Write the augmented matrix for the system of linear equations. (Do not perform any row operations.)
x − y + 8z = 8
3x − 9y + z = −1
8x + y = 0
Answer:
Step-by-step explanation:
To create an augmented matrix, we need to transfer the coefficients of each system of equations into its respective place in the matrix. The first row will be the coefficients of the first equation and so on. The number to the right of the equals sign is the last column of the augmented matrix.
[tex]\left[\begin{array}{ccc|c}1&-1&8&8\\3&-9&1&-1\\8&1&0&0\end{array}\right][/tex]
Find the approximate area under the curve by dividing the intervals into n subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you n1and n2y = 2x underroot x^2 + 1 betwee x=0 and x=6 n1 and n2Find the exact area under the curve using integrationy = 2x underroot x^2 + 1 between x = 0 and x = 6
Explain the reason for the difference in your answers.
n1=12
n2=5
Answer and Step-by-step explanation: There are a number of ways of calculating an area under a curve. The more precise way is to use Definite Integral:
The function is [tex]2x\sqrt{x^{2}+1}[/tex], then the area under, with interval between 0 and 6 is:
[tex]\int\limits^6_0 {(2x\sqrt{x^{2}+1}) } \, dx[/tex]
To solve this integration, use substitution method, in which:
[tex]u=x^{2}+1[/tex]
[tex]\frac{du}{dx}=2x[/tex]
du = 2xdx
Replacing into the integral:
[tex]\int\limits^a_b {\sqrt{u} } \, du[/tex]
Solving:
[tex]\int\limits^a_b {\sqrt{u} } \, du=\frac{2}{3} \sqrt{u^{3}}[/tex]
Replacing it back to x:
[tex]\int\limits^6_0 {2x\sqrt{x^{2}+1} } \, dx =\frac{2}{3}\sqrt{(x^{2}+1)}[/tex]
Substituing limits between 0 and 6:
[tex]= \frac{2}{3}[\sqrt{(6^{2}+1)^{3}}-\sqrt{(0^{2}+1)^{3}} ][/tex]
= 149.37
Area under the curve using Integration is 149.37 square units
Another way of calculating area under the curve is dividing the area into a number of small rectangles and then adding the area of each one. This method is called Riemann Sums and it is an approximation of the area.
The method is done by the following relation:
in which
i is the n, the number of subintervals the area is dividing into
Δx is width of each subintervals.
For the function f(x) = [tex]2x\sqrt{x^{2}+1}[/tex], interval between 0 and 6:
subinterval n1 = 12:[tex]\Delta x=\frac{6-0}{12}[/tex]
[tex]\Delta x=[/tex] 0.5
[tex]A=\Sigma f(x_{i}).\Delta x[/tex]
[tex]A = f(0)*0.5+f(0.5)*0.5+f(1)*0.5+f(1.5)*0.5+f(2)*0.5+f(2.5)*0.5+f(3)*0.5+f(3.5)*0.5+f(4)*0.5+f(4.5)*0.5+f(5)*0.5+f(5.5)*0.5[/tex]
[tex]A=0+1.12*0.5+2.83*0.5+...+50.99*0.5+61.49*0.5[/tex]
A = 131.575 square units
subinterval n2 = 5:[tex]\Delta x=\frac{6-0}{5}[/tex]
Δx = 1.2
[tex]A=f(0)*1.2+f(1.2)*1.2+f(2.4)*1.2+f(3.6)*1.2+f(4.8)*1.2[/tex]
[tex]A=0*1.2+3.75*1.2+12.48*1.2+26.90*1.2+47.07*1.2[/tex]
A = 108.24 square units
Comparing results, notice that with less subintervals, the area is far from the exact measure. It occurs because Riemann Sums is an approximation method. So, if there are more subintervals, more approximate is the area, therefore, more precise it will be.
Find the mean monthly subscription fee? Round your answer to the nearest cent.
$8.78
$6.78
$5.78
Answer:
$6.78
Step-by-step explanation:
Add $10 +$6 +$2.75+$3+$5+$10+$10+$4+$12+$5 =$67.75
Now divide $67.75 by 10 which is the number of values you added up
$67.75/ 10 = 6.775
Now round to nearest cent = $6.78
Please help!!! I need to know the answer to this question quickly please
Which year group is this question from?
Is the equation a linear function or nonlinear function?
y = 0.5x – 1
Answer:
Linear.
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = 0.5x - 1
Step 2: Compare
y = mx + b
y = 0.5x - 1
m = 0.5
b = -1
The equation is a linear function. It's proportional.
Which of the following values are solutions to the inequality 1 + 5x < 4?
Step-by-step explanation:
you cant add 1 to 5x, so subtract 1 on both sides leaving you with 1 + 5x < 4 that equals 5x < 3 -1 -1
then divide 5 from both sides 5x < 3 This leaves 5 5
you with x < 3/5
what is 3/4 + 1/2 and what is 1/3 + 11/48 in simplest form and a mixed number
Answer:
1) 5/4 or 1 1/4
2) 9/16
Step-by-step explanation:
3/4+1/2: you multiply 1/2 by 2 to get a common denominator then get 2/4, 3+2=5, 5/4 or 1 1/4
1/3+11/48: you multiply 1/3 by 16 to get common denominator & get 16/48, 16+11= 27/48, divide by 3 & get simplest form of 9/16
Answer:
3/4+1/2= 1 5/8 and 1/3+11/48 is not a mixed number 9/16
Step-by-step explanation:
Stuck on this last question
Answer:
C.
because both of those decimals can be turned into fractions.
Step-by-step explanation:
Hope this helps and have a great day :)Answer:
C
Step-by-step explanation:
.752 is a rational number and .232323... is a non-terminating repeating number, which is also rational
Find the measure of each angle
Answer:
Answer is in the screenshot provided.
Step-by-step explanation:
Work is also in the screenshot provided.
Talbot Family has a monthly income of $3,200. They spend $800 on rent what percentage of the Talbot family is spent of rent?
Answer:
800/3200= .25 or 25%
you must divide the rent by the monthly income.
The enrollment at a small college each year is growing at a rate of 2%. If the college has 2,700 students in 2015, then which of the following models the population n years from 2015?
HELP ME ASAP!
What is the result when the number 44 is decreased by 75%?
Answer:
11
Step-by-step explanation:
Researchers are interested in estimating the percentage of Americans who will get a flu shot this year. How many Americans should be surveyed to be 80% confident that the sample proportion of Americans who will get a flu shot this year is within 0.100 of the population proportion Assume we have a prior estimate of 45%. Round your z critical value to four decimal places.
Answer:
The sample size bedded is [tex]n =41[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.100[/tex]
The sample proportion is [tex]\^ p = 0.45[/tex]
From the question we are told the confidence level is 80% , hence the level of significance is
[tex]\alpha = (100 - 80) \%[/tex]
=> [tex]\alpha = 0.20[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.282[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.282}{ 0.100} ]^2 *0.45 (1 - 0.45 ) [/tex]
=> [tex]n =41[/tex]
Find the slope of the line passing through the points (-3,-4) and (2, -4). Slope:
Answer:
0
Step-by-step explanation:
Slop of the line=y1-y2/x1-x2
Where x1,y1 point (-3,-4)
And X2,y2 point (2,-4)
So slop= (-4+4)/(-3-2)
=0/-5
So slop is 0
Find the least common multiple of 7,9 and 21
The sum of two numbers is 60 and the difference is 6. What are the numbers?
Answer:
33 and 27
Step-by-step explanation:
60 ÷ 2 is 30
33 is 6 more than 27
5. You make $50 a week and you want to buy a car with an expected payment of $200 a month.
Answer:
what is the question
Step-by-step explanation:
you will not have enough money to pay your car bill though
Find the area of the triangle whose one angle measure is 55°, the other angle is a right angle and the side opposite the 55° angle is 15 units.
Answer:
Step-by-step explanation:
Area of the right angles triangle will be expressed as;
Area of a triangle = 1/2base * height
Let the height of the triangle be 15 units
Get the base;
The base will be the adjacent;
Using the TOA trig identity;
tan 55 = opp/adj
tan 55 = 15/adj
adj = 15/tan 55
adj = 15/7.42
adj = 2.022 units
Area of the triangle = 1/2 * 15 * 2.022
Area of the triangle = 15 * 1.011
Area of the triangle = 15.165units²
yoo someone help me with this im at school right now and its due in like 10 mins !
Someone please help thank you
Y=-5x+2 fill in the table using this function rule
X Y
-6 4
-3 1
0 6
3 -9
That’s the real answer
The required table will be:
X Y
-6 32
-3 17
0 2
3 -13
Since we are not given the x - values, let the x values be -6, -3, 0 and 3
Given the function of y with respect to x;
y = -5x + 2
We need to get all the y-values for the given values of x as shown;
If x = -6
y = -5 (-6) + 2
y = 30 + 2
y = 32
If x = -3
y = -5 (-3) + 2
y = 15 + 2
y = 17
If x = 0
y = -5 (0) + 2
y = 0 + 2
y = 2
If x = 3
y = -5 (3) + 2
y = -15 + 2
y = -13
Hence the required table will be:
X Y
-6 32
-3 17
0 2
3 -13
Learn more here: https://brainly.com/question/15011804
what is x-(3)/(5)=(5x)/(6)? with steps answer fast
hi
x- 3/5 = 5x/ 6
6x - 18/5 = 5x
6x -5x = 18/5
x = 18/5
let's check : 18/5 - 3/5 = 15/5 = 3
5 * 18/5 / 6 = 18/6 = 3
result is correct.
Please answer this correctly without making mistakes
Answer:
What is the question?
Step-by-step explanation:
Plz mark brainliest!!!
Faith invested \$1,100 in an account paying an interest rate of 5.1\% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 18 years?
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=1100\hspace{35px}r=0.051\hspace{35px}t=18
P=1100r=0.051t=18
Given values
A=1100e^{0.051(18)}
A=1100e
0.051(18)
Answer: 2,750
Explanation:
Plug in
A=1100e^{0.918}
A=1100e
0.918
Multiply
A=2754.70450683
A=2754.70450683
Use calculator (with e button)
A\approx 2750
A≈2750
Round to nearest ten dollars
please heart!
VVV and rate stars! VVV :D
The amount of money after 18 years nearest to ten will be $2,750.
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm A=P_o \times e^{r \times t}\\[/tex]
Faith invested $1,100 in an account paying an interest rate of 5.1% compounded continuously.
Then the amount after 18 years is calculated as,
[tex]\rm A = \$1,100 \times e^{0.051 \times 18}\\A = \$1,100 \times e^{0.918}[/tex]
Simplify the equation further, then we have
A = $1,100 x 2.504
A = $2,754.7
The amount of money after 18 years nearest to ten will be $2,750.
More about the continuous compounding link is given below.
https://brainly.com/question/19522540
#SPJ3
Solve 3x2 + 4x = 2. (2 points)
Answer:
The answer is (-2±√10)/3
Step-by-step explanation:
so if it is 3x^2+4x=2 then
set one side to zero
subtract 2 from both sides
3x^2+4x-2=0
this is not factorable by normal means so use quadratic formula which is if you have the equation in ax^2+bx+c=0 form you can solve for x if you put it into this equation quadratic formula so if you were to input it into this equation you would get
a=3
b=4
c=-2
the solution is: (-2±√10)/3
21-7y+3x-xy solve by factoring by grouping
Answer:
-(y-3)(x+7)
Step-by-step explanation:
NEED HELP PLEASE!!!!
Answer:x=35
Step-by-step explanation:
(x-8)(2x+5)=0 solve the equation
Answer:
x=8
Step-by-step explanation:
x= -5/2=-2 1/2= -2.5. If you add all of those up you will get x=8
Hope this helps and have a great day :)I need help with this question.
Answer: W=V/lh
Step-by-step explanation:
You know that the formula to find the volume is length * width* height.
So l*w*h=V
divide lh on both sides, and you get
W=V/lh, The top right answer
Martin is interested in joining a gym and has researched the cost of two gyms close to his
house Gym A has a $50 registration fee and costs $30 per month. Gym B has a $100
registration fee and costs $10 per month. The cost of joining each gym can be modeled by the
expressions below, where m represents the number of months.
• Gym A: 30m + 50
• Gym B: 10m + 100
Answer:
I suppose that you want to find which gym will be cheaper for you.
We have two equations:
• Gym A: 30m + 50
• Gym B: 10m + 100
First, let's find the value of m such that both gyms cost exactly the same:
30*m + 50 = 10*m + 100
Let's solve this for m
30*m - 10*m = 100 - 50
20*m = 50
m = 50/20 = 2.5
now:
for m < 2.5, Gym A will be cheaper, because the y-intercept is smaller.
for m > 2.5, Gym B will be cheaper, because the slope is smaller,
Then depending on the number of months that Martin wants to go to the gym, he can se the info above to pick the one that is cheaper.