Answers
Answer:
ST is longest
Step-by-step explanation:
Theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter sideThe values of the angles are:
∠S= 50°, ∠T= 60°,∠R= 180°- (50°+60°)= 180° - 110° = 70°Since ∠R is the largest angle, the side ST is longest
Related Questions
Consider the following function
Answers
Answer:
Step-by-step explanation:
Everything to know about a and b!
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0, −5)
Focus: (0, [tex]-\frac{19}{4\\}[/tex]−)
Axis of Symmetry: x = 0
Directrix: y = [tex]-\frac{21}{4}[/tex]
For Part b
Table:
x | y
______
−2 −1
−1 −4
0 −5
1 −4
2 −1
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $
(Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $
(Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answers
Answer:
a) 100 $
b) 566,66 $
c) 566,66 $
Step-by-step explanation:
Mak 85,000 $ /per year, means 85000/12 per month that is 7083,33
8% of 7083,33 is 566,66 $ . Then
a) 200 < 566,33 then my company will contribute with 0,5*200 = 100 $
b) If I contribute with 830 $ ( 830 > 566,66 ) then my company will contribute with 566,66 $ the biggest amount
c) 566,66 s the maximm amount of money
There are 12 teams, each representing a different country, in a women’s Olympic basketball tournament. In how many ways is it possible for the gold, silver, and bronze medals to be awarded? Use the formula for permutations to find your answer.
Answers
Answer:
1320 ways
Step-by-step explanation:
To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!
12! is the same as 12x11x10x9x8... etc
But in this problem, we are only looking for the top 3.
We can set up a formula
[tex]\frac{n!}{(n-r)!}[/tex]
N is the number of options that are available and r represents the amount we are choosing
In this case, we have 12 teams so n=12
We are looking for the top 3 so r=3
[tex]\frac{12!}{(12-3)!}[/tex]
[tex]\frac{12!}{9!}[/tex]
We expand the equation and cancel out
[tex]\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}[/tex]
Notice how both sides can cancel out every number 9 and below
That leaves us with 12x11x10
1320 ways
The possible ways for the gold, silver, and bronze medals to be awarded is 1320
What is permutation?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.
We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,
Using the concept of permutation, to find the number of ways
ⁿPₓ = n!/(n-x)!
= 12! / (12-3)!
= 12! / 9!
= 1320
Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320
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The state of Wisconsin would like to understand the fraction of its adult residents that consumed alcohol in the last year, specifically if the rate is different from the national rate of 70%. To help them answer this question, they conduct a random sample of 852 residents and ask them about their alcohol consumption.
Answers
Answer:
The answer is below
Step-by-step explanation:
What we should do is the following:
First, from the random sample of 852 researchers, it is necessary to obtain the number of adult residents who consumed alcohol in the past year.
After the above, we must calculate the proportion of adult residents who consumed alcohol in the last year by dividing the number of adult residents who consumed alcohol in the last year by 852.
After this, we must compare if the proportion is exactly 70% or different from it.
We have the following hypotheses:
Null Hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is exactly 70%
Alternative hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is not equal to 70%
Please help!!!!! I'm on a timerrrrrrrrrrrrrr!
Answers
Step-by-step explanation:
6
[tex]6 \sqrt{6} [/tex]
Answer:
6√6is the exact answer
Suppose that E(θˆ1) = E(θˆ2) = θ, V(θˆ 1) = σ2 1 , and V(θˆ2) = σ2 2 . Consider the estimator θˆ 3 = aθˆ 1 + (1 − a)θˆ 2. a Show that θˆ 3 is an unbiased estimator for θ. b If θˆ1 and θˆ2 are independent, how should the constant a be chosen in order to minimize the variance of θˆ3?
Answers
Answer:
Step-by-step explanation:
Given that:
[tex]E( \hat \theta _1) = \theta \ \ \ \ E( \hat \theta _2) = \theta \ \ \ \ V( \hat \theta _1) = \sigma_1^2 \ \ \ \ V(\hat \theta_2) = \sigma_2^2[/tex]
If we are to consider the estimator [tex]\hat \theta _3 = a \hat \theta_1 + (1-a) \hat \theta_2[/tex]
a. Then, for [tex]\hat \theta_3[/tex] to be an unbiased estimator ; Then:
[tex]E ( \hat \theta_3) = E ( a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]
[tex]E ( \hat \theta_3) = aE ( \theta_1) + (1-a) E ( \hat \theta_2)[/tex]
[tex]E ( \hat \theta_3) = a \theta + (1-a) \theta = \theta[/tex]
b) If [tex]\hat \theta _1 \ \ and \ \ \hat \theta_2[/tex] are independent
[tex]V(\hat \theta _3) = V (a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]
[tex]V(\hat \theta _3) = a ^2 V ( \hat \theta_1) + (1-a)^2 V ( \hat \theta_2)[/tex]
Thus; in order to minimize the variance of [tex]\hat \theta_3[/tex] ; then constant a can be determined as :
[tex]V( \hat \theta_3) = a^2 \sigma_1^2 + (1-a)^2 \sigma^2_2[/tex]
Using differentiation:
[tex]\dfrac{d}{da}(V \ \hat \theta_3) = 0 \implies 2a \ \sigma_1^2 + 2(1-a)(-1) \sigma_2^2 = 0[/tex]
⇒
[tex]a (\sigma_1^2 + \sigma_2^2) = \sigma^2_2[/tex]
[tex]\hat a = \dfrac{\sigma^2_2}{\sigma^2_1+\sigma^2_2}[/tex]
This implies that
[tex]\dfrac{d}{da}(V \ \hat \theta_3)|_{a = \hat a} = 2 \ \sigma_1^2 + 2 \ \sigma_2^2 > 0[/tex]
So, [tex]V( \hat \theta_3)[/tex] is minimum when [tex]\hat a = \dfrac{\sigma_2^2}{\sigma_1^2+\sigma_2^2}[/tex]
As such; [tex]a = \dfrac{1}{2}[/tex] if [tex]\sigma_1^2 \ \ = \ \ \sigma_2^2[/tex]
Please help I’m struggling:(
Jose's taxi charges $5 plus $0.30 per mile for fare in a city. Kathy's taxi charges $8
plus $0.20 per mile for fare in the city. At what distance would the charges for the
two taxis be the same?
Answers
Answer:
30 miles
Step-by-step explanation:
Jose's charges are ...
j = 5 + 0.30m . . . . . for m miles
Kathy's charges are ...
k = 8 +0.20m . . . . . for m miles
The charges are the same when ...
j = k
5 +0.30m = 8 + 0.20m
0.30m = 3 + 0.20m . . . . subtract 5
0.10m = 3 . . . . . . . . . . . . subtract 0.20m
m = 30 . . . . . . . . . . . . . . . multiply by 10
The charges will be the same for a distance of 30 miles.
John comes across a recent survey and wants to gauge the strength of the results.
Which of the following would best reflect upon the researcher.
O a margin of error of +/- 10%
O a margin of error of +/- 3%
O a margin of error of +/- 98%
O a margin of error of +/-8%
Answers
Answer:
A margin of error of +/- 3%
Step-by-step explanation:
Strenght of surveys:
The lesser the margin of error, the more precise, stronger, the confidence interval is.
The margin of error depends of the number of people surveyed. The more people are surveyed, lower the margin of error is, giving a stronger interval.
In this question:
We want the smaller margin of error, which is given by:
A margin of error of +/- 3%
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
Step-by-step explanation:
Step1 : Verify Sn is valid for n = 1
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
&
given circleR, how is it known that QS = YT?
(idk the answers i guessed)
Answers
Answer:
Step-by-step explanation:
In an isosceles triangle, the base angles are equal. This also means that the length of two sides of the triangle are equal. Looking at triangle ABC, to prove that it is an isosceles triangle, then
Angle CAB = angle CBA
For the second question, to determine how it is known that QS is equivalent to YT, we would recall that the diameter of a circle passes through the center and from one side of the circle to the other side. Assuming R is the center of the circle, then QS and YT are the diameters of the circle and also the diagonals of the rectangle. Thus, the correct option is
The diameters act as diagonals
10) BRAINLIEST & 10+ Points!
Answers
Answer:
20Solution,
Complement of 70°
=90°-70°
=20°
hope this helps...
Good luck on your assignment..
Answer:
20°
Step-by-step explanation:
Complement of 70° is 90°-70°= 20°
To determine the complement, subtract the given angle from 90.
whats the answer help !!!!
Answers
Answer: B) 110
Step-by-step explanation:
It is stated that DE and XY are parallel.
Therefore, 110° and x° are Corresponding Angles, which means they are congruent (equal).
110° = x°
110 = x
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface that lies above the disk x2 + y2 ≤ 81
Answers
Answer:
A(s) = 255.8857
Step-by-step explanation:
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.
Given that:
[tex]Z = e^{-x^2-y^2}[/tex]
By applying rule; the partial derivatives with respect to x and y
[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]
[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]
The integral over the general region D with respect to x and y is :
[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]
By relating the equation to cylindrical coordinates
[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]
The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9
[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]
[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]
Using integral calculator to estimate the integral,we have:
A(s) = 255.8857
The five-number summary for the number of teams in each of "Brad's fantasy football" leagues is shown in the following table. \text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 444 777 101010 141414 181818 The five-number summary suggests that about 50\%50%50, percent of Brad's fantasy football leagues have fewer than how many teams?
Answers
Answer:
(B) 25%
Step-by-step explanation:
Eye Color Each of two parents has the genotype brown>blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is more complicated than that.) a. List the different possible outcomes. Assume that these outcomes are equally likely. b. What is the probability that a child of these parents will have the blue>blue genotype? c. What is the probability that the child will have brown eyes?
Answers
Answer:
A) Brown-Brown ,Brown-Blue, Blue-Brown, Blue-Blue B) 1/4 =0,25 C)3/4=0,75
Step-by-step explanation:
Lets mother's "BROWN" is "BROWN-M",
mother's "BLUE" is " BLUE-M"
Lets father's "BROWN" is "BROWN-F" and
father's "BLUE " is "BLUE-F"
The kid can have the genotype as follows (list of possible outcomes) :
1. BROWN-M>BROWN-F ( received BROWN as from mother as from father)
2. BROWN-M>BLUE-F ( Received BROWN from mother and BLUE from father)
3. BLUE-M>BROWN-F ( Received BLUE from mother and Brown from father)
4. BLUE-M>BLUE-F ( Received BLUE as from mother as from father)
b) As we can see in a) only 1 outcome from 4 is BLUE-BLUE. So the probability of BLUE-BLUE genotype is
P(BLUE>BLUE)=1/4=0.25
c) As we know that if the child has at least one brown allele, that color will dominate and the eyes will be brown.
It means that outcomes BROWN-BROWN, BROWN-BLUE and BLUE-BROWN determine brown color of eye. So the number of these outcomes is 3. Total amount of outcomes is 4.
So probability that eyes are brown is P(Brown eyes)=3/4 =0.75
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally. Define the following in terms of the study. Give examples where appropriate.
The sample:
a. The sample is all of the people taking skiing or snowboarding lessons.
b. The sample is all of the children taking skiing or snowboarding lessons.
c. The sample is a group of the people taking skiing or snowboarding lessons.
d. The sample is a group of the children taking skiing or snowboarding lessons.
Answers
Answer:
Option D
Step-by-step explanation:
A sample can be described as a small part or potion that is intended to describe what the whole population is like.
In this study, the sample is a group of the children taking skiing or snowboarding lessons: this group is taken out of the whole population of children taking skiing or snowboarding lessons.
Find the amount in an account where $500 is invested at 2.5% compounded continuously for period of 10 years
Answers
Hi
500 *1.025^10 ≈ 640.04
In the parallelogram below, solve for x and y. (Give your answer as a decimal, when necessary)
Answers
Answer: x = 15, y = 12.5
Step-by-step explanation:
The sum of the three angle measures of a triangle equals 180ᴼ
Since these triangles are vertical, the measures are congruent.
45 + 60 = 105
180 - 105 = 75
So now we know that 5x = 75ᴼ and 6y = 75ᴼ.
To find x, divide 75 by 5
75 / 5 = 15
x = 15
To find y, divide 75 by 6
75 / 6 = 12.5
y = 12.5
Which phrases can be used to represent the inequality 6.5 x + 1.5 less-than-or-equal-to 21? Select two options. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and a number, when increased by 1.5, is at most 21. The sum of 1.5 and the product of 6.5 and a number is at least 21.
Answers
Answer:
The option with “at most” and “no more than”
Step-by-step explanation:
These two phrases mean “greater than or equal to”
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
What is inequality ?In which mathematical expression both sides are not equal, i.e. one side is greater or less or greater equal or less equal than other side, is called inequality.
Example : 4x+5>3x-2
What are the required phrases ?The given inequality is [tex]6.5x+1.5\leq 21[/tex]
Firstly, The sum of 1.5 and the product of 6.5 and a number (say x) is 6.5x+1.5, which is no greater than 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Again, The product of 6.5 and a number (say x) is 6.5x, when increased by 1.5, it will be 6.5x+1.5 which is at most 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Hence, the correct options are,
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
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Please help!!! I'm really confused.
Answers
The value of root 10 is between 3 and 3.5
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. y=(3x+4)(-2x-3)
Answers
Answer:
[tex] y = -6x^2 -17 x -12[/tex]
And since the higher exponent for the x term is 2 we can classify the equation as quadratic
Quadratic term: -6
Linear term: -17
Constant term: -12
Step-by-step explanation:
For this problem we have the following equation:
[tex] y = (3x+4)(-2x-3)[/tex]
And we can distribute the terms and we got:
[tex] y = -6x^2 -9x -8x -12[/tex]
And solving we got:
[tex] y = -6x^2 -17 x -12[/tex]
And since the higher exponent for the x term is 2 we can classify the equation as quadratic
Quadratic term: -6
Linear term: -17
Constant term: -12
Which fraction listed is between 4/7 and 6/7
Answers
Answer:
5/7
Step-by-step explanation:
4/7 < x < 6/7
Let x be the middle value of 4/7 and 6/7.
(4/7 + 6/7)/2
(10/7)/2
10/14 = 5/7
4/7 < 5/7 < 6/7
What is the Circumference of Aand B?
Answers
Answer:
4
Step-by-step explanation:
C1= 2π*8= 16π
C2= 2π*2= 4π
C1/C2= 16π/4π= 4
Answer:
4
Step-by-step explanation:
The circumference is pi*d.
pi*16/pi*4
Cancel pi.
16/4
= 4
Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
Answers
Answer:
x = -1.796, 7.796
Step-by-step explanation:
3x² - 18x + 5 = 47
3x² - 18x - 42 = 0
use quadratic equation
x = -1.796, 7.796
Answer:
x = 3 +/- √23
Step-by-step explanation:
got it right on edg
The vector matrix[ 27 ]is dilated by a factor of 1.5 and then reflected across the X axis if the resulting matrix is a B then a equals an VE
Answers
Correct question:
The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???
Answer:
a = 3
b = 10.5
Step-by-step explanation:
Given:
Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]
Dilation factor = 1.5
Since the vector matrix is dilated by 1.5, we have:
[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]
= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]
Here, we are told the vector is reflected on the x axis.
Therefore,
a = 3
b = 10.5
Answer:
a = 3
b = -10.5
Step-by-step explanation:
got a 100% on PLATO
The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution of the scores is roughly bell shaped. to find the percentage of scores that lie between 60 and 80.
Answers
Answer:
47.5%.
Step-by-step explanation:
60 is 2 standard deviations below the mean.
According to the emperical rule, there is approximately 90% of normally distributed data within 2 standard deviations of the mean. Your interval is half of that because it is the data between the mean and two standard deviations
below the mean. therefore, the answer is 47.5%.
The percentage of scores that lie between 60 and 80 is 47.75%
Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation[/tex]
Given that:
μ = 80, σ = 10
[tex]For\ x=60:\\\\z=\frac{60-80}{10} =-2\\\\For\ x=80:\\\\z=\frac{80-80}{10} =0[/tex]
P(60 < x < 80) = P(-2 < z < 0) = P(z < 0) - P(z < -2) = 0.5 - 0.0228 = 47.75%
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The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)
Answers
Answer:
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Step-by-step explanation:
The equation of the curvature is:
[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]
The parametric componentes of the curve are:
[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]
The first and second derivative associated to each component are determined by differentiation rules:
First derivative
[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]
[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]
Second derivative
[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]
[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]
[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]
[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]
Now, each term is replaced in the the curvature equation:
[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]
And the resulting expression is simplified by algebraic and trigonometric means:
[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]
[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]
[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]
[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]
[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Please answer this question in two minutes
Answers
Answer:
W = (18,0)
Step-by-step explanation:
I found the slope of the line from point M to point V. The slope is -3.875. I continued this slope starting with point V to find the coordinates of point W. The coordinates of point W are (18,0).
I graphed the coordinates and the line of VW on the graph below.
A bus can carry a maximum of 60 passengers. Each row accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry maximum number of passengers. Determine number of rows in the bus and no. Of passengers per row
Answers
Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Find the magnitude of side R. Show work please!
Answers
Square root of 472.25
= 21.73131....
Answer:
21.7 metres (assuming the triangle is a right triangle)
Step-by-step explanation:
Assuming this is a right triangle, we can simply use the Pythagorean Theorem, which states that in a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, a = 20, b = 8.5, and R = c. Plug these in:
a² + b² = c²
20² + 8.5² = R²
400 + 72.25 = R²
472.25 = R²
R = √472.25 ≈ 21.7 m
Thus, R is about 21.7 metres.
~ an aesthetics lover