question is in the picture pls help me. much appreciated
You stand 20 ft from a bottle rocket on the ground and watch it as it takes off vertically into the air at a rate of 18 ft/sec. Find the rate at which the angle of elevation from the point on the ground at you feet and the rocket changes when the rocket is 40 ft in the air. At the moment the rocket is 40 ft in the air, the angle of elevation is changing at a rate of rad/se.
Answer:
9/50 rad/sec
Step-by-step explanation:
let the angle be represented as ∅
distance form bottle rocket on the ground = 20 ft
height of rocket = 40 ft
solution
first we differentiate w.r.t.time
= sec²(∅)*(d(∅)/dt))=(1/20)*dh/dt --------- ( 1 )
= d(∅)/dt = (1/20)cos²(∅)* (dh/dt) ------- ( 2 )
note : 1/sec(∅) =cos(∅)
therefore ; dh/dt = 18 ft/sec
applying Pythagoras theorem
Tan ∅ = 40 / 20
h^2( hypotenuse ) = a^2( height ) + b^2 ( distance from bottle rocket )
h = √ 40^2 + 20^2 = √ 2000
also cos ( ∅ ) = b / h = 20 / √ 2000
hence cos²∅ = 1/5
Back to equation 2
d(∅)/dt=(1/20)×(1/5)×(18)
= 18/100 = 9/50 ( changing rate of angle of elevation )
Use x for the unknown number.
Twice an unknown number added to 48 is six times the same unknown number.
Answer:
2x+48=6x
Step-by-step explanation:
Jonathan went shopping for a new camera. The listed price of the camera was $43, but the price with tax came to 46.87. Find the percent sales tax
Answer:
x = 8,25%
Step-by-step explanation:
46,87 - 43 = 3,87
$46,87 ----- 100%
$3,87 ------ x
46,87x = 100 . 3,87
x = 387 / 46,87
x = 8,25%
This symbol means that both sets could have the same elements. (A ⊆ B)
True
False
Answer:
true
Step-by-step explanation:
because it is
Answer:
True
Step-by-step explanation:
30 is 2/3 of what number
Answer:45
Step-by-step explanation:
Key Word:of
30*2/3 = 45
Answer:
Step-by-step explanation:
let the number be x.
then,
2/3 of x = 30
=> 2/3x = 30
=> x = 30 × 3/2
=> x = 45
so, the required number is 45 .
hope it helps...!!!
I NEED HELP ASAP PLEASE
Order the numbers from least to greatest.
-5 1/2
-5.2
-5
-5/2
5.5
Answer:
Least to greatest: -5 1/2, -5.2, -5, -5/2, 5.5
What is the y-intercept of the parabola defined by y=−2x2+6x−8 and what is the equation of the axis of symmetry?
Answer:
y-intercept = (0, 8)
axis of symmetry= -b/2a
Step-by-step explanation:
Also when you want something to be squared use this symbol ^
A mail carrier travels at 15 miles per hour through a neighborhood. Which table
represents the distance the mail carrier travels in x hours?
2
G
H
0 1 3
yo 16 18
0 24
yo 30 55
x 135
y 15 45 75
x 134
y 15 40 55
Answer:
Step-by-step explanation:
the table is not copied correctly, I assume
the mail carrier will travel a distance of 15x
What is the answer to the following?
1. 8/9 divide by 2/3
2. 4 divided by 3/4
3. 2 1/2 divided by 3/4
4. 4/9 divided by 5 1/3
5. 7/8 divided by 14
i would go with either a or b
Which statement about these triangles is true?
Answer:
It's the last one
I hoped that helped
what are all values of x for which the series shown converges?
Answer:
One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:
Iaₙ₊₁I < IaₙI
This means that the absolute value of the terms must decrease as n increases.
Then we must have:
[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}[/tex]
We can write this as:
[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}[/tex]
If we assume that n is a really big number, then:
n + 1 ≈ 1
And we can write:
[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}[/tex]
Then we have the inequality
[tex]1 > (x - 2)/3[/tex]
And remember that this must be in absolute value, then we will have that:
-1 < (x - 2)/3 < 1
-3 < x - 2 < 3
-3 + 2 < x < 3 + 2
-1 < x < 5
The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.
w pewnym trapezie o wysokości 6cm jedna z podstaw ma długość 9cm ,a druga jest od niej o 2cm krótsza . Pole tego trapezu wynosi:
Odpowiedź:
48 cm
Wyjaśnienie krok po kroku:
Jeśli się uwzględni:
Wysokość trapezu = 6 cm
Długość podstaw:
Podstawa 1 = a = 9 cm
Podstawa 2 = b = (a - 2) = 9 - 2 = 7 cm
Uaing relacji:
Powierzchnia trapezu = 1/2 (a + b) * h
Powierzchnia trapezu = 0,5 (9 + 7) * 6
Powierzchnia trapezu = 0,5 (16) * 6
Powierzchnia trapezu = 8 * 6
Powierzchnia trapezu = 48 cm
Jessica, Hans, and Tom sent a total of 95 text messages during the weekend. Tom sent 3 times as many messages as Hans. Jessica sent 10 more messages than Hans. How many messages did they each send?
Answer: Manal = 27 messages
Elisa = 17 messages
Abdulrahman = 51 messages
Step-by-step explanation:
Let tye number of messages that Manal sent be x.
Since Eissa sent 10 fewer messages than Manal, this will be:
= x - 10
Abdulrahman sent 3 times as many messages as Eissa. This will be:
= 3(x - 10) = 3x - 30
We are also told that Manal, Abdulrahman, and Eissa sent a total of 95 text messages. This will be:
x + (x - 10) + (3x - 30) = 95
x + x - 10 + 3x - 30 = 95
x + x + 3x - 10 - 30 = 95
5x - 40 = 95
5x = 95 + 40
5x = 135
x = 135/5
x = 27
Manal = x = 27
Elisa = x - 10 = 27 - 10 = 17
Abdulrahman = 3x - 30 = 3×27 - 30 = 81 - 30 = 51
Manal = 27 messages
Elisa = 17 messages
Abdulrahman = 51 messages
Solve – 4y – 10 = 4(y - 3)
Answer:
y= 1/4
Step-by-step explanation:
Answer:
y=-7/8
Step-by-step explanation:
-4y-10=4y-3
add 10 on both sides
-4y=4y+7
subtract the four on the right from both sides
-8y=7
divide -8 on both sides
answer: -7/8
A sample of 29 boxes of cereal has a sample standard deviation of 0.81 ounces. Construct a 95% confidence interval to estimate the true standard deviation of the filling process for the boxes of cereal.
a. ( 0.427,1.144)
b. (0.515,1.105)
c. (0.726,0.726)
Answer:
The 95% confidence interval is [tex]0.6428 < \sigma < 1.0954[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 29
The sample standard deviation is [tex]s = 0.81[/tex]
Generally the 95% confidence interval to estimate the true standard deviation is mathematically represented as
[tex]\sqrt{\frac{(n- 1)s^2 }{ X^2_( \frac{\alpha }{2 } , n-1)} } < \sigma < \sqrt{\frac{(n- 1)s^2 }{ X^2_(1- \frac{\alpha }{2 } , n-1)} }[/tex]
Generally from the chi -distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 29 - 1 = 28[/tex] is
[tex]X^2 _{\frac{\alpha }{2} , 28 } =44.46079184[/tex]
Generally from the chi -distribution table the critical value of [tex]1 - \frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 29 - 1 = 28[/tex] is
[tex]X^2 _{(1 - \frac{\alpha }{2}) , 28 } = 15.30786055[/tex]
So
[tex]\sqrt{\frac{(29- 1)0.81^2 }{ 44.46079184 } } < \sigma < \sqrt{\frac{(29- 1)0.81^2 }{15.315.307860551 }[/tex]
=> [tex]0.6428 < \sigma < 1.0954[/tex]
What is the constant in this expression? X/5 - 9
Answer:
-9
Step-by-step explanation:
the constant is a single number
Solve the following quadratic equation.
(x - 16)2 = 256 The 2 is the exponent so please don't misunderstand it lol, thank you for who ever helps me.
A. x = 30 and x = 8
B. x = -30 and x = -8
C. x = -32 and x = 0
D. x = 32 and x = 0
Answer:
D. x = 32 and x = 0
Step-by-step explanation:
You can solve it a multitude of ways one of the easiest ways for me was the quadratic formula.
What is the approximate surface area of the sphere? Round to the nearest hundredth and use 3.14 for 7. Recall the
formula SA-4x7
Answer:
Option (3)
Step-by-step explanation:
Formula to get the surface area of a sphere is,
Surface area of a sphere = 4πr²
Here 'r' = Radius of a sphere
Since, r = 9 units and π = 3.14
Surface area of the sphere = 4(3.14)(9)²
= 1017.36 square ²units
Therefore, Option (3) will be the correct option.
Answer:
c
Step-by-step explanation:
on edge
The cost of an iPhone is $899.99 plus 8.5% tax. What is the cost of tax for the iPhone?
Answer:
724.0915
Step-by-step explanation:
multiply 899.99 and 8.5 you get 724.0915
hope this helps
Which is the best description for the graph?
O The graph is increasing everywhere.
O The graph is decreasing everywhere.
O The graph is increasing, then decreasing.
O The graph is decreasing, then increasing.
ASAP PLZ
Which of the following is a conditional statement?
I will eat anything that is dipped in chocolate.
Chocolate can be white or brown.
I like chocolate.
Chocolate chip cookies are the best kind.
Answer:
im pretty sure its the first
Step-by-step explanation:
Please help!!! I need help
Answer:
Step-by-step explanation:
What the hell is that oh no I am not doing that
A friend recently planned a camping trip. He had two flashlights, one that required a single 6-V battery and another that used two size-D batteries. He had previously packed two 6-V and four size-D batteries in his camper. Suppose the probability that any particular battery works is p and that batteries work or fail independently of one another. Our friend wants to take just one flashlight. For what values of p should he take the 6-V flashlight
Answer:
The values of p = 0 < p ≤ 2/3
Step-by-step explanation:
First we write the probability of 6V flashlight working representing it as a binomial mass function of a binomial random variable
P ( 6v flashlight working ) = P ( at least one 6V battery works )
= P ( 1 6v battery work ) + P ( 2 6v battery work )
= b( 2; 2, p ) + b( 1; 2, p )
write out a formula of b( 2; 2, p ) + b( 1; 2, p )
P ( 6v flashlight working ) = p^2 + 2p( 1 - p )
Next we write the probability of D flashlight working representing it as a binomial mass function of a binomial random variable
P ( D flashlight works ) = p ( at least two D batteries works )
= b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )
write out a formula of b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )
P ( D flashlight works ) = [tex]P^4 + 4p^3 ( 1- p ) + 6p^2 ( 1- p)^2[/tex]
attached below is the remaining solution
Need answerrrrrrrrrrrrr fast
geometry :
find the measure of the exterior angle
Answer:
45
Step-by-step explanation:
i believe its 45 or 55
Answer:
92°
Step-by-step explanation:
(2x - 2)° = x ° + 45°
(2x - 2 - x)° = 45°
(x - 2)° = 45°
x - 2 = 45
x = 45 + 2
x = 47
(2x - 2)° = (2*47 - 2)° = (94 - 2)* = 92°
A student said that since –9 is less than 4, then |–9| is less than |4|. Is the student correct? Explain why or why not.
Answer:
The student is incorrect because I I or absolute value would make the -9 to positive 9.
Step-by-step explanation:
-9<4
on a numberline
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
but the absolute value of -9 (or) |–9|
is actually positive 9
9>4
on a number line
4 5 6 7 8 9
John runs a computer software store. He counted 122 people who walked by his store in a day, 60 of whom came into the stores. Of the 60, only 23 bought something in
the store. Estimate the probability that a person who walks by the store will enter the store?
Answer:
unlikely
Step-by-step explanation:
60/122
60 ÷122=0.49
0.49 × 100 =49
49% chance
answer is unlikely
Help guys, I’m sure it’s easy for y’all
Answer:
(x, y) -------- ( -x,-y)
Rule : Rotation center (0,0) , angle of rotation 180° or -180°
Step-by-step explanation:
The vertices of the object and image have coordinates at ;
D(-4,2), --------D'( 4,-2 ),
E (-1,3), --------E'( 1,-3 ),
F (-1,-3),--------F'(1,3),
G (-3,-4),------G'( 3,4 ),
You notice that after the rotation ;
( x, y )-------change to (-x,-y),
This rule is rotation center origin angle 180°
Let g (2) = 22 – 5 and h (2) = 22 +1.
Find (g+h) (2)
Answer:
23 + 17 = 40 :)