Answer:
The differential equation is [tex]\frac{dR}{dt} = -kR[/tex]
Step-by-step explanation:
Differential equation for the rate of change in radiation level:
Radiation level is R.
Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:
[tex]\frac{dR}{dt}[/tex]
After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.
Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:
[tex]\frac{dR}{dt} = -kR[/tex]
Given that cos A 165 and sin B = 72, and that angles A and B are both in
Quadrant I, find the exact value of sin(A + B), in simplest radical form.
Given:
[tex]\cos A=\dfrac{4}{\sqrt{65}}[/tex]
[tex]\sin B=\dfrac{1}{\sqrt{2}}[/tex]
A and B both lies in I quadrant.
To find:
The value of [tex]\sin (A+B)[/tex].
Solution:
We know that, all trigonometric ratios are positive in first quadrant.
[tex]sin^2\theta +\cos^2\theta =1[/tex]
Using this we get
[tex]\sin^2A +\cos^2A =1[/tex]
[tex]\sin^2A +\left(\dfrac{4}{\sqrt{65}}\right)^2 =1[/tex]
[tex]\sin^2A +\dfrac{16}{65}=1[/tex]
[tex]\sin^2A =1-\dfrac{16}{65}[/tex]
Taking square root on both sides, we get
[tex]\sin A =\sqrt{\dfrac{65-16}{65}}[/tex] [Only positive because A lies in I quadrant]
[tex]\sin A =\sqrt{\dfrac{49}{65}}[/tex]
[tex]\sin A =\dfrac{7}{\sqrt{65}}[/tex]
Similarly,
[tex]\sin^2B +\cos^2B =1[/tex]
[tex]\left(\dfrac{1}{\sqrt{2}}\right)^2 +\cos^2B =1[/tex]
[tex]\dfrac{1}{2}+\cos^2B =1[/tex]
[tex]\cos^2B =1-\dfrac{1}{2}[/tex]
Taking square root on both sides, we get
[tex]\cos B =\sqrt{\dfrac{2-1}{2}}[/tex] [Only positive because B lies in I quadrant]
[tex]\cos B =\sqrt{\dfrac{1}{2}}[/tex]
[tex]\cos B =\dfrac{1}{\sqrt{2}}[/tex]
Now,
[tex]\sin (A+B)=\sin A\cos B+\cos A\sin B[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}+\dfrac{4}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{130}}+\dfrac{4}{\sqrt{130}}[/tex]
[tex]\sin (A+B)=\dfrac{11}{\sqrt{130}}[/tex]
Therefore, the exact value of [tex]\sin (A+B)[/tex] is [tex]\dfrac{11}{\sqrt{130}}[/tex].
What is cot(A)?
A. -3 sqrt 7/7 correct
Step-by-step explanation:
[tex]to \: help \: you \\ \cot(A) = { (\tan(A)) }^{ - 1} = \frac{ \cos(A) }{ \sin(A) } \\ or : \\ \cot(A) = \sqrt{(1 + {( \tan(A) )}^{2} } [/tex]
Answer:
A is correct :)
Step-by-step explanation:
edge 2021
thank you! have a great day
Two rectangular prisms have the same volume.the first prism has a length of 10 meters a width of 6 meters and a height of 2 meters. The second prism has a length of 6 meters and a width of 4 meters
Answer:
height of second rectangular prism is 5 meters
Step-by-step explanation:
Please quickly help me with this question please please please please please I’m beggig
Answer:
D: Point A is 1 unit to the right of the origin and point B is 3 units to the right of the origin.
Step-by-step explanation:
The coordinate (1, 3) is in quadrant 1 with a positive y, moving the point up, and a positive x, moving the point right. Because the x is 1, the point moves 1 unit right from the origin.
The coordinate (3, 1) is also in quadrant 1 with a positive y and x, but this time the x is 3, moving the point 3 units right from the origin.
Determine the amplitude or period as requested . Amplitude of y = - 1/5 * sin x a - 1/5 1/5 b 5 d. pi/5
Answer:
The amplitude is 1/5
Step-by-step explanation:
Given
[tex]y = -\frac{1}{5}\sin(x)[/tex]
Required
Determine the amplitude
The general cosine function is:
[tex]y = A\sin(k(x + c)) +d[/tex]
Where
[tex]Amplitude = |A|[/tex]
Compare [tex]y = A\sin(k(x + c)) +d[/tex] and [tex]y = -\frac{1}{5}\sin(x)[/tex]
[tex]A = -\frac{1}{5}[/tex]
So:
[tex]Amplitude = |-\frac{1}{5}|[/tex]
[tex]Amplitude = \frac{1}{5}[/tex]
A cube with sides that are 2 cm has a mass of 48 g and its density would be
___________ g/cm3.
Answer:
6g/cm^3
Step-by-step explanation:
The density of the cube would be 6 grams/cm^3. I got this answer by first finding the volume of the cube, 2^3 which gives me 8 cm as the initial volume of the cube. Then, the 48 grams of mass the cube has allows me to divide 48 / 8 which gave me 6. And 6 would be the density of the cube in grams.
Answer: 6g/cm^3
Hope this helps!
Answer:
p = 6 g/cm³
Step-by-step explanation:
Given: cube sides= 2 cm and 48 g
To find: The cube's density
Formula: [tex]{p} \frac{m}{V}[/tex]
Solution: Measure the height, width, and depth of the shipment in inches.
Multiply the three measurements (height x width x depth).
Divide the total cubic inches by 1,728 (the number of cubic inches in a cubic foot).
Divide the weight (in pounds) of the shipment by the total cubic feet.
p = density
m = mass
V = volume
She has 12 watermelons, 30 pears, and 42 apples
For each basket Kerra makes they must have the same number of fruit.
She must use all the fruit.
What is the greatest number of baskets that Kerra can make?
Find the length of the cable in the diagram below.
Answer:
13.4
Step-by-step explanation:
it is A square +b square =c square which is just 12×12=144 + 6×6=36 and then add them together which is 180, then just square root 180 can do it for every type of question like that and always remember the longest side is c, and the other two it doesn't matter which is A or B.
Which phrase describes the shape of the data?
.
.
.
12
13
14
15
10
17
18
A. Symmetric, not bell-shaped
B. Not symmetric, bell-shaped
C. Not symmetric, not bell-shaped
D. Symmetric bell-shaped
Answer:
C. Not symmetric; not bell-shaped.
Step-by-step explanation:
In a symmetric data distribution, the shape on the left side is almost the same as the shape on the right side of the middle. In this type of data distribution, if different measure of centers are calculated (mean, median, and mode), they will have a similar figures that are close together. Symmetric distributions are bell-shaped.
On the other hand, if the data distribution is not symetric, it means the left and the right side of the distribution are not equal and do not have the same shape.
The data in the dot plot above is considered as NOT SYMMETRIC. Also, it is not bell-shaped.
Answer:
c
Step-by-step explanation:
Find the value of x in the triangle shown below.
a. x=80
b. x=48
c. x= 32
d. x=12
h.c gjsussisuse udrih eieeiee Getty e
Please help. I NEED GOOD GRADES
Answer:
The circle should be open and the arrow should go the other way.
hey guys i'm having a rough night and i can't figure out my homework rn i'm just too stress please help
Answer:
3a) 54/99
3b) 257/999
Hope this'll help you!
Please help, I will give brainliest!!!
The table models the flight of the projectile from Part A
Which of these statements is true?
A) h(4) < h(20)
B) The flight is symmetric about the line t=10
C) The projectile will hit the ground at some value of t less than 24.
D) If 0<a<12, then h(12-a) = h(12+a).
If 0 < a < 12, then h(12 – a) = h(12 + a) is true. Then the correct option is D.
What is a projectile motion?When a body is thrown in the air at an angle, then the term is known as projectile motion.
The table is given in the question.
A) h(4) < h(20), this statement is incorrect, because the h(4) = h(20).
B) The flight is symmetric about the line t = 10, this statement is incorrect, because symmetric about t = 12.
C) The projectile will hit the ground at some value of t less than 24. This is incorrect, because t > 24.
D) If 0 < a < 12, then h(12 - a) = h(12 + a). This statement is correct.
Then the correct option is D.
More about the projectile motion link is given below.
https://brainly.com/question/11049671
#SPJ1
For every 3 boys in a class, there are 2 girls.
If there are 20 children in the class, how many girls are in there?
The distance by road from town A to town B is 242km.
What is 50% of that distance? A484 b 121 c 242 d
13
Answer: Option b 121km
50% means half, so the half of 242km is 121km, so option B 121 is correct.
Step-by-step explanation:
242/2=121
Have a nice day!
and can I maybe have brainliest? Thanks!
Answer:
Step-by-step explanation:
36 - 4
Step-by-step explanation:
(6x - 2)(6x + 2)
= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)
= 36 - 12x + 12x - 4
= 36 - 4
You withdrew $36.25 from your checking account. Now your balance is −$14.75. Write and solve an equation to find the amount of money in your account before you withdrew the money?
Answer:
SIMPLE, −$14.75 + $36.25 = $21.50
Step-by-step explanation:
TO CHECK OURSELVES:
21.50 - 36.25 = -14.75
YOUR WELCOME
1-4: Find the measures of central tendency, then determine the range of the data.
Daily High Temperatures (°F) for a week: 68 70 67 68 75 75 74 (1 pt each)
1. Mean:
2. Median:
3. Mode(s):
4. Range:
Answer:
Step-by-step explanation:
1=71
2=70
3= 68 and 75, they both appear twice
4= 8
if 16c 1 gal then 1 1/4 gal __= c
Answer:
20 cups
Step-by-step explanation:
16 x 1.25 = 20
Answer:
11/4 c = 44 gal
I hope it's helps you
You own a truck that has a trailer in the shape of a rectangular prism. It has a height of 15 m and a length of 40m, and a width of 10 m. If you wish to fill this trailer with 5m x 5m x 5m cubic boxes, how many boxes will fit into
the trailer
Answer:
48 boxes
Explanation:
First, find the volume of the rectangular prism (l*w*h) to find out how much it can hold.
15*40*10= 6,000
Then, find the volume of the cubic boxes (l*w*h) to find how much space each of them take up.
5*5*5= 125
Finally, divide the rectangular prism's volume by the boxes' to find out how many can fit inside.
6,000/125= 48 boxes
Find the value of x in the triangle shown below
a.x=28
b.x=56
c.x=28
d.x=20
Answer:
D.
Step-by-step explanation:
Answer:
[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]
by using Pythagoras law:
h²=p²+b²
x²=16²+12²
x=√400
x=20 units.
What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answer:
Step-by-step explanation:
i think you forgot to link or import the question
You need to establish _____ for how to judge a concept.
Answers
Questions
Points
Criteria
Answer:
Criteria.
Step-by-step explanation:
A series of criteria is a set of parameters established by whoever seeks to interpret a certain information or quantity of concepts, by means of which a set of interpretive rules is established that should be equal to all the concepts to be analyzed. Thus, the criteria allow a set of data to be analyzed under the same parameters or information processing requirements.
PLS HELLP PLS PLS
Aarons bedroom measures. feet by 14 feet by 8 feet. how many cubic feet of space does the room contain? round ur answer to the nearest hundredth
Answer:
it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt
Step-by-step explanation:
How much water will be needed to completely fill a rectangular tank that has a length of 3 meters a width of 3 meters
and a height of 18 meters?
(A) 162 cubic meters
(B) 24 cubic meters
(C) 324 cubic meters
(D) 108 cubic meters
Answer:
A
Step-by-step explanation:
because when you multiply 3x3 (the base) times 18(the height) you get= 162
In Mr. Thompson's first period class, there are 6 students with blue eyes, 8 students with brown eyes,
5 students with grey eyes, and 1 student with hazel eyes. If Mr. Thompson selects one student
randomly, what color eyes is the student most likely to have?
Answer:
blue
Step-by-step explanation:
There the most common eyes in the class?
Answer:the student would most likely have blue eyes
Step-by-step explanation:
8/20
6/20
5/20
1/20
The scatter plot shows the number of hours worked and money spent on entertainment by each of 24 students. Also shown is the line of best fit for the data. Fill in the blanks below.
The given scatter plot has a positive correlation.
Given that, the scatter plot shows the number of hours worked and money spent on entertainment by every 24 students.
What are scatter plots?A scatter plot is a means to represent data in a graphical format. A simple scatter plot makes use of the coordinate axes to plot the points, based on their values. The following scatter plot excel data for age (of the child in years) and height (of the child in feet) can be represented as a scatter plot.
A positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction.
The blanks for the given questions are filled below:
a) increase
b) strong positive
c) $22.50
Therefore, the given scatter plot has a positive correlation.
To learn more about the scatter plot visit:
https://brainly.com/question/13984412.
#SPJ2
Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game
Answer:
$32.40
Step-by-step explanation:
45% = 0.45
72(0.45) = 32.4
Based on the amount Kristian had and the percentage spent on the game, the price of the game is $32.40.
What is the Price of the Game?The price of the game can be found as:
= Amount Kristian has x Percentage spent on game
Solving gives:
= 45% x 72
= $32.40
In conclusion, the price of the game is $32.40.
Find out more about percentages at https://brainly.com/question/11570843
What is the value of 12(x + 5)?
Answer:
12(x+5)=
12x+60=
12x÷12 & 60÷12
x=5
Find the distance between the two points. (2, 4), (7, 2)
Answer:
5.38516480 or √ 29
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
5.385165 or sqrt 29
Step-by-step explanation:
d = distance
d= sqrt (7-2)^2+(2-4)^2
and when simplified fully you get
sqrt or 5.385165
7 1/2 x 4 1/3 x 3 3/5
Answer:
answer: 117
Hope this helps!
Answer:
117
Step-by-step explanation:
Convert mixed numbers to improper fractions:
7 1/2 = 15/2
4 1/3 = 13/3
3 3/5 = 18/5
15/2 x 13/3 x 18/5
Multiply and cross-cancel:
18/2 x 13/1
Multiply again:
117/1 = 117