Answer:
12x +4y + 3z=36
Step-by-step explanation:
The equation of plane is given by
z-zo = a(x-xo) + b(y-yo)
pass through (1,3,4)
Z -4 = a(x -1) +b(y-3)
The question is asking us to optimize a and b. To minimize the volume V both a and b should be negative as the normal vector should be towards the negative x and y direction so that a finite tetrahedron can be formed in the first octant.
we need x , y and z intercepts o define volume
x intercept( y, z =0) = [tex]\frac{a+3b-4}{a}[/tex]
y intercept (x, z =0) = [tex]\frac{a+3b-4}{b}[/tex]
z intercept ( x, y =0) = -(a+3b-4)
Base = [tex]\frac{(a+3b-4)^2}{2ab}[/tex]
Volume = [tex]\frac{1}{3}*base*height[/tex]
Volume(a, b) = [tex]\frac{-(a+3b-4)^3}{6ab}[/tex]
now we differentiate partially in terms to a and b the volume to minimize and get a and b.
ΔV(a, b) = [tex]\frac{-1}{6}(\frac{3(a+3b-4)^2ab-b(a+3b-4)^3}{a^2b^2}[/tex] ,[tex]\frac{-1}{6}(\frac{9(a+3b-4)^2ab-a(a+3b-4)^3}{a^2b^2}[/tex] = 0
Taking the first part of differential it will give
b(a+3b-4) [3a -(a+3b -4)] =0
(a+3b-4) [tex]\neq 0[/tex] because the volume will become zero if this becomes true
2a -3b = -4 ..................(1)
similarly the second part of the differential will give
a-6b=4 ................(2)
on solving 1 and 2 we get
a = -4 and b = -4/3
so the equation will be
Z -4 = -4(x -1) - 4/3*(y-3)
final equation
12x +4y + 3z=36
What is an equation for the line that passes through the coordinates (-1,2) and (7,6) ?
Answer: y =1/2x + 5/2
Step-by-step explanation: you have to use the slope formula y = mx + b to find the equation between those two points
The angles are Complementary. Find the value of x in the diagram.
Answer:
56
Step-by-step explanation:
90-34=56
Answer:
56°
Step-by-step explanation:
if the angles are complementary then 34° + x = 90°
So x = 56°
To complete a science experiment, Mrs. McWilliams divides 2,184 grams of a chemical equally among the 26 students in her science class. How many grams of the chemical does she give to each student?
Answer:
84 she will give 84
Step-by-step explanation:
the first thing you need to do is put 2184 in to a chart for dividing then just divide until you get the product your looking for in this problem the answer would be 84
At a grocery store , the price of pumpkins is determined by how many pounds the pumpkin weighs. The price of a 20.6 pound of pumpkin is $ 6.25. Write an equation that can be used to determine the price of any amount of bananas based on the number of pounds they weigh. Explain the process
Answer:
Step-by-step explanation:
sorry about my last text but the answer is you must divide 6.25 by 20.6 then find the equation that matches the answer.
Danny charges $26 for 2 hours of swimming lessons, Martin charges $60 for 4 hours of swimming lessons. Who offers a better deal?
Answer:
Danny has the better deal.
Step-by-step explanation:
26 x 2 = 52
Danny charges $52 for 4 hours while Martin charges $60.
what have you learned about dividing decimal
Answer: When we divide by a decimal, we move the decimal point in the divisor by enough places to the right such that it becomes a whole number. ... We then match this movement in the number 38.5. We move our decimal point one place to the right and end up with 385. Our division problem becomes: 385 ÷ 21.
1. What is the result when the SUM of 1/5
and 1/4 is divided by 3/4 ?
Answer:
3/5
Step-by-step explanation:
1/5 + 1/4 = 4/20 + 5/20 = 9/20 divided by 3/4
9/20 x 4/3 = 36/60 = 3/5. (Multiply by the reciprocal)
Which ordered pair is a solution of the equation?
-x– 4y = -10
Answer:
D - Neither
Step-by-step explanation:
I did the problem :)
Answer:
D. Neither
Step-by-step explanation:
Got it right on Khan Academy
Pete has a 15-foot ladder. The safety instructions recommend he should have the base of the ladder 6 feet from the base of the wall he will lean the ladder against. How high will the ladder reach on the wall?
whoever answers can have brainliest
Answer:
tbh i think it equals 9
Step-by-step explanation:
Answer:
13.74 because of pythagorean theorem.
It says choose all of the multiple choice answers that are true about the diagram
Answer:
d,e, g
Step-by-step explanation:
180 degrees = supplementary
Find the slope, if it exists, of the line containing the pair of points (4,−4) and (−2,−4).
Answer:
-6 is the answer of your question
5. Look at the following systems of equations.
3x – 2y = 14
6x = 4y + 28
Which of the following is a description of the solution for this system?
A. An infinite number of solutions
B. No solution
C. One solution
D. Two solutions
Answer:
An infinite number of solutions.
Step-by-step explanation:
A loan is paid off in 30 years with a total of $99,000. It had a 3% interest rate that compounded monthly. What was the principal?
Answer:
The principle will be "40295.63". A further explanation is given below.
Step-by-step explanation:
The given values are:
Total amount,
A = 99,000
Rate of interest,
R = 3%
Time period,
T = 30 years
= 360 months
As we know,
⇒ [tex]A=P(1+\frac{{\frac{R}{12} }}{100} )^T[/tex]
On substituting the values, we get
⇒ [tex]99000=P(1+\frac{\frac{3}{12}}{100})^{360}[/tex]
⇒ [tex]99000=P(1+\frac{\frac{1}{4} }{100}) ^{360}[/tex]
⇒ [tex]P=\frac{99000}{(1.0025)^{360}}[/tex]
⇒ [tex]P=40295.63[/tex]
The required value of principal will be p = "40295.63".
Given,
Total amount of loan is = A = $99,000
Rate of interest = R = 3%
Time period =T = 30 years
Convert into months = 12×30
= 360 months
According to the question,
[tex]A = P ( 1+ \frac{\frac{R}{12} }{100} )^{360}[/tex]
Put the value of A = 99,000 , T = 360 , R= 3
[tex]99,000 = P [ 1+ \frac{\frac{3}{12} }{100} ]^{360} \\\\P = \frac{99,000}{(1.0025)^{360} }[/tex]
P = 40295.63
The required value of principal p = 40295.63 .
For more information about Compound interest click the link given below.
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PLEASE HELP! Determine the slope and the y-intercept of the table.
Let's take the first 2 x and y values and use them. First, you need to fill in your formula: y2-y1/x2-x1. It should look like this: 5-2/4-2. Then solve and you should get 3/2. You can't simplify it. So, this is your slope.
Next, you need to put this is into another formula. The formula is y-y1=m(x-x1). Take the first coordinate pair and plug it in for x1 and y1. Plug in your slope for m. When it's filled in, you should have y-2+3/2(x-1). It's hard to explain how to solve it so i'll just write it out.
y-2=3/2(x-2)
y-2=3/2x-3
y=3/2x-1
So, we have our equation in slope intercept form so that we have our slope and our y-intercept.
Y-intercept: -1
Slope: 3/2
Please put this as brainliest it took awhile and I hope this helped :) reply with questions if you still need help or have questions about the steps
POOOOOOOOOG PLZZZZ!!!! DUE IN TEN MINUTES!!!!! HELP WILL DO BRAINLIEST!!! IMPORTANT!!!
Answer:
Table b
Step-by-step explanation:
In order to find the inverse proportion relationship between x and y, multiply the corresponding values of x and y given in the table. If the products are same for all, there would be inverse relation otherwise not.
Lets first work with table (a)
(a)
3*8 = 24
4*6 = 24
5*4.8= 24
5.5*4 = 22
Here in table a product of all corresponding numbers are not constant. Table (a) has no inverse relation between x and y.
Now, let's work with table (b)
0.1*300 = 30
0.5*60 = 30
45*0.4 = 30
100*0.3= 30
Here products are constant, therefore in table (b) x and y are inversely proportional.
How many solutions does this equation have?
1 solution
No solution
x – 5 – (2 - x) =
- 3
o Infinite solutions
Explain your thinking.
Answer:
one soulution
Step-by-step explanation:
you have 5x 2x and 3x subtract 5 by 3 get 2 divide u get 1 I am not certain but it's an attempt
The Alien Enemies Act of 1798 allowed the president to deport noncitizens considered dangerous. allowed the president to ignore laws he believed unconstitutional. made immigrants wait longer before becoming citizens. made it a crime to criticize the federal government.
Answer: Allowed the president to deport noncitizens considered dangerous.
Step-by-step explanation:
The Alien Enemies Act was part of the Alien and Sedition Acts which were passed through Congress by the Federalist party under President John Adams during a time when they feared going to war with France. These acts were meant to prevent support of the French amongst immigrants who habored French sentiments.
The Alien Enemies Act gave the President the power to arrest and then deport noncitizens of the US or rather citizens of other countries that the US were at war with as they were considered dangerous.
Answer:
its a
Step-by-step explanation:
What is the value of the expression below?
-8+19+8
0
11
19
35
Answer:
19
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
Finish the equation below to create a line that passes through the given points.
Determine the equation of a line that passes through the points (4, 3) and (8, 5). Can you do this without a graph?
Answer: y = 1/2x + 1
Step-by-step explanation:
1.) -27x(-39) please answer I need the answer NOW*
Answer:
1,053
Step-by-step explanation:
Use a Calculator
how many feet are in 508 cm ?
Answer:
16.7
Step-by-step explanation:
30.48cm = 1 foot
508/30.48= 16.6667
round up to 16.7
Solve the problem.
A die is rolled 9 times and the number of times that two shows on the upper
face is counted. If this experiment is repeated many times, find the mean for the
number of twos.
3
1.5
2.25
о
7.5
Answer:
1.5
Step-by-step explanation:
four equals the difference of eight and a number and the result is divided by four
Answer:
(8-n=4)/4 click brainliest please and click thanks
Step-by-step explanation:
The mathematical expression which represents the phrase four equals the difference between eight and a number and the result is divided by four is (4 = 8 - x)/4.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
Difference of 8 and a number x = 8 - x
4 equal to 8 - x
4 = 8 - x
Now,
The result is divided by 4
Therefore,(4 = 8 - x)/4
Hence "The mathematical expression which represents the phrase four equals the difference between eight and a number and the result is divided by four is (4 = 8 - x)/4".
To learn more about expression,
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Which expression results in a rational number?
1
Step-by-step explanation:
it will give u the correct number of it
Answer:
3) [tex]\sqrt{2}[/tex]·[tex]\sqrt{8}[/tex]
Step-by-step explanation:
[tex]\sqrt{2}[/tex]·[tex]\sqrt{8}[/tex]= [tex]\sqrt{16}[/tex]=4 (rational number)
Which of the following expressions has a value of 2/5 in the picture below?
Step-by-step explanation:
Step 1: List out all of the formulas for the trigonometric functions
sin(x) = opposite/hypotenuse
cos(x) = adjacent/hypotenuse
tan(x) = opposite/adjacent
Step 2: Find the following expression that has a value of 2/5
sin(B) = opposite/hypotenuse = ?/5 is FALSE
cos(B) = adjacent/hypotenuse = 2/5 is TRUE
tan(B) = opposite/adjacent = ?/2 is FALSE
Answer: The correction expression that has a value of 2/5 is option B
Answer:
B is the correct option
Step-by-step explanation:
What CANNOT be determined by the factors of a polynomial in factored form?
x-intercepts
solutions
degree of the
polynomial
y-intercept
Answer:Y intercept
Step-by-step explanation: THE OTHER GUY ANSWERED BUT SPELT IT WRONG
The factored form of a polynomial is a representation of the polynomial as a product of irreducible factors
The information that cannot be determined (directly) by the factors of a polynomial in factored form is the option;
y-intercept
Reason:
The factors of a polynomial are the smaller polynomials or expression that divides the polynomial having zero as the remainder
The solutions or x-intercept of a polynomial is given by the points where the value of a polynomial is zero, which is given by the x-values of a factor equated to zero The degree of a polynomial can be found by summing the powers of its factors
However, in the factored form, the y-intercept of the polynomial cannot be determined directly, because, the factored form has to be resolved with x = 0 to determine the y-intercept
Therefore;
The correct option is the y-interceptLearn more here;
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Jolene is making a line graph showing that the cost of grain is proportional to the number of pounds purchased. Jolene will plot the number of pounds on the x-axis and the cost in dollars on the y-axis. The coordinates Jolene graphs are shown in the table.
Which coordinate represents the unit rate, in dollars per pound of grain, and why?
Pounds Cost (in dollars)
1.0 0.25
4.0 1.00
Create an equation to represent the cost, y, in dollars, for x pounds of grain.
Answer:
a. [tex](1,0.25)[/tex]
b. [tex]y = 0.25x[/tex]
Step-by-step explanation:
Given
The data in the table
Solving (a): The coordinate that represents the unit rate
The unit rate is when its 1 pound
This is so because the unit rate is dollars per pounds.
Hence, the coordinate is [tex](1,0.25)[/tex]
Solving (b): Equation of the graph
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1,0.25)[/tex]
[tex](x_2,y_2) = (4,1.00)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1.00 - 0.25}{4 - 1}[/tex]
[tex]m = \frac{0.75}{3}[/tex]
[tex]m = 0.25[/tex]
The equation is then calculated as thus:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - 0.25 = 0.25(x - 1)[/tex]
[tex]y - 0.25 = 0.25x - 0.25[/tex]
Make y the subject
[tex]y = 0.25x[/tex]
Hence, the equation of the graph is: [tex]y = 0.25x[/tex]
3 = c/-11 Help me with this please.
Answer:
-33=c
Step-by-step explanation:
-11×3=c/-11×-11 which cancels out the -11 and c equals -33
Owen And Bella are eating a granola bar Bella eats 1/4 of the granola bar and Owen ate 1/3
Answer:
7/12
Step-by-step explanation:
1/4 x 3/3 = 3/12
1/3 x 4/4 = 4/12
3/12 + 4/12 = 7/12
Hope this helped! ;) Have a good day! :)
The scores on an exam are normally distributed, with a mean of 73 and a standard deviation of 5. What percent of the scores are less than 78?
16%
84%
50%
135%
Answer:im sorry
Step-by-step explanation:
