Answer:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
Step-by-step explanation:
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Let θ be the angle of elevation of the line of sight from the horizontal. Since the hot air balloon is rising at a speed of 100 m/min, its vertical distance in time, t is d = vt = 100t.
Since the point of the observer is 200 m away( the horizontal distance), then tanθ = vertical rise/horizontal distance = 100t/200 = t/2
tanθ = t/2
To find the rate of change of the angle of elevation, we differentiate with respect to t.
So, dtanθ/dt = d(t/2)/dt
sec²θdθ/dt = 1/2
dθ/dt = 1/(2sec²θ)
At 600 m high, tanθ = vertical rise/horizontal distance = 600 m/200 m = 3
Given that tan²θ + 1 = sec²θ
dθ/dt = 1/(2sec²θ)
dθ/dt = 1/(2[tan²θ + 1])
Since tanθ = 3
dθ/dt = 1/(2[tan²θ + 1])
dθ/dt = 1/(2[3² + 1])
dθ/dt = 1/(2[9 + 1])
dθ/dt = 1/(2[10])
dθ/dt = 1/20
dθ/dt = 0.05 rad/min
So, the rate of change of the angle of elevation of the observer’s line of sight when the balloon is 600 m high is 0.05 rad/min.Learn more about rate of change of angle of elevation here:
https://brainly.com/question/13932041
Find an equation of the sphere that passes through the point (6, -2, 3) and has center (-1, 2, 1). Find the curve in which the sphere intersects the yz-plane. Find the center and radius of the sphere
X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0
Answer:
A) x^2 + 2x+ y^2 - 4y + z^2 - 2z - 63 = 0
B) radius = 5
center = (4,-1,-3)
Step-by-step explanation:
[tex]x^2 + y^2 + z^2 - 8x + 2y + 6z + 1 = 0[/tex]
A ) Determine the curve in which the sphere intersects the yz-plane
determine the radius ( r ) = √((6-(-1))2+(-2-2)2+(3-1)2) = √69
next the equation of the sphere ( curve in which the sphere intersects the yz-plane )
x^2+2x+y^2-4y+z^2-2z-63 = 0
B) determine the center and radius of the sphere
X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0
(x-4)2+(y+1)2+(z+3)2 = 25 = 52
radius = 5
center = (4,-1,-3)
Una pizza grande de queso cuesta $18. Cada ingrediente extra cuesta $1.50
Answer:
3
Step-by-step explanation:
Toda la futura variación de pizzas se ha elaborado con cuatro ingredientes distintos: la base, la salsa, el queso y la cobertura. Pero, dado que no hay cobertura, la respuesta sería 3.
-LavenderVye
Samantha, Brooklyn, and Mary went to Bonnaroo music festival where they each attended various
concerts.
• Samantha only went to rock concerts where the sound level was normally distributed between 113
and 117 decibels.
• Brooklyn went to 4 concerts with Samantha and also went to 5 folk concerts where the sound level
was between 95 and 97 decibels.
• Mary got sick, so she only attended 2 shows - one rock concert and one folk concert.
Answer:
a, b, c
Step-by-step explanation:
Among the three girls, Samantha attended the concerts with the greatest mean sound level.
Among the three girls, Samantha attended the concerts with the greatest median sound level.
If Mary had attended an additional rock concert, the median sound level of concerts she attended would have been greater than it is now.
stream fineline lol
A zoo administrator must decrease the staff size by 1/4 because of budget cuts. If the zoo employs 456 people, how many people must be dismissed?
Answer:
114 people
Step-by-step explanation:
456*.25=114
Describe how you would simplify the given
expression.
Pan-talons
20xy
5x 'Y
X=0.y=0
Answer:
y^15/64x^24
Step-by-step explanation:
A glass is 1/3 full. Then 75cm3 of orange juice is poured in.
The glass is now 3/4 full. What is the total volume of the glass?
35 POINTS!!! Show your work and write an expression using the following criteria:
1. A dividend is greater than 1,000
2. The quotient is 37 with a reminder of 4
Answer: 3704 / 100=37R4
Step-by-step explanation:
3704 / 100=37R4
Answer:
listen
Step-by-step explanation:
Just breathe! I know Im late but please take notes and not ask everyone on here to do stuff for you! Thanks
The school hiking club has completed 4 out of 5 hikes so far this year. They have hiked 4.6 miles, 3.7 miles, 5.1 miles, and 2.9 miles. If their goal is to hike 20 total miles, how many miles does the last hike need to be?
1.7 miles
4.7 miles
2.7 miles
3.7 miles
Answer:
there last hike i think needs to be 7.2 miles long
Step-by-step explanation:
What is the base of this Scalene triangle?
Answer: like the measurement or ?
Step-by-step explanation:
At the store, 10 ounces of candy cost $3.20. What is the price of 6 ounce of candy?
divide $3.20 to get the cost per ounce, and multiply it by 6 to get the price for 6 ounces.
6 ounces = $1.92
hope this helps!! :)
Sarah had 16 stickers. Al gave her 25 more. How many stickers does Sarah have now?
Answer:
Sarah had 16 stickers. Al gave her 25 more. How many stickers does Sarah have now? 41
Step-by-step explanation:
Answer: 41
Step-by-step explanation: The key word in this sentence is more. She already has 16 and she is getting another 25. So that means you have to add 16 and 25 to find out how much she has now. The answer would be 41.
Pls look in file below for question
Answer:
the answer to the question is 7
Find the value of n for which the vectors a⃗ =(3,2)a→=(3,2) and b⃗ =(9,n)b→=(9,n) are collinear.
Answer:
For n=6, the given vectors will be collinear.
Step-by-step explanation:
Collinear vectors are the vectors which lie on the same line or parallel lines. In order to find if two vectors are collinear, their ratio is found. If the ratio is same for all unit vectors then the vectors are collinear.
Given
[tex]a = (a_1, a_2) = (3,2)\\b = (b_1, b_2) = (9,n)[/tex]
The ratio of first unit vectors is:
[tex]\frac{a_1}{b_1} = \frac{3}{9} = \frac{1}{3}[/tex]
In order for the vectors to be collinear the other ratio should also be 1/3
[tex]\frac{a_2}{b_2} = \frac{1}{3}[/tex]
Writing it mathematically
[tex]\frac{2}{n} = \frac{1}{3}\\2*3 = n\\n = 6[/tex]
Hence,
For n=6, the given vectors will be collinear.
can someone help me with this? I’m very confused and my results aren’t matching
You basically start at the start and whatever answer you get you go that way and if you get your answers right it should lead you to finish.
pretende-se guardar um cano de 42cm de comprimento em uma caixa de ferramentas retangular, cuja as medidas são 36cm de comprimento por 27cm de largura. Verifique se tal feito será possível de ser realizado, demonstrando numericamente seu raciocínio
Answer:
Step-by-step explanation:
Não porque a caixa seria muito menor que o cano.
A new drug on the market is known to cure 30% of patients with cervical cancer. If a group of 18 patients is randomly selected, what is the probability of observing, at most, one patient who will be cured of cervical cancer?
Answer:
Probability cured of cervical cancer = 18C0 (0.30)⁰(0.70)¹⁸ + 18C1(0.30)(0.70)¹⁷
Step-by-step explanation:
Given:
Patients cured = 30% = 0.30
Number of patients (n) = 18
Probability cured of cervical cancer = P(X≤1)
Probability cured of cervical cancer = P(X=0) + P(X=1)
Probability cured of cervical cancer = 18C0 (0.30)⁰(0.70)¹⁸ + 18C1(0.30)(0.70)¹⁷
If more airplanes and cars are used (both of which burn fossil fuels), carbon levels will increase.
Group of answer choices
True
False
Answer:
True
Step-by-step explanation:
Cars and planes use fossil fuels such as, gas, petroleum. These are unrenewable resources.
Answer:
true
Step-by-step explanation:
they both emit carbon so if they are both used more often then carbon emissions will increase.
NEED HELP ILL GIVE BRAINLIEST PLEASE!!!
Answer:
13 feet
Step-by-step explanation:
Select the correct answer.
Which equation represents the vertical line passing through (1,-9)?
A.
x = -9
B.
X = 1
y = -9
D.y = 1
Answer:
I think A because we can't see the thing
Answer:
x=1
Step-by-step explanation:
Please Help! Anyone know how to solve Rational Equations?
Answer:
The answer is D. x = 0 , 5
x equal to 0 and 5.
32. Parallelogram ABCD has vertices A(0,0), B(2,4), and C(10,4). Find the coordinates of D.
Answer:
Answer:
The fourth vertex is D(8, 0)
Step-by-step explanation:
Let A(0, 0), B(2, 4), and C(10, 4) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a, b).
Join AC and BD. Let AC and BD intersect at point O.
We have known that the diagonals of a parallelogram bisect each other.So, O would be the midpoint of AC as well as that of BD.
[tex]A\left(0,\:0\right)=\left(x_1,\:x_2\:\right)[/tex]
[tex]C\left(10,\:4\right)=\left(x_2,\:x_2\:\right)[/tex]
The midpoint of AC is:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\left(x_2,\:y_2\right)=\left(10,\:4\right)[/tex]
[tex]=\left(\frac{10+0}{2},\:\frac{4+0}{2}\right)[/tex]
[tex]=\left(5,\:2\right)[/tex]
The midpoint of BD is:
[tex]=\left(\frac{a+2}{2},\:\frac{b+4}{2}\right)[/tex]
so
∵ [tex]\frac{a+2}{2}=5[/tex]
[tex]a+2=10[/tex]
[tex]a=8[/tex]
∵ [tex]\frac{b+4}{2}=2[/tex]
[tex]b+4=4[/tex]
[tex]b=0[/tex]
Hence, the fourth vertex is D(8, 0)
I need to know the slope ASAP
Answer:
-3/1
Step-by-step explanation:
brainliest pls
Which expression is equivalent?
Answer:
this one i can not help you on sorry
Step-by-step explanation:
!!!PLEASE HELPPPP!!!! Select all options that are greater than 17. (the answer's are power)
2 to the power of 5
4 to the power of 2
2 to the power of 2 + 3 to the power of 2
3 to the power of 3 - 3 to the power of 2.
Answer:
it's 2 to the power of 5, 2 to the power of 2 + 3 to the power of 2 and the last one is 3 to the power of 3 - 3 to the power of 2
Someone help me solve this please, I'd appreciate it if you can walk me through the steps. If not, just answering it is okay :)
Answer:
c. -8
Step-by-step explanation:
Given:
[tex] \frac{4b \div c}{1 - a} [/tex]
a = 5, b = 8, and c = 1
To evaluate, plug in the values into the expression given.
Thus:
[tex] \frac{4(8) \div 1}{1 - 5} [/tex]
[tex] \frac{32 \div 1}{1 - 5} [/tex]
[tex] \frac{32}{-4} [/tex]
[tex] \frac{8}{-1} = - 8 [/tex]
I need help with this anyone?
Answer:
c is the correct answer
The vertex angle of an isosceles triangle is 10 less than three times the base angles. Find each angle of the triangle.
From the picture attached,
ΔABC is an isosceles triangle.∠B ≅ ∠C
Vertex angle ∠A is 10 less than 3 times the base angles.m(∠A) = 3[m(∠B)] - 10
By applying angle sum theorem in ΔABC,
m(∠A) + m(∠B) + m(∠C) = 180°
m(∠A) + m(∠B) + m(∠B) = 180° [From equation (1)]
m(∠A) + 2m(∠B) = 180°
[3m(∠b) - 10] + 2m(∠B) = 180°
5[m(∠B)] = 180° + 10°
m∠B = 38°
Therefore, m∠B = m∠C = 38°
Substitute the value of angle B in equation (2),
m(∠A) = 3[m(∠B)] - 10m(∠A) = 3(38) - 10
= 104°
Therefore, measure of angle A will be 104°.
Learn more,
https://brainly.com/question/4973154
WILL MARK BRAINIEST
Which expression is equivalent to
36/25sqaure root?
A.6/25
B.5/6
C.6/5
D.36/25
Answer:
it is C
Step-by-step explanation:
trust me
Tickets for a concert cost $25 each. You have $180 to spend. Write
an expression for the money that you have left after buying
t tickets. Evaluate the expression to find the amount of money left
after buying 6 tickets.
Answer:
180 - 25(T)= 30
T=6
180 - 25(6)= 30
Two lines are perpendicular. The slope of the first line is. What is the slope of the second line?
Answer:
Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.