Answer - Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(b) Use Formula 9 to find the curvature.
r(1) = (t , 1/2t2, t2)
Answer:
a. i. (i + tj + 2tk)/√(1 + 5t²)
ii. (-5ti + j + 2k)/√[25t² + 5]
b. √5/[√(1 + 5t²)]³
Step-by-step explanation:
a. The unit tangent
The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)
r(t) = (t, t²/2, t²)
r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)
|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)
So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²) = (i + tj + 2tk)/√(1 + 5t²)
ii. The unit normal
The unit normal N(t) = T'(t)/|T'(t)|
T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt
= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]
= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)
= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)
= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)
= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)
We multiply by the L.C.M [√(1 + 5t²)]³ to simplify it further
= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)
= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)
= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k
= -5ti + j + 2k
So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]
So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]
(b) Use Formula 9 to find the curvature.
The curvature κ = |r'(t) × r"(t)|/|r'(t)|³
since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt = (0, 1, 2)
r'(t) = i + tj + 2tk and r"(t) = j + 2k
r'(t) × r"(t) = (i + tj + 2tk) × (j + 2k)
= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k
= k - 2j + 0 + 2ti - 2ti + 0
= -2j + k
So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5
magnitude of r'(t) = |r'(t)| = √(1 + 5t²)
|r'(t)|³ = [√(1 + 5t²)]³
κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³
What is 7 and 1/3 times 2 and 2/11 equal?
Answer:
16
Step-by-step explanation:
First, convert both into improper fractions. 7 1/3=22/3. 2 2/11=24/11.
Lastly, multiply 22/3*24/11=528/33=16
Hope this helps!
The value of given expression is 28/33.
What is the product of two fractions?The product of two fractions is the product of the numerators and the product of the denominators.
Product of two fractions = Product of their numerators / Product of their denominators
Given that, 7 and 1/3 times 2 and 2/11.
Now, 7× [tex](\frac{1}{3} \times2)[/tex]× 2/11
= 7× 2/3× 2/11
= (7×2×2)/(3×11)
= 28/33
Therefore, the value of given expression is 28/33.
To learn more about the product of two fractions visit:
https://brainly.com/question/7335118.
#SPJ2
What is the probability of rolling a number less than or equal to 8 with the
sum of two dice, given that at least one of the dice must show a 6?
Answer:
I hope this helps
the outcomes are the compulsory 6, and 1 or 2
Step-by-step explanation:
[tex] \frac{3}{6} \\ \frac{1}{2} or \: 0.5[/tex]
Solve the inequality -6c< -12
Answer: c<2
Step-by-step explanation:
-6c<-12
c<-12/-6
c<2
A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 records of installations times of vertical blinds of each of the two employees and computes the following information. Test whether the new employee installs vertical blinds faster, on the average, than the veteran employee, at the level of significance 0.05.
New Employee Veteran Employee
Sample Size 10 10
Sample Mean 22.2 min 24.8 min
Standard Deviation 0.90 min 0.75 min
Required:
What is the appropriate conclusion for this test?
Answer:
we arrive at the conclusion that the new employee installs the vertical blinds faster on average.
Step-by-step explanation:
null hypothesis; m₁-m₂ =0
alternative hypothesis; m₁-m₂<0
Given the information in this question, we first have to solve for the t statistic
[tex]t=\frac{22-24.8}{\sqrt{\frac{0.90^{2} }{10}+\frac{0.75^{2} }{10} } }[/tex]
[tex]t=\frac{-2.6}{\sqrt{o.081+0.05625} }[/tex]
[tex]t=\frac{-2.6}{0.37047}[/tex]
t = -7.018
the degree of freedom = n₁+n₂-2
= 10+10-2
= 18
Alpha α = 0.05
from these results the t critical value = -1.734
because the test statistic -7.018 < -1.734,
at 0.05 level of testing, we arrive at the conclusion that the new employee installs the vertical blinds faster on average than the veteran.
1 +3 = ????????????????
One and three are both numbers. We can add the, together and get another number. The fact that these two numbers should be added is shown by the symbol between them. Adding 1 to 3 equals to 4.
Which graph shows the line y = 2x + 3?
C
НА
A
D
B
A. Graph A
Ο Ο
B. Graph D
C. Graph B
D. Graph C
the answer is letter B.graph D
I can’t get this answer right
Answer:
A
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
The perimeter of a triangle is 57 inches. Twice the length of the longest side minus the length of the shortest side is 22 inches. The sum of the length of the longest side and twice the sum of both the other side lengths is 94 inches. Find the side lengths
[tex]\begin{cases} a = shortest\\ b = medium\\ c = longest \end{cases} \begin{array}{llll} \stackrel{\textit{perimeter is 57}~\hfill }{a + b + c = 57}~\\\\\stackrel{\textit{twice longest minus shortest}}{2c-a=22~\hfill }\\\\ \stackrel{\textit{longest plus twice others}}{c + 2(a+b) = 94~\hfill } \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2c-a=22\implies 2c=a+22\implies \boxed{2c-22=a} \\\\\\ \stackrel{\textit{we know that}}{c+2(a+b)=94}\implies c+2a+2b=94\implies c+2(2c-22)+b=94[/tex]
[tex]c+4c-44+2b=94\implies 5c-44+2b=94\implies 5c+2b=138 \\\\\\ 2b=138-5c\implies \boxed{b = \cfrac{138-5c}{2}} \\\\\\ \stackrel{\textit{we know the perimeter is}}{57=a + b + c}\implies 57 = \stackrel{a}{(2c-22)}+\stackrel{b}{\cfrac{138-5c}{2}}+c \\\\\\ 57=2c-22+\cfrac{138}{2}-\cfrac{5c}{2}+c\implies 57=3c-22+69-\cfrac{5c}{2} \\\\\\ 57=3c-47+\cfrac{5c}{2}\implies 10=3c-\cfrac{5c}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{20=6c-5c}[/tex]
[tex]\blacktriangleright 20=c \blacktriangleleft \\\\\\ \boxed{2c-22=a}\implies 40-22=a\implies \blacktriangleright 18=a \blacktriangleleft \\\\\\ \boxed{b = \cfrac{138-5c}{2}}\implies b=\cfrac{138-5(20)}{2}\implies b=\cfrac{38}{2}\implies \blacktriangleright 19 \blacktriangleleft[/tex]
The graph below does not represent a function. Explain why.
Notice how points T and Z are vertically aligned, or vertically lined up. This is where the graph fails the vertical line test.
The input x = 2 leads to the outputs y = 3 and y = 5 (which are the y coordinates of points Z and T in that order).
A function is only possible when any given input leads to exactly one output only. It would be like saying "the conversion function from Celsius to Fahrenheit has 0 degrees C convert to both 32 degrees F and 50 degrees F at the same time". But such a statement makes no sense and it's not useful. So this is one example of why having one output makes sense for a function.
In short, we need one output for any given input. But the input x = 2 leads to more than one output. That's why we don't have a function.
As part of a board game, players choose 5 unique symbols from 9 different symbols to create their secret password. How many different ways can the players create a specific 5 symbol password?
Give your answer in simplest form.
Answer:
[tex]15,120[/tex]
Step-by-step explanation:
For the first symbol, there are 9 options to choose from. Then 8, then 7, and so on. Since each player chooses 5 symbols, they will have a total of [tex]9\cdot 8 \cdot 7 \cdot 6\cdot 5=\boxed{15,120}[/tex] permutations possible. Since the order of which they choose them matters (as a different order would be a completely different password), it's unnecessary to divide by the number of ways you can rearrange 5 distinct symbols. Therefore, the desired answer is 15,120.
Answer:15,120
Step-by-step explanation:
Help please!!! Will mark brainliest!!
A student was asked to solve for √x = -1. Is the student correct?
√x = -1
(√x)² = (-1)²
x = 1
(a) Yes, because x = 1 is the only real solution.
(b) Yes, because x has infinitely many solutions.
(c) No, because x is a complex number.
(d) No, because there is no solution for x.
Write a conclusion based on your answer.
Answer:
D
Step-by-step explanation:
the end result of a radical can never be negative unless the negative sign shows outside of the radical
A person invests $3,500 in an account that earns 7.5% interest compounded continuously. What is the value of the investment after 4 years?
I think it's: 4,674.14$
Answer:
A = $4724.36
Step-by-step explanation:
P = $3500
r = 7.5% = 0.075
t = 4years
n = 365
[tex]A = P(1 + \frac{r}{n})^{nt}\\\\[/tex]
[tex]=3500(1 + \frac{0.075}{365})^{365 \times 4}\\\\=3500(1.00020547945)^{365\times4}\\\\= 3500 \times 1.34981720868\\\\= 4724.36023037\\\\= \$ 4724.36[/tex]
7. Find the length of X (in the picture) plssss I need help. (GIVING PPINTS AND BRAINLY)
Answer:
[tex] \frac{8}{5} = \frac{4}{x} \\ 8x = 20 \\ x = 2.5[/tex]
Answer:
here the resize factor is 5/8
so we need to calculate
x = 4 *5/8
= 20/8
= 2.5
I assume you get the basic idea from the other question you posted.
I need to find the equal expression to -m(2m+2n)+3mn+2m². Help please?
[tex]m(2m+2n)+3mn+2m^2\implies \stackrel{\textit{distributing}}{2m^2+2mn}+3mn+2m^2 \\\\\\ 2m^2+2m^2+2mn+3mn\implies \stackrel{\textit{adding like-terms}}{4m^2+5mn}[/tex]
Obiwan is standing at a distance of 1.5m from the base of a tree. From where he is standing, he can see the top of the tree. If the tree is 15m high and Obiwan is 1m tall, what is the angle of elevation of the top of the tree?
Answer:
∅ = 83.9º
Step-by-step explanation:
tan = opp/adj
opp = 15 - 1 = 14
tan∅ = 14/1.5
∅ = arctan 14/1.5
use calculator
∅ = 83.884496433714593º
Rounded
∅ = 83.9º
For the function f(x)=−7x^3−8x+2x^2, Step 1 of 2 : Find the slope of the tangent line at x=1.
Answer:
The slope of the tangent line at x = 1 is -25.
Step-by-step explanation:
We are given the function:
[tex]f(x)=-7x^3-8x+2x^2[/tex]
And we want to find the slope of the tangent line at x = 1.
The slope of the tangent line at a point for a function is given by its derivative. Find the derivative of the function:
[tex]f'(x)=-21x^2+4x-8[/tex]
Then the slope of the tangent line at x = 1 is:
[tex]f'(1)=-21(1)^2+4(1)-8=-25[/tex]
the equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?
Answer:
The radius is 10
Step-by-step explanation:
Given
[tex]x^2 + y^2 + 21 = 40 + 18y.[/tex]
Required
The radius
Rewrite as:
[tex]x^2 + y^2 - 18y = 40-21[/tex]
Subtract 81 from both sides
[tex]x^2 + y^2 - 18y +81= 40-21+81[/tex]
Expand
[tex]x^2 + y^2 - 9y - 9y +81= 40-21+81[/tex]
Factorize
[tex]x^2 + y( y- 9) - 9(y -9)= 40-21+81[/tex]
Factor out y - 9
[tex]x^2 + (y- 9) (y -9)= 40-21+81[/tex]
Express as squares
[tex]x^2 + (y- 9)^2= 100[/tex]
[tex]x^2 + (y- 9)= 10^2[/tex]
The equation of a circle is:
[tex](x - a)^2 + (y- b)= r^2[/tex]
By comparison:
[tex]r^2=10^2[/tex]
[tex]r = 10[/tex]
If you apply these changes to the linear parent function, f(x) = x, what is the
equation of the new function?
• Vertically compress by a factor of 7.
• Shift up 9 units.
O A. DY) = 7x+9
O B. g(x) = = x+9
O C. () = 7(x-9)
O D. g(x) = + (x+9)
Answer:
The equation of the new function is [tex]g(x) = 7x + 9[/tex]
Step-by-step explanation:
Vertically compress by a factor of 7.
Vertically compressing a function by a units is the same as:
[tex]g(x) = f(ax)[/tex]
In this question:
[tex]f(x) = x, a = 7[/tex]. So
[tex]g(x) = f(7x) = 7x[/tex]
Shift up 9 units.
Shifting a function up a units is the same thing as adding a to the function. In this case, [tex]a = 9[/tex], and then:
[tex]g(x) = 7x + 9[/tex]
The equation of the new function is [tex]g(x) = 7x + 9[/tex]
In this figure below, lines m and n are parallel: image above ^
HELPP PLS ASAP
Answer:
83 or a
Step-by-step explanation:
if angle 6 is 97 then the total would be 180 meaning that 83 would be the answer to 5s angle
"83 degrees" is correct.
On a line, it can be assumed that all the angles must add up to 180 degrees. If you have two angle on a line and don't know the value of one of them, you can subtract that angle from 180 to find the missing angle. Considering this, 180 - 97 = 83.
Please help I don't understand
Answer:
Angle a is not the same as angle y
Step-by-step explanation:
I think
If using the method of completing the square to solve the quadratic equation x^2+15x+21=0, which number would have to be added to "complete the square"?
Step-by-step explanation:
the answer is in the above image
Answer:
my answer is 225/5 sorry comments for wrong
pls answer i’ll give brainliest if it lets me
Answer:
32.25
Step-by-step explanation:
1 quart = 32 fluid ounces
12 months = 1 year
86 quarts/1 month = 1032 quarts/12 months
1032/32 = 32.25 fluid ounces
Use a calculator to find the mean of the data. {217, 253, 214, 247, 217, 253, 232, 246, 223, 227, 229, 247, 206, 241, 239, 223, 222, 216, 252, 209, 236, 256}
Answer:
[tex]\frac{5105}{22}[/tex]
Step-by-step explanation:
Used Python function to get all the numbers and add them, then I divided it by 22, which is the number of numbers in the array.
The mean of the data is 232.045.
To find the mean of the data.
What is mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations). Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).
Given that:
The data are:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
=5105 / 22 = 232.045
So, the mean of the data is 232.045.
Learn more about mean here:
https://brainly.com/question/24072290
#SPJ2
The option is missing:
A. 230.811
B. 231.045
C. 232.045
D. 232.811
7x_=8x7 Nonsense report
Answer:
hope it help ful ✓ ......What is the value of log Subscript 5 Baseline 125?
Answer:
[tex]log_5 \ 125 = 3[/tex]
Step-by-step explanation:
[tex]log_5 \ 125 = log_2 \ 5^3 = 3 \times log_5 \ 5 = 3 \times 1 = 3[/tex]
The value of [tex]$\log _{5} 125$[/tex] can be estimated utilizing the logarithm rule. The value of [tex]$\log _{5} 125$[/tex] exists 3.
What is a logarithm?The logarithm stands for the inverse function of exponentiation. In logarithm base must be raised to yield a given number for an exponent.
Given:
[tex]$\log _{5} 125$[/tex]
Estimate the value of the given logarithm, we get
[tex]$\log _{5} 125=\log _{5}(5)^{3}$[/tex]
[tex]$\log _{5} 125=3 \log _{5} 5$[/tex]
From logarithm rule [tex]$\log m^{n}=n \log m$[/tex], we get
[tex]$\log _{5} 125=3 \times 1$[/tex]
[tex]$\log _{5} 125=3$[/tex]
Therefore, the value of [tex]$\log _{5} 125$[/tex] is 3.
To learn more about logarithm
https://brainly.com/question/26240264
#SPJ2
Madge has cut out two triangular shapes from a block of wood, as shown below. Are the two shapes similar? Show your calculations.
Find the height of this triangle.
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x^2 + 1 = 4
x^2 = 3
[tex]\sqrt{3}[/tex]
the single discount of two successive discounts 10% and 5% is
Answer:
14.5%
Step-by-step explanation:
Use the number 100 as an example to find the single discount.
Take a 10% discount off of this:
100(0.9)
= 90
Take a 5% discount:
90(0.95)
= 85.5
So, after the successive discounts, $14.5 was discounted.
This means that the single discount is 14.5%.
So, the answer is 14.5%
what is the highest common multiple of 120 and 150
Answer:
30 I suppose
Step-by-step explanation: