Answer:
So the way to express a vector( [tex]v = 2i - 2j - 2k[/tex]) as a product of its length and direction is
[tex]v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]
Step-by-step explanation:
Generally a vector is expressed as a product of its length and direction using the formula below
[tex]v = |v|\cdot u[/tex]
Here v is the vector
|v| is its magnitude (length)
u is its unit vector (direction)
Now let take an example
Let
[tex]v = 2i - 2j - 2k[/tex]
The magnitude is mathematically evaluated as
[tex]|v| = \sqrt{ 2^2 + (-2)^2 + (-2)^2 }[/tex]
[tex]|v| = \sqrt{12}[/tex]
The unit vector is mathematically represented as
[tex]u = \frac{v}{|v|}[/tex]
[tex]u = \frac{ <2 , -2 , -2>}{\sqrt{12} }[/tex]
[tex]u = \frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} }[/tex]
So
[tex]v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]
You have a bin full of the letters HGUSTWQ. If four letters are drawn at random, what is the probabilty the letters drawn will spell the word GUST ( in the order they are drawn )?
Answer:
see I need help for chemistry pls anyone here helps me I must submit before 10:30
Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=vt+vt2 / 2(e) v=x2 / at3(f) a3=x2v / t5(g) x=t(h) v=5at
Complete Question
The complete question is shown on the first uploaded image
Answer:
A
is dimensionally consistent
B
is not dimensionally consistent
C
is dimensionally consistent
D
is not dimensionally consistent
E
is not dimensionally consistent
F
is dimensionally consistent
G
is dimensionally consistent
H
is not dimensionally consistent
Step-by-step explanation:
From the question we are told that
The equation are
[tex]A) \ \ a^3 = \frac{x^2 v}{t^5}[/tex]
[tex]B) \ \ x = t [/tex]
[tex]C \ \ \ v = \frac{x^2}{at^3}[/tex]
[tex]D \ \ \ xa^2 = \frac{x^2v}{t^4}[/tex]
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex]
[tex]F \ \ \ x = 3vt[/tex]
[tex]G \ \ \ v = 5at[/tex]
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex]
Generally in dimension
x - length is represented as L
t - time is represented as T
m = mass is represented as M
Considering A
[tex]a^3 = (\frac{L}{T^2} )^3 = L^3\cdot T^{-6}[/tex]
and [tex]\frac{x^2v}{t^5 } = \frac{L^2 L T^{-1}}{T^5} = L^3 \cdot T^{-6}[/tex]
Hence
[tex]a^3 = \frac{x^2 v}{t^5}[/tex] is dimensionally consistent
Considering B
[tex]x = L[/tex]
and
[tex]t = T[/tex]
Hence
[tex]x = t[/tex] is not dimensionally consistent
Considering C
[tex]v = LT^{-1}[/tex]
and
[tex]\frac{x^2 }{at^3} = \frac{L^2}{LT^{-2} T^{3}} = LT^{-1}[/tex]
Hence
[tex]v = \frac{x^2}{at^3}[/tex] is dimensionally consistent
Considering D
[tex]xa^2 = L(LT^{-2})^2 = L^3T^{-4}[/tex]
and
[tex]\frac{x^2v}{t^4} = \frac{L^2(LT^{-1})}{ T^5} = L^3 T^{-5}[/tex]
Hence
[tex] xa^2 = \frac{x^2v}{t^4}[/tex] is not dimensionally consistent
Considering E
[tex]x = L[/tex]
;
[tex]vt = LT^{-1} T = L[/tex]
and
[tex]\frac{vt^2}{2} = LT^{-1}T^{2} = LT[/tex]
Hence
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex] is not dimensionally consistent
Considering F
[tex]x = L[/tex]
and
[tex]3vt = LT^{-1}T = L[/tex] Note in dimensional analysis numbers are
not considered
Hence
[tex]F \ \ \ x = 3vt[/tex] is dimensionally consistent
Considering G
[tex]v = LT^{-1}[/tex]
and
[tex]at = LT^{-2}T = LT^{-1}[/tex]
Hence
[tex]G \ \ \ v = 5at[/tex] is dimensionally consistent
Considering H
[tex]a = LT^{-2}[/tex]
,
[tex]\frac{v}{t} = \frac{LT^{-1}}{T} = LT^{-2}[/tex]
and
[tex]\frac{xv^2}{2} = L(LT^{-1})^2 = L^3T^{-2}[/tex]
Hence
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex] is not dimensionally consistent
We want to see which ones of the given expressions are dimensionally consistent. We will see that the correct options are:
a) x = 3*v*th) v = 5*a*tWhat means to be dimensionally consistent?
This means that we have the same units in the left and in the right side of the equation.
The units are:
a = [m/s^2]x = [m]v = [m/s]t = [s]Now we can analyze the expressions to see the units in each one, I will show you how to do it:
a) a = v/t + x*v^2
Replacing the units we have:
[m/s^2] = [m/s]/[s] + [m]*[m^2/s^2]
[m/s^2] = [m/s^2] + [m^3/s^2]
You can see that we have an m^3 in the right side, so these are not equivalent.
b) x = 3*v*t
Replacing the units we have:
[m] = 3*[m/s]*[s] = 3*[m]
So yes, the units are the same in both sides, so this is dimensionally consistent.
With the same procedure we can see that:
c) [m^3/s^2] = [m^3/s] not consistentd) [m] = [m] + [m*s] not consistente) [m/s] = [m^2] not consistentf) [m^3/s^6] = [m^3/s] not consistentg) [m] = [s] not consistenth) [m/s] = 5*[m/s] consistentSo the correct options are b and h.
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The average spending at Neco's salad bar is $8.73 with a standard deviation of $3.41. The distribution follows t-distribution. The management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
Answer:
Difference between upper and lower limits is : 1,816
Step-by-step explanation:
A CI (confidence interval ) for t student distribution is:
( μ₀ - t(α/2)* s/√n ; μ₀ + t(α/2)* s/√n )
Where:
μ₀ is the mean and s the standard deviation of the dstribution
n size of the sample
CI = 90 % means α = 10 % α = 0,1 α/2 = 0,05
and degree of freedom df = n - 1 df = 40
From t student table we get:
tα/2 = 1,6839
Then:
t(α/2)* s/√n = 1,6839* 3,41/√40
t(α/2)* s/√n = 0,908
8,73 - 0,908 = 7,822
8,73 + 0,908 = 9,638
CI (90%) = ( 7,822 ; 9,638 )
Difference between upper and lower cut-offs points is:
Δ = 1,816
Jack is packing snacks for him and his three brothers. He bought 10 1/2 ounces of pretzels. He wants to put the pretzels into bags so that he and his three brothers have the same of pretzels in their bags. How many ounces of pretzels should he put into each bag?
Answer:
3.5
Step-by-step explanation:
total pretzel=10 1/2 or10.5
no. of brother = 3
now,
10.5 pretzel for each borther= 10.5/3
=3.5 ans
What number line correctly shows one way to find 2-6 ?
please help :)) ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
The velocity of an object is given by the following function defined on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into the indicated number of subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles. v = 1/(2t + 4) (m/s) for for 0 ≤ t ≤ 88; n = 22
Answer:
The displacement of the object on this intervals is 1.33 m.
Step-by-step explanation:
Given that,
The function of velocity is
[tex]v=\dfrac{1}{2t+4}\ m/s[/tex]
For 0 ≤ t ≤8 , n = 2
We need to calculate the intervals
Using formula for intervals
For, n = 1
[tex]\Delta x=\dfrac{t_{f}-t_{i}}{n}[/tex]
[tex]\Delta x=\dfrac{8-0}{2}[/tex]
[tex]\Delta x=4[/tex]
So, The intervals are (0,4), (4,8)
We need to calculate the velocity
Using given function
[tex]v=\dfrac{1}{2t+4}[/tex]
For first interval (0,4),
Put the value into the formula
[tex]v_{0}=\dfrac{1}{2\times0+4}[/tex]
[tex]v_{0}=\dfrac{1}{4}[/tex]
For first interval (4,8),
Put the value into the formula
[tex]v_{4}=\dfrac{1}{2\times4+4}[/tex]
[tex]v_{4}=\dfrac{1}{12}[/tex]
We need to calculate the total displacement
Using formula of displacement
[tex]D=(v_{0}+v_{4})\times(\Delta x)[/tex]
Put the value into the formula
[tex]D=(\dfrac{1}{4}+\dfrac{1}{12})\times4[/tex]
[tex]D=1.33\ m[/tex]
Hence, The displacement of the object on this intervals is 1.33 m.
The displacement of the object whose velocity function is given is 1.33 m
The given parameters are:
[tex]\mathbf{v = \frac{1}{2t + 4},\ 0 \le t \le 8; n =2}[/tex]
The end point of intervals is calculated as:
[tex]\mathbf{\triangle t = \frac{b - a}{n}}[/tex]
So, we have:
[tex]\mathbf{\triangle t= \frac{8 - 0}{2}}[/tex]
[tex]\mathbf{\triangle t = \frac{8}{2}}[/tex]
[tex]\mathbf{\triangle t= 4}[/tex]
So, the intervals are (0,4) and (4,8)
Calculate the velocity at the beginning of each interval
[tex]\mathbf{v_0 = \frac{1}{2(0) + 4} = \frac 14}[/tex]
[tex]\mathbf{v_4 = \frac{1}{2(4) + 4} = \frac 1{12}}[/tex]
Calculate the displacement (S) using:
[tex]\mathbf{S = (v_0 + v_4) \times \triangle t}[/tex]
So, we have:
[tex]\mathbf{S = (1/4 + 1/12) \times 4}[/tex]
Expand
[tex]\mathbf{S = 1 + 1/3}[/tex]
Add
[tex]\mathbf{S = 1 \frac 13}[/tex]
Express as decimals to 2 decimal places
[tex]\mathbf{S = 1.33}[/tex]
Hence, the displacement is 1.33 m
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Question 1 (1 point)
When simplified [9(7 – 3) + 13] - [11 - (6 + 9)] equals:
53
39
43
None of these
Answer:45
Step-by-step explanation:
[9(7-3)+13]-[11-(6+9)]
[9(4)+13]-[11-(15)]
[36+13]-[4]
49-4
45
Answer: The answer is 53
Which of the following is an example of a translation?
a) The preimage is twice the size as the image.
b) The preimage is moved 5 spaces up.
c) The preimage is rotated 90 degrees about the origin.
d) The image is a mirror reflection of the preimage.
Answer:
Step-by-step explanation:
a)the pre image us twice the same size as the image
G(x) = 2x^2 and h(x) = √x^2+1 .What is (goh)^-1 and is it a function?
Answer:
Step-by-step explanation:
Hello,
[tex](goh)(x)=g(h(x))=2\left( \sqrt{x^2+1}\right)^2=2(x^2+1)\\\\x=(goh)((goh)^{-1}(x))=2((goh)^{-1}(x)^2+1)\\ \\\left((goh)^{-1}(x)\right)^2=\dfrac{x}{2}-1=\dfrac{x-2}{2}\\ \\(goh)^{-1}(x)=\sqrt{\dfrac{x-2}{2}}[/tex]
And this is a function defined for x-2 [tex]\geq[/tex] 0, meaning x [tex]\geq[/tex] 2
Thanks
Perform the following operations and write the answers in radical form. Part A:√7+√3+√98−√18 Part B:3√5−3√11+2√121−3√90
Answer:
[tex]\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex] [tex]3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]Step-by-step explanation:
Part A ;
[tex]\sqrt{7} +\sqrt{3} +\sqrt{98} -\sqrt{18} \\\\\sqrt{98}=7\sqrt{2}\\\sqrt{18}=3\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+7\sqrt{2}-3\sqrt{2}\\\\\mathrm{Add\:similar\:elements:}\:7\sqrt{2}-3\sqrt{2}=4\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex]
Part B ;
[tex]3\sqrt{5} - 3\sqrt{11} + 2\sqrt{121} -3\sqrt{90} \\\\2\sqrt{121}=22\\3\sqrt{90}=9\sqrt{10}\\\\=3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]
Find out the coordinates
If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?
Step-by-step explanation:
then put x valule into KL equation
The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Answer:
4 2/4 (NOT SIMPLIFIED)
Step-by-step explanation:
Comprising means made of (aka including). You just add 1 1/4+1 1/4+1 1/4.
=3 3/4
The 1/8 is for the front and back cover. The bookworm ate through 3 volumes so there is 6 covers. So times 1/8 by 6. I turned the 6 into a fraction by putting it over 1. So now you have 1/8×6/1=6/8. Now you are going to add the 3 3/4 to the 6/8. You are going to turn the whole fraction to an improper. You are going to multiply the whole number(3) to the denominator(4), add that to the numerator(3) , and put it over the original denominator (4)= 15/4. Now you are going to set up the problem were you add the 6/8 to the 15/4. To add fractions the denominator have to be the same. With this problem you have two options: you can either do an equation to change the 6/8 denominator equal to 4 or an equation to change the 15/4 denominator equal to 8. Either one would work fine. I'm going to show you how to set the 6/8 denominator to 4.
1. Set it up as an equation 6/8=x/4
2. Find what gets the first denominator to the second in this case dividing by 2 6/8=x/4
3. What you do to the bottom is what you have to do with the top. So to find x, you need to divide 6 by 2= 3
So now your new equation is now 3/4+15/4. Adding this should give you 18/4, but most likely you have to write it as a proper fraction. To do this you are going to divide the 18 by 4. Your remainder will become your new numerator and the 4 will still be you denominator. The number times 4 fully goes into 18 will be your new whole number.
18/4=4.5
Martin's average score after 4 tests is 89. What score on the 5th test would bring Martin's average up to exactly 90?
Answer:
104
Step-by-step explanation:
89x4=356 90x5=450
450=356=104
Answer:
94
Step-by-step explanation:
((89x4)+94) divided by 5 = 90
What is the fractional equivalent of the repeating decimal 0.2 ?
Answer:
1/5
Step-by-step explanation:
I put it in a graphing calculator and converted it into a fraction
I
rep
What is the solution of 4(2y + 1) = 2(y - 13)
What is the answer
Answer:
- 5
Step-by-step explanation:
Step 1:
4 ( 2y + 1 ) = 2 ( y - 13 )
Step 2:
8y + 4 = 2y - 26
Step 3:
6y + 4 = - 26
Step 4:
6y = - 30
Answer:
y = - 5
Hope This Helps :)
-1/2(-6x -5/2) +1= 9x
Answer:
x=3/8
Step-by-step explanation:
Multiplique dentro del paréntesis por -1/2.Después de haber multiplicado le ecuación le quedará así 3x + 5/4 +1 = 9x.Ahora vamos a calcular la suma de la ecuación y quedará a 3x + 9/4 =9x.Después vamos a multiplicar ambos lados de la ecuación por 4 y quedará a 12x + 9= 36x.Luego vamos a mover la constante ( que es 9) al lado derecho y cambié su signo y quedará a 12x = 36x - 9.Después vamos agrupar los términos semejantes ( en este caso x) y quedará a -24x = -9.Finalmente vamos a dividir ambos lados de la ecuación entre -24 y la respuesta nos quedará a x = 3/8.f(x) = x - 5, translated 6 units to the right.
Answer:
[tex]g(x) = x - 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 5[/tex]
Required
Translate to the right by 6 units
When a function is translated to the right, the resulting function becomes
[tex]g(x) = f(x - h)[/tex]
Where h is the number of units moved;
Since; h = 6
[tex]g(x) = f(x - h)[/tex]
becomes
[tex]g(x) = f(x - 6)[/tex]
Solving for f(x - 6);
[tex]f(x) = x - 5[/tex]
Substitute x - 6 for x
[tex]f(x - 6) = x - 6 - 5[/tex]
[tex]f(x - 6) = x - 11[/tex]
This implies that [tex]g(x) = x - 11[/tex] is the result of the translation
What is the sum of Negative 1 + (negative 3)?
Answer:
[tex]\huge\boxed{-4}[/tex]
Step-by-step explanation:
=> [tex]\sf -1 + (-3)[/tex]
According to the rule [tex]\sf + * - = -[/tex]
=> [tex]\sf -1-3[/tex]
=> -4Answer:
-4
Step-by-step explanation:
-1 + (-3)
To add two negative numbers, add their absolute values, and make the answer negative.
The absolute values of -1 and -3 are 1 and 3. We add 1 + 3 and get 4.
Then we make the answer negative.
-1 + (-3) = -4
Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he
records whether each plane he sees follows a north-south route or an east-west route. He also records the
day of the week that he sees each plane.
Unfortunately, Chris dropped his data in the mud and can't read all of his numbers. The absolute and
relative frequency tables below show the numbers that Chris is able to read. Can you help him figure out
the rest?
Fill in the missing values from each table.
Answer:
Kindly check explanation
Step-by-step explanation:
From the relative frequency below:
For NORTH - SOUTH:
Monday - Thursday = 115 ; has a relative frequency of 75.16%,
Hence, we can obtain the row total since it amounts to 100% thus;
75.16% of row total = 115
0.7516× row total = 115
Row total = 115 / 0.7516 = 153.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
153 - 115 = 38
FOR EAST - WEST:
Monday - Thursday = 21 ; has a relative frequency of 25.30%,
Hence, we can obtain the row total since it amounts to 100% thus;
25.30% of row total = 21
0. 253 × row total = 21
Row total = 21 / 0.253 = 83.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
83 - 21 = 62
x = (38 / 100) × 100%
x = 0.38 × 100%
x = 38.00 %
Answer:
The basic explanation:
North - South/Friday - Sunday- 38 // Row total- 153
East - West/Friday - Sunday- 62 // Row total- 83
x- 38
Angles 1 and 2 form a right angle. 2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2. Which word describes their measures? linear congruent complementary supplementary
Answer:
complementary
Step-by-step explanation:
yes
The word that describes their measures of ∠1 and ∠2 is: complementary.
Recall:
Angles that are complementary are angles whose sum equals 90 degrees.A right angle equals 90 degrees.From the information given, we know that:
m∠1 and m∠2 forms a right angle.
Since a right angle = 90 degrees, therefore:
m∠1 + m∠2 = 90° (complementary)
Therefore, the word that describes their measures of ∠1 and ∠2 is: complementary.
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Evaluate (5-3)^3+ -3^2(6-3)
Steps to solve:
(5 - 3)^3 + (-3)^2(6 - 3)
~Simplify
2^3 + (-3)^2(3)
2^3 + (-3)^6
~Solve exponents
8 + (-729)
~Subtract
-721
Best of Luck!
what is the domain and range of f(x)=2x+3
Answer:
D:{x∈R}
R:{y∈R}
Step-by-step explanation:
This is just a linear function. I know this because the degree of the x-variable is 1.
Domain and range are sets of possible values the function can have - though not necessarily at the same time.
Thus, there are no restrictions to the domain and range unless context is given.
Therefore, the domain and range is:
D:{x∈R}
R:{y∈R}
4x – 3y = 20
2x + y = 30
Using the two equations above, solve for y.
Answer:
4x-3y+20
Step-by-step explanation:
x=6.875
y=2.5
2x+y=30
x=12.5
y=-5
y=1/4x + 6
that passes through the point (-4, 3) in slope-intercept form.
Answer:
The answer is
[tex]y = \frac{1}{4} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line.
The equation is
y = 1/4x + 6
Comparing with the general equation above
Slope = 1/4
Since the lines are parallel their slope are also the same
That's
Slope of parallel line = 1/4
So the equation of the parallel line using point (-4 , 3) and slope 1/4 is
[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]We have the final answer as
[tex]y = \frac{1}{4} x + 4[/tex]Hope this helps you
I have 4 questions
1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units,
then what is TV?
131
194
68
80
2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x?
x = 3
x = 7
x = 12.5
x = 22
3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?
4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?
help me asap i don't know this
Answer:
y = 3
Step-by-step explanation:
Step 1: Write equation
-2(7 - y) + 4 = -4
Step 2: Subtract 4 on both sides
-2(7 - y) = -8
Step 3: Distribute
-14 + 2y = -8
Step 4: Add 14 to both sides
2y = 6
Step 5: Divide both sides by 2
y = 3
Solve the equation -4 = 5 -x.
Answer:
when x goes opposite side of equals to sign of x changes and same goes with 4 then x=5+4 then the answer will be 9
Help me please this is math
Answer:
c) none of the above
Step-by-step explanation:
this is because we should put the equation like:
1/3 - (-4/3) because the distance is 5 units and
1/3 + 4/3 = 5/3
this is because (-) × (-) = (+)