if the angle of elevation of the sun is 40 degrees, and is decreasing 1/3 radians/hour how fast is the shadow of a 35m tall pole lengthening?
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]
Step-by-step explanation:
Let y = height of the pole = 35 m (constant)
x = length of the shadow
They are related as
[tex] \tan \theta = \frac{y}{x} [/tex]
or
[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]
Taking the time derivative of the above expression and keeping in mind that y is constant, we get
[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]
Before we plug in the numbers, let's convert the degree unit into radians:
[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]
Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is
[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]
or
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]
A local chess tournament gives medals for first, second, and third place. There are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament.
Which statements are true? Check all that apply.
Order matters in this scenario.
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Leasburg High is 0.0046.
The probability that all three winners are from Cassville High is 0.0549
Answer:
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Cassville High is 0.0549
Step-by-step explanation:
Since a local chess tournament gives medals for first, second, and third place, and there are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament, to determine which of the following statements are true, the following calculations must be performed:
A) There are 2,184 ways to select a first-place, second-place, and third-place winner.
5 + 3 + 6 = 14
14 x 13 x 12 = X
182 x 12 = X
2.184 = X
B) The probability that all three winners are from Midland High is 0.0275.
5/14 x 4/13 x 3/12 = X
0.02747 = X
C) The probability that all three winners are from Leasburg High is 0.0046.
3/14 x 2/13 x 1/12 = X
0.00274 = X
D) The probability that all three winners are from Cassville High is 0.0549
6/14 x 5/13 x 4/12 = X
0.0549 = X
Answer:
A, B, C, E
Step-by-step explanation:
Edg 2021
Branliest?
QUESTION 2
Simplify the following
a5×a7
Answer:
[tex]a^{12}[/tex]
Step-by-step explanation:
Identity Used : [tex]a^x \times a^y = a^{x+ y}[/tex]
[tex]a^5 \times a^7 = a^{5 + 7} = a^{12}[/tex]
MCR3U1 Culminating 2021.pdf
#7.
A colony of bacteria is introduced into a growth medium. Its initial population
size is 350 thousand. 12 hours later, the colony has grown to a size of
800 thousand. If its population size increases exponentially, determine:
(a)
the exponential growth model for the size of the population Alt), after
t hours.
(b)
the population size after (i) 8 hours and (ii) 24 hours.
(c)
the rate of increase in the population size as a %/hour
(d)
the doubling time of the bacteria population.
Answer:
(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is 607,325
(ii) The population after 24 hours is 1,828,643
(c) The rate of increase of the population as a percentage per hour is 7.132%
(d) The doubling time of the population is approximately, 10.06 hours
Step-by-step explanation:
(a) The initial population of the bacteria, y₁ = a = 350,000
The time the colony grows, t = 12 hours
The final population of bacteria in the colony, y₂ = 800,000
The exponential growth model, can be written as follows;
[tex]y = a \cdot (1 + r)^t[/tex]
Plugging in the values, we get;
[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]
Therefore;
(1 + r)¹² = 800,000/350,000 = 16/7
12·㏑(1 + r) = ㏑(16/7)
㏑(1 + r) = (㏑(16/7))/12
r = e^((㏑(16/7))/12) - 1 ≈ 0.07132
The model is therefore;
[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is given as follows;
y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82
By rounding down, we have;
The population after 8 hours, y = 607,325
(ii) The population after 24 hours is given as follows;
y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571
By rounding down, we have;
The population after 24 hours, y = 1,828,643
(c) The rate of increase of the population as a percentage per hour = r × 100
∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%
(d) The doubling time of the population is the time it takes the population to double, which is given as follows;
Initial population = y
Final population = 2·y
The doubling time of the population is therefore;
[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]
Therefore, we have;
2·y/y =2 = [tex](1 + 0.07132)^t[/tex]
t = ln2/(ln(1 + 0.07132)) ≈ 10.06
The doubling time of the population is approximately, 10.06 hours.
what is the value of b
Answer:
Step-by-step explanation:
b is an inscribed angle. The rule for this is that the measure of an inscribed angle is half the measure of the arc it intercepts. The arc it intercepts is 56 degrees, so the measure of angle b is half of that at 28
Enter the slope-intercept equation of the line that has slope 12 and yintercept (0, 3).
Answer:
y= 12x+3
Step-by-step explanation:
The slope-intercept equation is basically y=mx+b
m is the slope and b is the intercept.
Plug the numbers in for those 2 and there's your answer :)
Answer:
y = 12x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 12 and c = 3 , then
y = 12x + 3
Using the diagram below, which of the following parts of the triangles are
congruent?
Answer:
C.
Step-by-step explanation:
ACE is a straight line that connects to line AB and line DE.
AB & ED have same gradient which mean that it is parallel.
The parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
What is congruent triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the otherCongruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.How to solve this problem?The steps are as follow:
As ACE is a straight line which connects to line AB and DEAlso the line AB and ED are parallel because their gradient are sameSo from above mention two reasons we can say that their is congruence between angle A and angle ESo the parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
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If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?
Answer:
x - y = 25
Step-by-step explanation:
3x - 4y = 15
-2x + 3y = 10
Add the two equations together
3x - 4y = 15
-2x + 3y = 10
----------------------
x - y = 25
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]
>> 3x - 4y = 15
>> -2x + 3y = 10
Add the two equations together
>> 3x - 4y = 15
>> -2x + 3y = 10
----------------------
Hence, x - y = 25
The probability that a newborn baby at a certain hospital is male is 50%. What is the probability that exactly 2 out of 3 babies born in the hospital on any given day are male?
Answer:
50/50 bc you dont know until he/she is born
The requried probability that exactly 2 out of 3 babies born in the hospital on any given day are male is 0.375 or 37.5%.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
This is a binomial probability problem with n = 3 (three babies) and p = 0.5 (probability of a baby being male).
The probability of exactly 2 out of 3 babies being male can be calculated using the binomial probability formula:
[tex]P(X = 2) = (n choose X) * p^X * (1 - p)^{(n - X)}[/tex]
where "n choose X" is the binomial coefficient, equal to n! / (X! * (n - X)!) and X is the number of successes (in this case, 2).
Substituting the values, we get:
[tex]P(X = 2) = (3 choose 2) * 0.5^2 * (1 - 0.5)^{(3 - 2)}[/tex]
= 3 * 0.25 * 0.5
= 0.375
Therefore, the probability that exactly 2 out of 3 babies born in the hospital on any given day are male is 0.375 or 37.5%.
Learn more about probability here:
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helppp plzzzz i need this asap!!!!!! i need the domain and range
39.76÷7.94
use compatible numbers and estimate
Answer:
5
Step-by-step explanation:
As for estimation, you may round 39.76 to the whole number, resulting in 40.
7.94 to 8
40 / 8 = 5
5 is your answer for the result of estimation
Kendra is saving to buy a new computer write an expression to represent them out of money she will have if she has a dollar saved and adds D dollar per week for the next 12 weeks
In a game of chess, a player can either
win, draw or lose.
The probability that Vishi wins any
game of chess is 0.5
The probability that Vishi draws any
game of chess is 0.3
Vishi plays two games of chess.
Work out the probability that Vishi will
lose exactly one of the two games.
Pls answer fast
Answer:
3.4
Step-by-step explanation:
0.5x + 0.3=2
then I subtracted 0.3 from both sides which I got 1.7 then I divided by 0.5x and then I got 3.4
can someone please help for brainlest
Answer:
3:1
Step-by-step explanation:
It’s three times the original
for the following right triangle find the side length 19,12 x. Round the nearest hundredth
Answer:
Step-by-step explanation:
c^2 - a^2 = b^2
19^2 - 12^2 = b^2
361 - 144 = 217
[tex]\sqrt{217\\}[/tex] = 14.7309198627
Round to the nearest hundredth = 14.73
Hope this helps!
the volume of a cuboid is 480cm cube,it's breadth and height are 8cm are 6cm respectively find its length
Find the area of the polygon
Answer:
[tex]it \: is \: a \: polygon \: having \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ base = 5cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ height = 3cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ area \: of \: polygon \: = base \times height \\ \\ area \: of \: polygon \: = (5 \times 3)cm \\ \\ area \: of \: polygon = 15cm ^{2} [/tex]
how do you do this?
Step-by-step explanation: 6 22 22 51
one orange box is 10 the other box looks like 15
the scale factor is 15/10 or 1.5
the smaller triangle blue box is a 4
multiply 4 by the scale factor 1.5
4 × 1.5 = 6
Which of the following expressions is undefined
cot180°
sec0°
csc(-90°)
Answer:
Step-by-step explanation:
cot x = adjacent side / opposite side
So cot 180 = x / 0 which is undefined.
A total of 937 people attended the play.
Admission was $2.00 for adults and $0.75
for students. The total ticket sales
amounted to $1,109. How many students
and adults attended the school play?
Answer:
612 adults & 361 students
Step-by-step explanation:
Can someone help please ?!
Step-by-step explanation:
53 is the correct answer
!!URGENT PLEASE HELP!!
A line segment has endpoints A(-6, 1) and B(0, 7). When AB is reflected in the y-axis, triangle ABA’ is formed. Graph ABA’ , you will see and you will be able to prove it is a right triangle. Name the parts of the right triangle, identify the two legs and the hypotenuse. And, Explain how you would prove ABA' is a right triangle?
Answer:
im not sure i need points though
Step-by-step explanation:
The proof is given below
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. A right angled triangle is a triangle with one of the angles as 90 degreesHow to solve this problem?The steps are as follow:
Reflection about y-axisp(x,y) = p'(-x,y)
A(-6,1) = A'(6,1)
The longest side is AA' is the hypotenuseThe right angle of right triangle is opposite the hypotenuseAB and A'B are the two legs of triangleAB is opposite side
A'B is adjacent side
Length of AA' is 12 unitsThe vertical distance y=6ΔABC = ΔA'BC (both right angle)[tex]A'B=AB=\sqrt{6^{2}+6^{2} }=8.5[/tex]Sin∅=8.5/2∅ = 45° (Angle between AB and AA')Hence we can prove that triangle is right angle triangle
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Find the volume of the irregular
figure.
Answer:
59 cm^3
Step-by-step explanation:
You can split the shape into two rectangular prisms.
3*3*1=9
10*5*1=50
9+50=59
Can somebody pls help
Answer:
A, c, d
Step-by-step explanation:
Answer:
C & D
Step-by-step explanation:
In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.
w+L+w+L or w+w+L+L or 2w+2L
Hope this helps!
--Applepi101
how many tons is 9,000 lbs?
Answer:
9000 Pounds (lbs) = 4.017859 Tons (t)
1 lbs = 0.000446 t
1 t = 2,240 lbs
Step-by-step explanation:
Factor the common factor out of each expression: 30+6k+18k^5
WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing
Answer:
A.)
Step-by-step explanation:
A.)
Answer:
A :)
Step-by-step explanation:
Determine the vertex of the quadratic relation y= 4x2 + 32x – 11
Answer:
vertex = (- 4, - 75 )
Step-by-step explanation:
Given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² + 32x - 11 ← is in standard form
with a = 4, b = 32 , then
x = - [tex]\frac{32}{8}[/tex] = - 4
Substitute x = - 4 into the equation for corresponding y- coordinate
y = 4(- 4)² + 32(- 4) - 11
= 4(16) - 128 - 11
= 64 - 139
= - 75
vertex = (- 4, - 75 )
Which line of best fit is the best choice for the data given below?
Answer:
B
Step-by-step explanation:
Points need to be above and below a line of best fit.
4. There are 10 people in a room. If everyone high fives everyone else exactly once, how many hig flves took place in the room?
Answer:
45
Step-by-step explanation:
Let's do it for smaller numbers first.
0 people -> 0 high fives
1 people -> 0 high fives
2 people -> 1 high fives
3 people -> person 1 high fives 2 then 3
And person 2 high fives 3
->2+1= 3 high fives
4 people -> person 1 high fives 2,3, then 4
And person 2 high fives 3 then 4
And 3 high fives 4
->3+2+1=6
5 people -> person 1 high fives 2,3,4, then 5
And person 2 high fives 3,4, 5
And 3 high fives 4,5
And 4 high fives 5
-> 4+3+2+1=10
So for n people there would be (n-1)+(n-2)+....+3+2+1 high fives or (n-1)n/2 people.
Test:
3 people -> (3-1)3/2=(2)3/2=3
4 people -> (4-1)4/2=(3)4/2=6
5 people -> (5-1)5/2=(4)5/2=10
10 people-> (10-1)10/2=(9)10/2=90/2=45
or you could do 9+8+7+6+5+4+3+2+1 which also gives 45.
The other person has a great answer. Here's another approach.
Let's say we're selecting 2 people to fill slots A and B.
Slot A has 10 choices and slot B has 9 choices (since we can't pick the same person again to fill both slots simultaneously).
We have 10*9 = 90 ways to do this if order mattered.
However, we don't care about the order so we actually have 90/2 = 45 ways
---------------------------
Put another way: we can form a table that has 10 rows and 10 columns.
This table has 10*10 = 100 cells inside it.
Cross off the main diagonal that runs from the upper left corner to the bottom right corner. Any of these cells represent a certain person handshaking with themself, which we don't consider.
We cross of 10 items along this diagonal so we have 100-10 = 90 cells leftover.
Now consider that person A shaking with B can be notated as AB. This is identical to BA because the order doesn't matter. So we have twice as many handshakes counted.
That's why we divide by 2 to go from 90 to 90/2 = 45
-----------------------------
Another way to find the answer is to use the nCr combination formula with n = 10 and r = 2.
Yet another way to find the answer is look at Pascal's triangle. Find the row that has 1,10,45... in it at the start. These values correspond to r = 0, 1 and 2 respectively. We can see that 45 is when r = 2, which means we have 2 people shaking hands and there are 45 ways to have ten people shake hands.
So there are many approaches you can take with this problem.
