How to express a vector as a product of its length and direction?
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]
Which of the following units measures the volume of a solid? Can choice more than one answer. A) mL B) m³ C) cm³ D) L
Answer: B and C
explanation: The volume of solids are expressed in cubic measurements such as cubic centimeters (cm^3) or cubic meters (m^3).
Lavender grew from 38 inches to 52 inches in one month; what was
the % increase in growth ?
3^3-5(6) simplify this equation
Answer:
-3
Step-by-step explanation:
27-30
Answer:
-3
Step-by-step explanation:
3³-5(6)
3*3*3-30
27-30
-3
The volume of a volleyball is about 288 cubic inches. what is the radius of the volleyball, to the nearest tenth of an inch? use 3.14 for π.
[tex]r = \sqrt{ \frac{3v}{4\pi} } [/tex]
Answer:
The radius of the volleyball is 8.3 inches
Step-by-step explanation:
Given
[tex]r = \sqrt{\frac{3v}{4\pi}}[/tex]
[tex]v = 288[/tex]
Required
Determine the value of r
To do this, we simply substitute 288 for v and 3.14 for π in the given equation.
This gives
[tex]r = \sqrt{\frac{3v}{4\pi}}[/tex]
[tex]r = \sqrt{\frac{3 * 288}{4 * 3.14}}[/tex]
[tex]r = \sqrt{\frac{864}{12.56}}[/tex]
[tex]r = \sqrt{68.7898089172}[/tex]
[tex]r = 8.29396219651[/tex]
[tex]r = 8.3\ inch[/tex] (Approximated)
Hence;
The radius of the volleyball is 8.3 inches
Answer: 4.1 inches
Step-by-step explanation:
Find the quotient.
56,000 10
Answer:
5,600
Step-by-step explanation:
i used calculator.
The area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the wall of the barn.
Answer: 258
Step-by-step explanation: 270-12=w
The width of the wall is 9 feet and length is 30 feet.
What is perimeter of a rectangle ?The perimeter of a rectangle is the sum of all the sides.
According to the given question the area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width.
Assuming the width of the rectangular wall to be x feet.
∴ From the given data length is 2x + 12 feet.
We know area of a rectangle is product of it's length and width.
So, { x × ( 2x + 12 ) } = 270.
2x² + 12x = 270.
2x² + 12x - 270 = 0
x² + 6x - 135 = 0
x² + 15x - 9x - 135 = 0
x(x + 15) - 9(x + 15) = 0
( x + 15 ) = 0 OR ( x+ 9 ) = 0
∴ x = -15 OR x = 9. ( we know length can note be negative )
So, Width of the rectangle is 9 feet and length is 30 feet.
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The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. (Due to budgeting constraints, only one new picture can be undertaken at this time.) She feels that script 1 has a 70 percent chance of earning about $10,000,000 over the long run, but a 30 percent chance of losing $2,000,000. If this movie is successful, then a sequel will be produced, with an 80 percent chance of earning $5,000,000, but a 20 percent chance of losing $1,000,000. On the other hand, she feels that script 2 has a 60 percent chance of earning $12,000,000, but a 40 percent chance of losing $3,000,000. If successful, its sequel would have a 50 percent chance of earning $8,000,000, but a 50 percent chance of losing $4,000,000. Of course, in either case, if the original movie were a flop, then no sequel would be produced. What is the probability that script 1 will be a success, but its sequel will not?
Answer: $9,000,000
Step-by-step explanation:
Probability is simply defined as the chance or likelihood that an event is going to happen or occur.
The probability that script 1 will be a success, but its sequel will not is the success of script 1 added to the failure of its sequel.
The total payoff will simply be the sum of the individual layoffs of both the success and the failure. This will be:
= $10,000,000 + (- $1,000,000)
= $10,000,000 - $1,000,000
= $9,000,000
Using conditional probability, it is found that there is a 0.14 = 14% probability that script 1 will be a success, but its sequel will not.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this question:
Event A: Script 1 is a sequel.Event B: It's sequel is not.Sequel 1 has a 70% probability of being a success, hence [tex]P(A) = 0.7[/tex].If it is a success, the sequel has a 80% probability of being a success, hence a 20% probability of being a failure, thus [tex]P(B|A) = 0.2[/tex]Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)P(B|A)[/tex]
[tex]P(A \cap B) = 0.7(0.2)[/tex]
[tex]P(A \cap B) = 0.14[/tex]
0.14 = 14% probability that script 1 will be a success, but its sequel will not.
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Of 57 cars making up a freight train, 23 are boxcar. What fraction of the cars are not boxcars?
Answer:
total no of cars =57
Cars which are not boxcars =57-23=34
23/34×57=1339/34
Solve for y in terms of x. 16x + 4/3 y = 21
Answer:
y= -12x+63/4
Step-by-step explanation:
16x + 4/3 y = 21
4/3 y =21-16x
4y=3(21-16x)
4y=63-48x
y=63/4-48/4 x
y=-12x+63/4
PLEASE HELP ASAP!!!!!!!!!!!!
Answer: D
Step-by-step explanation: becasue i did it
I need help with this
Answer:
b
Step-by-step explanation:
b is the answer
the range is all real number
The answer to the problem rhenbehejrjrjrhjfjf
Through my trials and tribulations I have decided that the answer is.
Y E S
the circumference of a circle is22 cm find the radiusof the circle
Answer:
3.5cm
Step-by-step explanation:
[tex]C = 22cm\\r = ?\\\\C = 2\pi r\\\\r = \frac{C}{2\pi} \\\\r = \frac{22}{2(3.14)}\\ \\r = \frac{22}{6.28} \\\\r = 3.5[/tex]
You just found 13,406,190 pennies! How many dollars did you actually find? If each penny weighs 4 grams, how much did all that loot weigh in lbs?
Answer:
congrats you just found 118,222.36 pounds of pennies worth $134,061.9
you should buy a house or car with 59 tons of pennies
Given that 4x - 2y < 8, solve for y. Put them in order from steps . plz help
Answer:
y > 2x - 4
Step-by-step explanation:
Step 1: Write out inequality
4x - 2y < 8
Step 2: Subtract 4x on both sides
-2y < -4x + 8
Step 3: Divide both sides by -2
y > 2x - 4
What is the solution to the linear equation?
를 글 - +
5
- X
6
x = -5
Ox=
0 x=
Ox=5
x=-5 ___________________
The question is an illustration of linear equation, and the solution to the linear equation is x = -5
How to determine the solution?The equation is given as:
[tex]\frac 23x - \frac 12 = \frac 13 + \frac 56x[/tex]
Multiply through by 6
4x - 3 = 2 + 5x
Collect like terms
4x - 5x = 2 + 3
Evaluate the like terms
-x = 5
Divide both sides by -1
x = -5
Hence, the solution to the linear equation is x = -5
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can someone answer 5,6,7? can you also tell me how to solve them so i can do better in the future?
A _ is a constant, variable, or the product of a constant and variables.
Answer:
term
Step-by-step explanation:
term is a constant, variable, or the product of a constant and variables.
Term
An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.
An algebraic expression that is a number, a variable, or a product or quotient of numbers and variables is known as a term.
So,
A term is a constant, variable, or the product of a constant and variables.
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please help me. Given the explicit formula for an arithmetic sequence find the 52nd term.
a =-41 + 30n
A) a52= 1519
B) a52= -1541
C) a52=-1492
D) a52=-1490
Answer:
a = -41 +30n
52nd term is
a52 = -41 + 30(52)
a52 = -41 + 1560
a52 = 1519
The sum of a number and 12
Answer:
the sum of 6+6 is 12
Step-by-step explanation:
so the sum of the number 6+6 is 12 plz like and rate
Which is a factor of 5x2 − 15x − 20?
Answer:
x= -1, x=4
Step-by-step explanation:
5x²-15x-20
5x²-20x+5x-20=0
5x(x-4) +5(x-4)
(5x+5) (x-4) =0
5x=-5 or x=4
x= -5/5. or x=4
x= -1 or x=4
Consider the point. (1, 4, 5) What is the projection of the point on the xy-plane?
Given :
A point ( 1 ,4 ,5 ).
To Find :
The projection of the point on the xy-plane .
Solution :
Now , to find projection of a point in a plane in a plane we need to replace the coordinate of that remaining axis which is not in the plane .
Here , the plane given is xy-plane . So , remaining axis is z .
So , we replace coordinate of z =0 .
Therefore , the projection of the point ( 1 ,4 ,5 ) on the xy-plane is ( 1 ,4 ,0 ) .
Hence , this is the required solution .
please help its multiplying rational numbers
-3.2(-5.6)(4)
= -3.2 - 5.6 x 4
= -3.2 - 22.4
= -25.6
3. At the start of summer, Ben has $250 . He takes a summer
job and saves $ 150 per week. Tim has $ 1,650 at the start of
summer , he travels and spends $ 200 per week. At the end of
which week do Ben and Tim have the same amount of money ?
Answer:
Week 4
Step-by-step explanation:
Ben has $250 in the beginning. He saves $150 per week.
y = 150x + 250
Tim has $1,650 in the beginning. He spends $200 per week.
y = 1650 - 200x
We are trying to find which x-value produces the same y-value for both equations. You can do this by setting both equations equal to each other.
150x + 250 = 1650 - 200x
(150x + 250) + 200x = (1650 - 200x) + 200x
350x + 250 = 1650
(350x + 250) - 250 = (1650) - 250
350x = 1400
(350x)/350 = (1400)/350
x = 4
By week 4, they will have the same amount of money.
Solve for x. Show steps.
7x - 17 = 4x + 1
-x + 5 = x - 11
5x + 8 = 7x + 2
Combine the same numbers and do the opposite of either subtraction or addition.
Then, multiply or divide with the coefficient.
Answer:
see below
Step-by-step explanation:
⇒ 7x - 17 = 4x + 1
combine like terms
7x - 4x = 1 + 17
3x = 18
x = 18/3
x = 6
⇒ -x + 5 = x - 11
combine like terms
- x - x = - 11 - 5
-2x = -16
x = 16 / 2
x = 8
⇒ 5x + 8 = 7x + 2
combine like terms
5x - 7x = 2 - 8
- 2x = - 6
x = 6 / 2
x = 3
Simplify (X2/3) ^4/5
The answer to your questions is x8/15. Hope this helps!
Which equation can be used to solve for x in the following diagram? Choose 1 answer:
Answer:
D) 60=(x+45)
Step-by-step explanation:
D. Since the two are equal, you need to put the two on opposite sides of the equation. The equation doesn’t involve 90 or 180 degrees, so no reason to have them.
Solving for x this way, you’d get 15, which is correct.
An airplane cruises 1 kilometer in 1 12 of a minute. What is its cruising speed?
Answer:
Step-by-step explanation: 12 ur welcome
Speed is Distance traveled/time, then 12 kilometer per min is the cruising speed of airplane when airplane cruises 1 kilometer in 1 12 of a minute.
What is speed?Speed=Distance traveled/time
An airplane cruises 1 kilometer in 1 12 of a minute. We need to find the speed.
Given distance=1 km
time=1/12 min
We need to find speed.
Speed=Distance traveled/time
=1/(1/12)
=1*12/1
=12kilometerperminute
Therefore 12 kilometer per meter is the speed required.
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Solve in detail plzzzzz
Answer:you need to multiply it by 4.
Step-by-step explanation:
If the number is multiplied by 4 it square root is effectively doubled.
Example: if you take the square root of 64, its 8.
to double the square root, you multiply 64 by 4---> 256.
And the square root of 256, is 16, double that of the square root of 64.