Answer:
(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
Step-by-step explanation:
Given:
u = (−2, 3, 1)
=> u = -2i + 3j + k --------------------------(i)
v = (−1, −1, 2)
=> v = -i - j + 2k --------------------(ii)
3u − 2v − 4w = (3, 2, −3)
=> 3u − 2v − 4w = 3i + 2j - 3k ------------------(iii)
(A) TO FIND THE VECTOR w
Let:
w = (a, b, c) = ai + bj + ck
(a) Substitute u, v and w into equation (iii)
3u − 2v − 4w = 3i + 2j - 3k
3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k
(b) Solve the equation in step (a) by opening the brackets and collecting like terms
(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k
open brackets
-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k
collect like terms
-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k
i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k
(c) Solve for a, b and c in step (b)
Comparing both sides of the equation, we have;
-4 - 4a = 3 ----------(*)
11 - 4b = 2 -----------(**)
-1 - 4c = -3 ------------(***)
From (*)
4a = -4 - 3
4a = -7
a = [tex]\frac{-7}{4}[/tex]
From (**)
4b = 11 - 2
4b = 9
b = [tex]\frac{9}{4}[/tex]
From (***)
-1 - 4c = -3
4c = -1 + 3
4c = 2
c = [tex]\frac{2}{4}[/tex]
c = [tex]\frac{1}{2}[/tex]
Remember that
w = (a, b, c)
w = ai + bj + ck
Therefore,
w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
(B) TO FIND -2u + 3v - 5w
Remember that;
u = (−2, 3, 1)
v = (−1, −1, 2),
w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
Substitute u, v, w into the expression as follows;
-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
Expand
(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]
Collect like terms
(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])
Solve
([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
twice this number is 1 less than half of 26
Answer:
2x = (1/2)(26) - 1
The number is 6.
Step-by-step explanation:
2x = (1/2)(26) - 1
2x = 13 - 1
2x = 12
x = 6
Determine whether the equation is always, sometimes, or never true.
2/3 x + 4 = 2x
Answer:
Always true
Step-by-step explanation:
Given
[tex]\frac{2}{3}x + 4 = 2x[/tex]
Required
Determine its type of solution
[tex]\frac{2}{3}x + 4 = 2x[/tex]
Collect Like Terms
[tex]2x - \frac{2}{3}x = 4[/tex]
Take LCM
[tex]\frac{6x - 2x}{3} = 4[/tex]
[tex]\frac{4x}{3} = 4[/tex]
Multiply both sides by [tex]\frac{3}{4}[/tex]
[tex]\frac{4x}{3} * \frac{3}{4}= 4 * \frac{3}{4}[/tex]
[tex]x = 4 * \frac{3}{4}[/tex]
[tex]x = 3[/tex]
Hence, the equation is always true for x = 3
Someone please help me ❤️
Answer:
week 5!
Step-by-step explanation:
Answer:
yes, week 55️⃣
Step-by-step explanation:
just see the little blue points
y varies inversely with x. If y = 5 when x = 60, find y when x = 150
Answer:
y =2 when x = 150
Step-by-step explanation:
Inverse variation is
xy = k
5*60 = k
300 = k
xy = 300
150y = 300
Divide by 150
150y/150 = 300/150
y = 2
The sum of all of the exterior angles of an octagon is:
Answer:
1080°
Step-by-step explanation:
sum = 180 ( n - 2)
note that octagon has 8 sides
therefore
sum = 180 ( 8 - 2)
sum = 1080°
Answer:
c. 1080
Step-by-step explanation:
= 180 x ( 8 - 2)
= 1080
order the number from greatest to least
3 1/3,3.34,300%
Answer:
3.34, 3 1/3 300%
Someone help
Plssssssssssssssssssssssssss
What is the solution to the equation?
{+55 - 466
{+55 = 466
O [+55-55-466+55
f=521
+55 = 466
O +55+55-466+55
{ = 521
(+55 = 466
O +55-55-466-55
f=411
f+55 = 466
Of+ 55+55-466-55
f = 411
Answer:
f=55=466
f+55-55=466-55
Step-by-step explanation:
Find the solution of the term.
A carpenter sands of a dresser in hour. At this rate, how long does it take the
carpenter to sand 1 dresser?
o hour
o hour
O 1 hours
O 23 hours
Question:
A carpenter sands 1/2 of a dresser in 3/4 hour. At this rate, how long does it take the carpenter to sand 1 dresser?
Answer:
[tex]1\ dresser = \frac{3}{2} hour[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]
Required
How long will it take to sand 1 dresser
[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]
Multiply both sides by 2
[tex]2 * \frac{1}{2} dresser = \frac{3}{4} hour * 2[/tex]
[tex]1\ dresser = \frac{3}{4} hour * 2[/tex]
[tex]1\ dresser = \frac{3}{2} hour[/tex]
Hence;
It'll take 3/2 hour to sand 1 dresser
Answer:
Step-by-step explanation:
hey babe
How do you do this question?
Step-by-step explanation:
Use the first fundamental theorem of calculus.
∫₆¹⁰ f'(x) dx = f(10) − f(6) = 8 − 8 = 0
Employee Time Card
DATE
IN
OUT
IN
OUT
HOURS
Sun.
Mon.
7:00 AM
11:00 AM
12:00 P.M.
a.
4:04 PM
3:59 P.M.
Tue.
7:05 AM
11:55 PM
b.
Wed.
7:01 AM
11:10 AM
10:59 AM
10:55 AM
12:05 PM
C.
Thur.
6:59 AM
3:58 P.M.
4:03 P.M.
3:49 PM
12:01 PM
12:02 PM
d.
Fri.
6:55 AM
11:01 AM
e.
Sat
TOTAL HOURS
Answer:
31 hours 57 minutes.
In most jobs, the employees round up so that would make it 32 hours.
32x7.50= 240
If they wanted to be technical you could do 31.57x7.5 and that would make it 236.78
It’s up to you which one you go with
Step-by-step explanation:
What is $12.78 rounded to the nearest dollar?
Answer:
$13
Step-by-step explanation:
[tex]\$12.78 = \$13[/tex]
Answer:$13
Step-by-step explanation:
.7 rounds to 1 if it is 5 or above it rounds up
A chocolate company makes chocolate malt balls that have a radius of 0.34
inches. The carton they are to be packed in is approximately a rectangular prism with
dimensions 1.5 inches by 2.5 inches by 6 inches. How many malt balls will fit in the
carton
Answer:
Approximately 141 malt ballsStep-by-step explanation:
this problem is on the mensuration of solids shapes.
first we need to calculate the volume of the rectangular prism
volume of prsim= l*b*h
given that
length= 1.5 in
breath=2.5 in
hieght= 6 in
volume= 1.5*2.5*6
volume=22.5 in^3
secondly we then calculate the volume of a malt ball
given that
raduis r= 0.34
volume of sphere = 4/3πr^3
volume of sphere = 4/3*3.124*(0.34)^3
volume of sphere = 1.33*3.142*0.039
volume of sphere = 0.16 in^3
now we can calculate the amount of sphere that can fit into the prism as
= volume of prism/volume of sphere
= 22.5/0.16
=140.6
approximately 141 malt balls
Use the position function s(t) = –4.9t2 + 500, which gives the height (in meters) of an object that has fallen for t seconds from a height of 500 meters. The velocity at time t = a seconds is given by the following.
lim t->a: (s(a) - s(t)) / (a - t)
Find the velocity of the object when t = 3. (Round your answer to two decimal places.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value is [tex]v(3) = 29.4 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
[tex]s(t) = -4.9t^2 + 500[/tex]
And
[tex]\lim_{t \to a} \frac{s(a) - s(t)}{a-t}[/tex]
Generally s(t) at t = a is mathematically evaluated as
[tex]s(a) = -4.9a^2+ 500[/tex]
So
[tex]s(a) - s(t) = -4.9a^2 + 500 - ( -4.9t^2+500)[/tex]
[tex]s(a) - s(t) = -4.9a^2 + 500 +4.9t^2-500)[/tex]
[tex]s(a) - s(t) = 4.9(t^2 - a^2)[/tex]
Thus the velocity is represented as
[tex]v(t) =\lim_{t \to a} \frac{s(a) - s(t)}{a-t} \equiv \lim_{t \to a} \frac{4.9(t^2 - a^2 )}{ a-t}[/tex]
=> [tex]v(t) = \lim_{t \to a} - 4.9(a + t )[/tex]
=> [tex]v(t) = -4.9 (a + a )[/tex]
=> [tex]v(t) = -9.8a[/tex]
Now at t = 3
=> [tex]v(3) = -9.8 (3)[/tex]
=> [tex]v(3) = 29.4 \ m/s[/tex]
Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number.
Answer:
[tex]\frac{1}{w^{29}}[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{w^{-7}(w^{-9})^2}{w^4}[/tex].
Since, [tex]w^{-7}=\frac{1}{w^7}[/tex]
And [tex]w^{9}=\frac{1}{w^9}[/tex]
Expression will become,
[tex]\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^7\times w^{18}}}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^{(7+18)}}}{w^4}[/tex]
[tex]=\frac{1}{w^{25}}\times \frac{1}{w^4}[/tex]
[tex]=\frac{1}{w^{25}\times w^4}[/tex]
[tex]=\frac{1}{w^{29}}[/tex]
Therefore, Simplified form of the given expression will be [tex]\frac{1}{w^{29}}[/tex].
7k-k+19 Combine like terms
Step-by-step explanation:
7k-k+19
6k+19 should be fine
Steps to solve:
7k - k + 19
~Combine like terms
6k + 19
Best of Luck!
The sum of all of the exterior angles of an octagon is:
Answer:
the answer is 360 degrees
Step-by-step explanation:
How many days are in a week ?the answer is measured in the
Answer:
7 days are in a week. 5 week days, 2 days for the weekend hope this helps.
Ellie drives 22.5 miles in 45 minutes. If she drove three hours in total at the same rate, how far did she go?
Answer:
90
Step-by-step explanation:
3 hours = 180 mins
180 ÷ 45 = 4. so Ellie will drive 4x more miles in 3 hours.
22.5 × 4 = 90
33 points!!! The line contains the point (8,2) and is parallel to a line with a slope of -2/3 The equation of the line is
Answer:
y=mx+b
y=-2/3x+2
Step-by-step explanation:
-2/3=slope
x= y coord.
-2.5 + d = -3.6 What is the sum?
Answer:
-1.1
Step-by-step explanation:
we take -3.6 minus -2.5
which we get -1.1 hav a nice day :]
Answer:
d = -1.1
Step-by-step explanation:
-3.6 - ( -2.5) = -1.1
What is the product of (5/5)(614) ? Simplify your answer.
Answer:
614
Step-by-step explanation:
5/5 is just 1 because 5÷5=1
1 multiplied by 614 = 614
Hope this helped!
Rewrite with positive exponents a^-3 b^-5
Answer:
1/a^3 and 1/b^5
I am a pair of numbers and my product is 1, what am I?
Answer:
Step-by-step explanation:
How I Al's have doubts
Rosa is currently x years old. In 28 years, Rosa will be 3 times the age she is now. Which equation can be used to find Rosa's age?
Answer:
multiple 28 and 3 u will get the answer
Step-by-step explanation:
I think It will help you
Where is the point of intersection? x − 2y + 2 = 3 and x − y = 3
Answer:
Step-by-step explanation:
x -2y = 1
x - y = 3
x - 2y = 1
-x + y = -3
-y = -2
y = 2
x - 2 = 3
x = 5
(5, 2)
Evaluate the expression when c=-6.
c? +6c+5
Answer: -31
Step-by-step explanation: 1.) Plug in -6 for c
2.) equation will then be: 6(-6)+5
3.) use PEMDAS: multiply first then addition
4.) 6(-6) equals -36
5.) add -36+5 which equal -31
Therefore your answer should be -31
One-third of a number decreased by four
Answer: (X/3)*4
Step-by-step explanation:
(1/3)*x
decreased by 4: (1/3)*x-4
Miles traveled, miles to go, fill in the “?”
Answer:
The blank is 170
Step-by-step explanation:
The ratio from miles traveled to miles to go is 1:-1
520-0=520
520-100=420
520-200=320
520-350=170
520-520=0
2. A stock price rose 2.2 points in
Week 1. The stock price fell 5.4
points in Week 2. Write and solve
an equation to represent the total
price change in stock.
Answer: the total price change in stock is fall of 3.2 points or -3.2 points.
Step-by-step explanation:
In integers , we use positive integers to show rise in amount whereas we use negative integers to show fall .
Given: A stock price rose 2.2 points in Week 1.
i.e. +2.2 points rise.
The stock price fell 5.4 points in Week 2.
i.e. fall of -5.4. (Much greater, than it rose)
The equation to represent the total price change in stock would be
Total price change = price rose in Week 1 + price fell in Week 2.
= [+2.2 + (-5.4)] points
= 2.2 - 5.4 points [ (+)(-) = (-)]
= -3.2 points
Hence, the total price change in stock is fall of 3.2 points.