Answer:
23
Step-by-step explanation:
Here is the complete question
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).
Solution
We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.
So, (1, 0, -3), (1, 2, 4) and (5, 1, 0)
[tex]A = \left[\begin{array}{ccc}1&1&5\\0&2&1\\-3&4&0\end{array}\right][/tex]
The determinant of A is the volume of the parallelepiped. So,
detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)
= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)
= 1(-4) - 1(3) + 5(6)
= -4 - 3 + 30
= 23
So the volume of the parallelepiped is 23
PLEASE HELP ME QUICK
A serving dish has a parabolic surface with the vertex (0, 0) at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y = ax2. What is the value of a?
1/12
1/3
1/2
1
Answer:
B
Step-by-step explanation:
1/3
The required value of a is 1/3 for parabola [tex]y = 1/3x^2[/tex].
A parabolic dish with vertex (0,0) at the center, width is 6 inches and depth is 3 inches. y = ax² where a is to be determined.
A parabola is a cross-section cut out of the cone and represented by an equation [tex]y=4ax^2[/tex].
Here,
Vertex is at the center of the parabolic plate (0,0),
with the help of the width and depth coordinate of the one corner is(3,3).
Now put these coordinates in y = ax²
3 = a3²
a = 3/3²
a = 1/3
Thus, The required value of a is 1/3 for the parabola [tex]y = 1/3x^2[/tex].
Learn more about parabola here:
brainly.com/question/4074088
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What is the volume of a cylinder, in cubic feet, with a height of 5 feet and a base
diameter of 10 feet? Round to the nearest tenths place
Answer: 392.7
Step-by-step explanation:
2х + y = 4
у = 3х – 1
its 2 because 2plus is 2
Please give me the correct answer
Answer:
the first one; 3*1/10^-4
Step-by-step explanation:
10^-4 can be ocnverted into a fraction: 1/10^4
Answer:
3 times 1/10,000
Step-by-step explanation:
The sum of x and y equals 26.
If x= 17, which equation can be used to find the value of the y?
Given f(x) = 5(2-x), what is the value of f(-3) ?
Answer:
f(-3) = 25
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 5(2 - x)
f(-3) is x = -3
Step 2: Evaluate
Substitute: f(-3) = 5(2 - -3)Simplify: f(-3) = 5(2 + 3)Add: f(-3) = 5(5)Multiply: f(-3) = 25Please give me the correct answer
jerry's softball team is made up of 15 players,and 9 of them are boys.On the team,what is ratios to boys to girls?
Answer:
9:6
Step-by-step explanation:
boys= 9 teammates
girls= 6 teammates
what is the product in simplest form? -8/9 times 5/6 All the ANSWERS:
-1
-13/15
-20/27
-1/5
Evaluate the surface integral.
S(x + y + z) dS, S is the parallelogram with parametric equations
x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.
Answer:
[tex]\frac{115\sqrt{14} }{2}[/tex]
Step-by-step explanation:
∫∫ ( x + y + z ) ds
where :
x = u + v , y = u - v , z = 1 + 2u + v ,
0 ≤ u ≤ 5,
0 ≤ v ≤ 1
R ( u,v ) = < u+v , u-v , 1 + 2u +v > next we have to differentiate
attached below is a detailed solution
The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex] and this can be determined by integrating the given expression.
Given :
The surface integra S(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.
The following calculation can be used in order to determine the surface integral.
[tex]\rm R_u\times R_v = <3,1,-2>[/tex]
[tex]\rm ||R_u\times R_v|| = \sqrt{14}[/tex]
Now, evaluate the surface integral.
[tex]\rm I = \rm \int\int_s(x+y+z)dr[/tex]
[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)||R_u\times R_v||dA[/tex]
[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)\sqrt{14} \;du\;dv[/tex]
[tex]\rm I = \sqrt{14} \int^5_0(v+4uv+\dfrac{v^2}{2})^1_0\;du[/tex]
[tex]\rm I = \sqrt{14} (\frac{3}{2}u+4\frac{u^2}{2})^5_0[/tex]
Simplify the above expression.
[tex]\rm I = \dfrac{115\sqrt{14} }{2}[/tex]
The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex]
For more information, refer to the link given below:
https://brainly.com/question/22008756
Find the slope of the line containing the two given points.
(9,-5) and (6,8)
Answer:
13/-3
Step-by-step explanation:
Answer:
-13/3
Step-by-step explanation:
The slope is rise over run.
From the first point to the other, the line goes 13 units up and -3 units to the right.
Putting it in the form of rise over run we have:
13/-3 which is the same as -13/3
Does this scatter plot show a positive trend, a negative trend, or no trend?
Answer:
no trend
a positive trend would start in the bottom left and go toward the top right
a negative trend would start at the top left and go town the bottom right
this is an example of no trend
Step-by-step explanation:
a "trend" shows an increasing or decreasing relationship between the x and y values, in this they don't have any sort of relationship. you can tell by the repeating y values for multiple different x-values, or the repeating x-values for multiple different y-values.
In metrics, the meter is the standard unit of: mass distance volume length
What of the following lines is perpendicular to the line passing across the points (1,1) and (-5,-6)?
y = 6/7x + 1
y = -6/7x + 1
y = -6/7x - 1
y = 6/7x - 1
Zelda rode her bike at a steady rate of 12 miles per hour for 3
Answer:
36miles
Step-by-step explanation:
Given parameters:
Rate = 12mph
Time = 3hr
Unknown:
Distance = ?
Solution:
The given rate amount is the speed. Speed is the distance divided by the time.
It is mathematically expressed as:
Speed = [tex]\frac{distance}{time}[/tex]
Distance = Speed x time
Distance = 12 x 3 = 36miles
What is the slope of the line graphed below
Find the equation of the line above. Write the equation in slope intercept form.
Find the coefficient of x^2 y^3 in the expansion of (-4x+y)^5. Give your answer as an integer.
Select the correct answer
Answer:
Option B
Step-by-step explanation:
Domain of a function is represented by the set input values or x-values
Range of the function is represented by the set of output values or y-values.
From the graph attached,
y-values are varying from y = - 9 to y = 8.
Therefore, range of the function from the given graph will be,
-9 ≤ y ≤ 8
Option B will be the correct option.
What is the quotient of 1/10 and 9/10
Answer:
1/9 = 0.1111111
Step-by-step explanation:
a rental car company charges drivers a flat fee to rent a car plus $0.25 for each mile they drive. If a drivers pays $100 drives 160 miles , which equation can he use to find his total cost y in terms of the number of miles driven ?
Edmund made a scale drawing of the rectangular floor of his kitchen. In the scale
drawing, 1 inch represents 2.5 feet. The measurements of the scale drawing are
shown in the diagram.
6.4 in.
4.8 in.
what is the perimeter of the actual kitchen floor in feet?
Answer:
324
Step-by-step explanation:
Write the quadratic function in vertex form, then identify the vertex
h(x)=x^2+20x+90
h(x)=
Vertex:
I need this answered ASAP please !
Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
HELP PLEASE.............
I'm pretty sure it is the fourth answer.
WILL MARK BRAINLIEST
please help geometry problem in the picture
Ava plays on the softball team at her school. The team won 8 of its first 12 games. At that rate, how many games will Ava's team win if it plays 60 games in all?
Answer:
She wins 40 games
Step-by-step explanation:
I'm not the best at explaining but 5x12=60 so then we multiply 8 by 5 aswell and bam we have 40.
Question is in the image
Answer:
4.
Step-by-step explanation:
y = -2x + 3
-1 = -2(2) + 3
-1 = -4 + 3
-1 = -1
y = x - 3
-1 = 2 - 3
-1 = -1
Express 76.5% as a decimal and a fraction
PLEASE SHOW FULL SOLUTIONS!! Will Mark Brainliest for the best answer. The radius of a spherical balloon is 3.5 cm. What is the volume of air in the balloon? Show your answer in terms of pi or round your answer to one decimal place.
THANKS
9514 1404 393
Answer:
343π/6 cm³ ≈ 179.6 cm³
Step-by-step explanation:
The formula for the volume of a sphere is one of the volume formulas worth memorizing. It is ...
V = (4/3)πr³
For r = 3.5 cm, the volume is ...
V = (4/3)π(3.5 cm)³ = 343π/6 cm³ ≈ 179.6 cm³
The volume of air in the balloon is about 179.6 cm³.
K mola ofkg o okdgmbo9k
Answer: c
Step-by-step explanation:
Identify the following parasite provided and draw a large labelled diagram of each
specimen
Answer:
Spiced eye gonna flush my toilet now ;)
Answer:
hes right
Step-by-step explanation: