Answer:
0.16
Step-by-step explanation:
Let u = (−2, 3, 1), v = (−1, −1, 2), and 3u − 2v − 4w = (3, 2, −3). Find: a. The vector w.b. -2u + 3v - 5w
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])
A group of 37 families will share the cost of building a new playground in their neighborhood  The playground Will cost 3,145 how much will each family have to pay
Answer:
37÷3,145
=85+5
=90-37
=53
Area= 7 1/4 x 11 2/3
Answer:
Area=84.5833333333
Step-by-step explanation:
Answer:
Step-by-step explanation:
To make this easy, convert them both into improper fractions.
Multiply 7x4= 28 + 1 = 29/4
Multiply 11 x 2 = 22 +3= 25/2
29/4 x 25/2 = 725/8
simplified it is 90 5/8
Hope this helps :)
Need help quick Solve each equation for x. x to the power of 2= 1/100
Answer:
x=1/10
Step-by-step explanation:
x^2=1/100
x=root(1/100)
x=1/10
Answer:
[tex]x = \frac{1}{10}[/tex]
Step-by-step explanation:
If x squared gets us [tex]\frac{1}{100}[/tex], then we can create the equation [tex]x^2 = \frac{1}{100}[/tex].
To solve for x, we find the square root of both sides.
[tex]\sqrt{x^2} = \sqrt{\frac{1}{100}}[/tex]
The square root of [tex]\frac{1}{100}[/tex] is [tex]\frac{1}{10}[/tex], since [tex]10\cdot10=100[/tex].
This means [tex]x = \frac{1}{10}[/tex].
Hope this helped!
describe the correct error a student made when solving the equation 4=-2(x-3) what is the correc scolution?
Answer:
x =1
Step-by-step explanation: Correct solution
[tex]4=-2(x-3) \\\\\mathrm{Switch\:sides}\\-2\left(x-3\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x-3\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x-3=-2\\x-3+3=-2+3\\\\Simplify\\x = 1[/tex]
A 47-inch piece of steel is cut into three pieces so that the second piece is twice as
long as the first piece, and the third piece is two inches more than six times the
length of the first piece. Find the lengths of the pieces
2x
6x+2
First, find an equation that represents the total length of the piece of steel in terms of x by adding the three pieces together,
Answer:
first piece: 5 in second piece: 10 in third piece: 32 inStep-by-step explanation:
x - the length of the first piece
2x - twice the length of the first piece (the length of the second piece)
6x - six times the length of the first piece
two inches more:
6x+2 - the length of the third piece
first + second + third = 47 in {total length of the pieces of steel}
x + 2x + 6x + 2 = 47
9x + 2 = 47
9x = 45
x = 45:9
x = 5 in
first piece: 5 in
second piece: 2×5 = 10 in
third piece: 6×5 + 2 = 30 + 2 = 32 in
What is equal to 4 1/2 dividend by 2 2/3
Answer:
Step-by-step explanation:
9/2 / 8/3
9/2 x 3/8
27/16 = 1 13/16
Answer:
9/2 / 8/3
IS THE POSSIBLE ANSWER TO THIS EQUATION.
Which of the following are quadratic functions A. Y =5x-3/2+x^2 B. Y=x^2+5x-2 C. Y=-x+2 D. Y=x-1/x
Answer:
A and B
Step-by-step explanation:
Quadratic Equations: f(x) = a(bx - h)² + k
Quadratic equations always have a degree of 2. That means that we will always have an x² term. Of the 4 choices, only A and B offer a term of x², making them a quadratic.
Answer:
Y = 5x - 3/2 + x^2
Y = x^2 + 5x - 2
Step-by-step explanation:
The function must contain x^2.
That is have a degree of 2.
Simplify (2^3)^–2 ment to put this
Answer:
[tex]\frac{1}{64}[/tex]
Step-by-step explanation:
[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\=2^{-6}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\2^{-6}=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]
Answer:
1/64
Step-by-step explanation:
[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\\\=2^{-6}\\\\=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]
{7, 8, 9, 10} {9, 10, 11, 12} Which of the following shows the intersection of the sets? A. {9, 10} B. {7, 8, 9, 10} C. {9, 10, 11, 12} D. {7, 8, 9, 10, 11, 12}
Answer:
{ 9 , 10 }Option A is the correct option.
Step-by-step explanation:
Let the sets be A and B
A = { 7 , 8 , 9 , 10 }
B = { 9 , 10 , 11 , 12 }
The intersection of sets A and B is the set of all ements which belongs to both A and B.
The intersection of sets A and N is denoted by ( A ∩ B ) and read as A intersection B.
A ∩ B = { 7 , 8 , 9 , 10 } { 9 , 10 , 11 , 11 , 12 }
Now, list the elements which are present in both sets. A ∩ B = { 9 , 10 }
Hope I helped!
Best regards!
Answer:
its a
Step-by-step explanation:
A total of 6.2 percent of the prime time viewing audience watched shows on ABC, 8.1 percent watched shows on CBS, 7.4 percent on Fox, 6.4 percent on NBC, 3.1 percent on Warner Brothers, and 2.8 percent on UPN. A total of 66 percent of the audience watched shows on other cable networks, such as CNN and ESPN.
What will be the prime time viewing percentage of the pie chart for the following data? (Only consider the viewers watching non-cable news.) (Round your answers to 2 decimal places.)
Answer:
For each one it is shown below
Step-by-step explanation:
The computation of the prime time viewing percentage for the following data is shown below:l;
but before that we need do the total which is
= 6.2% + 8.1% + 7.4% + 6.4% + 3.1% + 2.8%
= 34%
Now for each one the viewing percentage is
For ABC
[tex]= \frac{6.2}{34}[/tex]
= 18.24%
For CBS
[tex]= \frac{8.1}{34}[/tex]
= 23.82%
For NBC
[tex]= \frac{6.4}{34}[/tex]
= 18.82%
For Warner brothers
[tex]= \frac{3.1}{34}[/tex]
= 9.12%
For fox
[tex]= \frac{7.4}{34}[/tex]
= 21.76%
For UPN
[tex]= \frac{2.8}{34}[/tex]
= 8.24%
Riley worked 5 1/4 hours on Monday 3 3/8 hours on Tuesday and 2 5/6 hours on Wednesday he rounded the hours to five 3 and 2 before adding them together to get 10 hours did he make a high or low estimate
Answer:
Low estimate
Step-by-step explanation:
2 5/6 rounded is 3 so the total would be 11 hours if everything is rounded.
Answer:
The answer is low
solve for x: -2x - 4 > 8
Steps to solve:
-2x - 4 > 8
~Add 4 to both sides
-2x > 12
~Divide -2 to both sides
x < -6
Best of Luck!
the value of the function f(x)=6x + 3 at 4 is
solution
Answer:
here we go 6×4+3
now 24+3
hence the answer is
27 ans
Answer:
x = -2
Step-by-step explanation:
f(x) = 6 x + 3×4
f(x) = 6 x + 12
6 (x + 2) = f(x)
x = -2
Hope I helped! Please label me as Brainliest!
HELLLLLPPPPPPP PLZZZZZZ HELP A$AP PLZZZZZZZZZ I WILL MARK BRAINLEST
Answer:
$430
Step-by-step explanation:
Step 1:
300 - 50
Step 2:
350 + 20
Step 2:
370 + 60
Answer:
$430
Hope This Helps :)
The sport of korfball is played by teams of eight players. Each team has fourmen and four women on it. Halliday High School has seven men and 11 women interested in playing korfball.In how many ways can they form a korfball team from their 18 interested students
Answer:
There are 11550 possible selections
Step-by-step explanation:
Given
[tex]Men = 7[/tex]
[tex]Women = 11[/tex]
Required
How many ways can 4 men and 4 women be selected
The keyword in the question is SELECTION and it means COMBINATION;
So, number of selection is:
[tex]Number = Men * Women[/tex]
[tex]Number = ^7C_4 * ^{11}C_4[/tex]
This gives
[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]
[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]
[tex]Number = 7 * 5 * 330[/tex]
[tex]Number = 11550[/tex]
Hence;
There are 11550 possible selections
In a game, the two players scored a total of 121 points. One player had 13 more points than the other player. How many points did the player with the fewer points score? Group of answer choices 67 54 108 52
Answer:
Answer is 54 . IT is the correct answer
Step-by-step explanation:
Hope it is helpful for you
What is the value of x in 3x-9
Answer:
x could be anything. you have to have a equation to solve for x.
Step-by-step explanation:
what’s -14 = -2(2x+2)
The relative growth rate for a certain type of bacteria population is 85% per hour. A small culture has formed and in just 2 hours the count shows to be 12,500 bacteria in the culture. What is the initial number of bacteria in the culture?
Answer:
3663 bacteria
Step-by-step explanation:
-8=x+11/2 please help me
Answer:
Hey there!
-8=x+11/2
-16/2=x+11/2
-27/2=x
Let me know if this helps :)
Answer: -27/2 or -27
Step-by-step explanation:
You didn't use parentheses so the equation isn't clear.
I answered for both possibilities.
[tex]-8=x+\dfrac{11}{2}\\\\\\-8-\dfrac{11}{2}=x\\\\\\-\dfrac{16}{2}-\dfrac{11}{2}=x\\\\\\\large\boxed{-\dfrac{27}{2}=x}[/tex]
[tex]-8=\dfrac{x+11}{2}\\\\\\-8(2)=\dfrac{x+11}{2}(2)\\\\\\-16=x+11\\\\\\-16-11=x\\\\\\\large\boxed{-27=x}[/tex]
Jeremy Sullivan delivers newspapers for the Dispatch. He receives 14.20 per
paper, 6 days a week (for the daily paper), and 500 for the Sunday paper. He
delivers 124 daily papers each day and 151 Sunday papers each week. What is
his total pay for the week?
Answer:
Total earnings per week
=18114.8¢
Step-by-step explanation:
He receives 14.20¢ per paper, 6 days a week.
He receives 50¢ for the Sunday paper.
He delivers
124 daily papers each day
He earns= 124*14.20*6
He earns=10564.8¢
151 Sunday papers each week.
He earns= 151*50
He earns= 7550¢
Total earnings per week
=10564.8+7550
=18114.8¢
Which equation has no solution?
Answer:
B) -6 (w - 4) + 8w = 2 (w + 9) has no solution
Step-by-step explanation:
two poles 8m and 13m high
are placed opposite to each other across a 12
metre long road find the distance
between their tops
Answer:
13 m
Step-by-step explanation:
The distance x is:
x = √12² + (13 -8)² = √144 + 25 = √169 = 13 m
Josie found a job with an annual salary of $67.3K. What is her monthly pay, rounded to the nearest dollar?
Answer:
$5,608
Step-by-step explanation:
Since there are 12 months in one year, divide her annual salary by 12.
$67,300/12 = $5,608.33 ≈ $5,608
Josie makes $5,608 per month.
Answer:
5608
Step-by-step explanation:
annual salary=$67.3k
it is annual
so
monthly salary=$67.3÷12
=$5608.33333333
rounded off top the nearest dollar= $5608
please mark as brainliest
if you could generate energy by fusing the hydrogen in solution a, how much of the solution would you need to generate the electrical energy used daily in a certain home? energy released by fusion of hydrogen in 1 liter of solution A = 7.6*10^10 Electrical energy used daily in a certain family home = 3*10^4
Answer:
We know that:
Energy released by fusion of hydrogen in 1 liter of solution A = 7.6x10^10 J
Energy used daily in a certain family home = 3x10^4 J
(you did not write the units, so i suppose that are the same in both cases)
Then, if x is the number of liters of solution A used, the energy produced will be:
E(x) = x*7.6x10^10 J
And we want this equal to 3x10^4
then:
E(x) = x*7.6x10^10 J = 3x10^4 j
now we solve this for x.
x = (3x10^4 j)/(7.6x10^10 j) = 3.9x10^-7
Then you need to use 3.9x10^-7 L of solution a.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec(x), −π 3 ≤ x ≤ π 3 , y = 3; about y = 1
Using the washer method, the volume is given by the integral
[tex]\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx[/tex]
where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
[tex]\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}[/tex]
Find an equation of the line having the given slope and containing the given point. m=-5 (5,7)
Answer:
y = -5x + 32
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write in known variables
slope m = -5
y = -5x + b
Step 2: Find b
7 = -5(5) + b
7 = -25 + b
b = 32
Step 3: Write linear equation
y = -5x + 32
Answer:
y - 7 = -5(x - 5)
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope of -5 and contains the point (5,7).
We want to write the equation of this line.
The equation of this line can be written in three ways:
Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Either one of these ways works, but let's use point-slope form, as that form is the easiest.
SolvingWe can immediately substitute the values into the formula to get the equation.
We can start with the slope; replace m with -5 in the formula.
[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]
Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:
y - 7 = -5(x - 5)
In 9 days a group of workers can plant 54 acres what’s there rate in acres per day
Answer:
Step-by-step explanation:
9 3/4 acres in 3 3/8 days = 9 6/8 acres in 3 3/8 days
(72 + 6)/8 = 78/8
(24 + 3)/8 = 27/8
78/8 divided by 27/8 = 78/27 = 26/9 or 2 8/9 acres/day
A ball is thrown into the air. Its height (in feet) t seconds later is given by h(t)=64t−16t^2 a) What is the height of the ball 1 second after it has been thrown? b) After how many seconds does the ball hit the ground? c) At what time(s) is the ball 30 feet above the ground?
Answer:
A) 48 feet
B) 4 seconds
C) 0.54 seconds and 3.46 seconds
Step-by-step explanation:
So we have the function:
[tex]h(t)=64t-16t^2[/tex]
Which represents the height h(t) of the ball after t seconds.
A)
To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:
[tex]h(1)=64(1)-16(1)^2[/tex]
Simplify:
[tex]h(1)=64-16[/tex]
Subtract:
[tex]h(1)=48[/tex]
So, after 1 second, the height of the ball is 48 feet above the ground.
B)
To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:
[tex]0=64t-16t^2[/tex]
Solve for t. Factor out a 16t:
[tex]0=16t(4-t)[/tex]
Zero Product Property:
[tex]16t=0\text{ or } 4-t=0[/tex]
Solve for t:
[tex]t=0\text{ or } t=4[/tex]
We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.
C)
To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:
[tex]30=64t-16t^2[/tex]
First, divide everything by 2 to simplify things:
[tex]15=32t-8t^2[/tex]
Subtract 15 from both sides:
[tex]-8t^2+32t-15=0[/tex]
Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]
Simplify:
[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]
Use a calculator. Approximate:
[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]
So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.
And we're done :)