What is the first step in solving the equation Two-thirds x + one-third x + 2 = 5? Subtract One-third from each side of the equation. Add 2 to each side of the equation. Combine like terms. Multiply each side of the equation by 5. PLEASE HURRY I WILL MARK BRAINLIEST!
Hey There!! ⚘~
The answer to this is: add 1/2x to both sides.
multiply both sides by 6/7
Hope It Helped!~
〰️~ItsNobody~〰️
Answer:
Combine Like Terms
Step-by-step explanation:
5x−6=3x+10 PLSPLS HELP
Answer:
x = 8
Step-by-step explanation:
Let's solve your equation step-by-step.
5x−6=3x+10
Step 1: Subtract 3x from both sides.
5x−6−3x=3x+10−3x
2x−6=10
Step 2: Add 6 to both sides.
2x−6+6=10+6
2x=16
Step 3: Divide both sides by 2.
2x /2 = 16/ 2
x=8
Answer:
So x=8 is the answer.
Step-by-step explanation:
5x-6=3x+10
Adding 6 on both sides to find out the value of x
5x-6+6=3x+10+6
5x=3x+16
Subtracting 3x on both sides to find out the value of x
5x-3x=3x-3x+16
2x=16
Dividing 2on both sides
2x/2=16/2
x=8
I hope this will help you :)
The distance from Gillette, New Jersey, to Irvington, New Jersey, is 1 mile more than four times the distance from Irvington to Newark. If the total distance from Gillette to Newark is 2 miles less than six times the distance from Irvington to Newark, what is the distance from Irvington to Newark if all three cities are in a straight line?
Answer:
distance from Irvington to Newark
.= 3 Miles
Step-by-step explanation:
distance from Irvington to Newark.= X
distance from Gillette, New Jersey, to Irvington, New Jersey,= y
Y= 1+4x
total distance from Gillette to Newark
= z
Z= 6x-2
But total distance = x+y
Total distance= x+1+4x
Total distance= 1+5x
1 +5x= 6x-2
1+2= 6x-5x
3= x
distance from Irvington to Newark.= X
distance from Irvington to Newark
.= 3 Miles
distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+4x
distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+4(3)
distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+12
distance from Gillette, New Jersey, to Irvington, New Jersey,= 13 miles
Total distance= 1+5x
Total distance= 1+5(3)
Total distance= 16 miles
Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}. Find the number indicated. n(A) + n(B)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \bold{9}}}}}[/tex]
Step-by-step explanation:
Given,
A = { Dirk , Johan , Frans , Sarie }
B = { Frans , Sarie , Tina , Klass , Henrika }
To find : n ( A ) + n ( A )
Now, count the number of member of a set A
n ( A ) = 4
Also, Count the number of members of a set B
n ( B ) = 5
Finding n( A ) + n ( B )
= 4 + 5
= 9
Hope I helped!
Best regards! :D
Daisy walked two-fifths of a mile in one-fifth of an hour. Walking at the same pace, how far will Daisy walk in 1 hour?
Answer:
2 miles
Step-by-step explanation:
2/5 mile = 1/5 hour
x mile(s) = 1 hour
Cross multiplying.
x · 1/5 = 2/5 · 1
x/5 = 2/5
Multiplying both sides by 5.
x = 10/5
x = 2
Daisy will walk 2 miles in 1 hour.
Answer:
[tex]\Huge \boxed{\mathrm{2 \ miles}}[/tex]
Step-by-step explanation:
2/5 mile = 1/5 hour
x mile(s) = 1 hour
Cross multiplying.
x · 1/5 = 2/5 · 1
x/5 = 2/5
Multiplying both sides by 5.
x = 10/5
x = 2
Daisy will walk 2 miles in 1 hour.
Which of the following shows as a mixed number and as an improper fraction?
There's no following. You need to post a picture or complete the question.
Express the inequality using interval notation. 3<×≤5
Answer:
(3,5]
Step-by-step explanation:
5! The office needs cabinets. The price for the first type of cabinet is $10, it
needs 6 ft2 of floor space, and it has a storage volume of 8 ft. The price
for the second type of cabinet is $20, it needs 8 ft? of floor space, and it
has a storage volume of 12 ft. The company wants to spend no more
than $140 and the office can hold up to 72 ft2 of cabinets. How can the
storage volume be maximized?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of 6 ft² to be purchased and y represent the number of 8ft² cabinet to e purchased.
x > 0 and y > 0
6 ft² cabinet cost $10 and 8 ft² cabinet cost $20, only $140 is available to spend, therefore the cost equation is:
10 x + 20 y ≤ 140
Also the office can hold only 72 ft², the space equation is:
6x + 8y ≤ 72
The volume equation is:
V = 8x + 12y
From the graph attached, we have to find the point with maximum volume by testing the point (12, 0), (0,7) , (8,3)
For (12, 0): V = 8(12) + 12(0) = 96 ft³
For (0, 7): V = 8(0) + 12(7) = 84 ft³
For (8, 3): V = 8(8) + 12(3) = 100 ft³
The (8,3) point has the maximum volume. That is 8 6 ft² cabinet and 3 8ft² cabinet
calculate the max shear of cantilever balcony 2m wide 0.2m deep and 1.5m length.
Answer:
14.4 kN
Step-by-step explanation:
cantilever balcony 2m wide 0.2m deep and 1.5m length.
= 2 x 0.2 x 1.5
= 0.6 m³
weight of the balcony
= 0.6 x 24
= 14.4 kN.
therefore the max shear 14.4 kN and is acting at support.
A book sold 33,700 copies in its first month of release. Suppose this represents 9.3% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
Answer: 362,365 copies
Step-by-step explanation: Using proportions, I set it up like 33700/? (total copies)= 9.3/100. I multiplied 33700 and 100 to get 3370000 and divided by 9.3 and rounded.
find the length of the hypotenuse !!
Answer:
17
Step-by-step explanation:
To find the hypotenuse, you would use the Pythagorean theorem.
[tex]A^{2} +B^{2} =C^{2}[/tex]
We can plug 8 and 15 into A and B\
[tex]8^{2} +15^{2} =C^{2}[/tex]
We can simplify this to
64+225=[tex]C^{2}[/tex]
289 = [tex]C^{2}[/tex]
To get C by itself not squared, we can do the square root of both sides.
[tex]\sqrt{289} =\sqrt{C^{2} }[/tex]
If we simplify, we get
17 = C or C = 17
Therefore the length of the hypotenuse is 17.
Mrs. Robertson is taking a picture of three students-Zach, John, and
Reginald. How many different ways can these three students stand in a line
to have their pictures taken?
Allie received a gift card for her local coffee shop. Every time she goes to part
the shop, she gets a medium coffee. The graph shows the gift card balance
ot two points. Use the two points to determine the slope of the line, Report
your answer in decimal form..
y
24
My Coffee
20
(1,17.50)
Gift Card
16
Gift Card Balance (5)
12
(5, 7.50)
8
4
0
0 2. 4 6 8 10
Medium Cups of Coffee
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10:34
Answer:
The slope of the line is -2.5.
Step-by-step explanation:
The formula to compute the slope of a straight line is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The graph shows the gift card balance after buying 2 and 5 cups of medium coffee.
The two points provided are:
A = (1, 17.50)
B = (5, 7.50)
Compute the slope of the line as follows:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\frac{7.50-17.50}{5-1}\\\\=\frac{-10}{4}\\\\=-2.5[/tex]
Thus, the slope of the line is -2.5.
Which expression is equivalent to-10w - 15.5? A. -5(2w-15.5) B. -5(2w+3.1) C. -5(5w-15.5) D. -5(5w+10.5).
Answer:
D
Step-by-step explanation:
The required expression that is equivalent to the given expression is -5(w+3.1) . Option D is correct.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The given expression,
= -10w - 15.5
taking 5 commons from both the terms,
= -5(2w + 3.1)
Thus, the required expression that is equivalent to the given expression is -5(w+3.1) . Option D is correct.
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(-6+1 1/2+5)^2...I'm getting 1 but when I put it in the calculator I get .25...What am I do wrong?
Answer:
Step-by-step explanation:
your doing the calculation wrong
Simplify the expression below, matching the correct steps in the order of operations. Identify the step as parentheses, exponents, multiplication, division, addition, or subtraction.
Answer:
PE,PS,E,M,A
Step-by-step explanation:
Do the phrases 6 less a number y and 6 less than a number y mean the same thing? Explain. A. No, they do not both mean the same thing. 6 less a number y can be represented by the expression 6 - y. 6 less than a number y can be represented by the expression y - 6. B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.
Answer:
B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.
Step-by-step explanation:
Given
Phrase 1: 6 less a number y
Phrase 2: 6 less than a number y
Mathematically,
Phrase 1 can be represented as follows;
[tex]y - 6[/tex]
Mathematically,
Phrase 2 can be represented as follows;
[tex]y - 6[/tex]
Since the representation of both phrases are the same, then option B answers the question.
in which number does the 7 have the greater place value 47,593 or 602.785 heeeeeeeeeeellllllllllppppppppppppp
Answer:
47,593
Step-by-step explanation:
The 7 is representing 7,000 whereas the 7 in 602.785 is representing 0.7, which is 10,000 times smaller than 7,000, giving the 7 in 47,593 a greater place value
the Red Line in the figure is an altitude of triangle hjl. Using right angle trig and properties of equality, y sin L = x = z sin H, write the Law of Sines for this triangle
Answer:
[tex]\Large \boxed{\mathrm{\bold{C}}}[/tex]
Step-by-step explanation:
[tex]\sf \displaystyle sin(\theta) =\frac{opposite}{hypotenuse }[/tex]
[tex]\sf \displaystyle sin(L) =\frac{x}{y}[/tex]
[tex]\sf \displaystyle sin(H) =\frac{x}{z}[/tex]
[tex]\displaystyle \sf \frac{sinL}{z} =\frac{sinH }{y}[/tex]
[tex]\displaystyle \sf \frac{\frac{x}{y} }{z} =\frac{\frac{x}{z} }{y}[/tex]
Simplifying the expression.
[tex]\sf \displaystyle \frac{x}{yz } = \frac{x}{yz} \ (true)[/tex]
[tex]\displaystyle \sf \frac{z}{sinL} =\frac{y}{sinH}[/tex]
[tex]\displaystyle \sf \frac{z}{\frac{x}{y}} =\frac{y}{\frac{x}{z}}[/tex]
Multiplying both sides by x.
[tex]\sf yz=yz \ (true)[/tex]
Answer:
d
Step-by-step explanation:
The law of Sines applied to a Δ ABC is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
Using this in Δ HJL
[tex]\frac{z}{sinL}[/tex] = [tex]\frac{y}{sinH}[/tex] → (b)
Which may be expressed in reciprocal form as
[tex]\frac{sinL}{z}[/tex] = [tex]\frac{sinH}{y}[/tex] → (a)
Thus the law of Sines can be expressed as either (a) or (b)
Select the expression that is equal to (9x + 3) – (5z - 7)
Answer:
9x+10-5z
Step-by-step explanation:
(9x + 3) – (5z - 7)
9x+3-5z + 7)
9x+10-5z
-r(3r^{2}+1)r=4 the 2 is to the power
Answer:
For the r alone
Step-by-step explanation:
Which of the numbers below is greater than zero? Select all that apply.
A)0.8
B)4.5
C)1/4
D)-2.25
E)-0.5
Answer:
The answers are letters A,B,and C
Solve the inequality for x. –2x + 3 < –13
Answer:
x > 8
Step-by-step explanation:
When you divide or multiply both sides of an inequality by a negative number, the equality is switched.
-2x + 3 < -13
(-2x + 3) - 3 < -13 - 3
-2x < -16
-2x/-2 < -16/-2
x > 8
Answer:
x > 8
Step-by-step explanation:
In order to solve the inequality for x, we must get x by itself on one side of the equation.
-2x + 3 < -13
3 is being added to -2x. The inverse of addition is subtraction. Subtract 3 from both sides of the equation.
-2x + (3-3) < (-13-3)
-2x < -13 -3
-2x < -16
x is being multiplied by -2. The inverse of multiplication is division. Divide both sides of the equation by -2.
-2x/-2 < -16/-2
When dividing or multiplying by a negative number, remember to flip the inequality sign.
-2x/-2 > -16/-2
x > -16/-2
x > 8
The solution to the inequality is x>8
Simplify the expression using Distributive Property
−20 ( 8x + 20 )