A ladder 18 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π 3 ?
Answer: [tex]9\ ft/rad[/tex]
Step-by-step explanation:
Given
Length of the ladder is [tex]l=18\ ft[/tex]
Angle between the wall and the ladder is [tex]\theta[/tex]
from the figure, we can write
[tex]\Rightarrow \sin \theta=\dfrac{x}{18}\\\\\Rightarrow x=18\sin \theta[/tex]
Differentiate the above equation w.r.t [tex]\theta[/tex]
[tex]\Rightarrow \dfrac{dx}{d\theta}=18\cos \theta\\\\\text{at }\theta=\dfrac{\pi }{3}\\\\\Rightarrow \dfrac{dx}{d\theta}=18\cos(\dfrac{\pi}{3})\\\\\Rightarrow \dfrac{dx}{d\theta}=18\times 0.5\\\\\Rightarrow \dfrac{dx}{d\theta}=9\ ft/rad[/tex]
On a piece of paper, graph f(x)=16x0.5^x. Then determine which answer choice matches the graph you drew.
9514 1404 393
Answer:
A
Step-by-step explanation:
You can use x=0 and x=1 to find points that must be on the graph.
f(0) = 16·0.5^0 = 16
f(1) = 16·0.5^1 = 8
Only graph A matches these points.
Identify the: a) class width, b) class midpoints, and c) class boundaries for the given frequency distribution. Ages of Best Actors Age % 26-35 30 36-45 35 46-55 25 56-65 4 66-75 3 76-85 3
Answer:
Kindly check table below :
Step-by-step explanation:
Given :
Ages of Best Actors Age %
26-35 30
36-45 35
46-55 25
56-65 4
66-75 3
76-85 3
The class width = difference between the intervals = (35 - 26) = 10
Class midpoint = (sum of interval) / 2 = (26 + 35) / 2 = 61 / 2 = 30.5
The class boundaries :
Lower - 0.5 = 26 - 0.5 = 25.5
Upper + 0.5 = 35 + 0.5 = 35.5
Ages _ F ___Class Bound.__ classW__midpoint
26-35 _ 30 _ 25.5-35.5 ____ 10 _____ 30.5
36-45 _ 35 _ 35.5-45.5 ____ 10 _____ 40.5
46-55 _ 25 _ 45.5-55.5 ____ 10 _____ 50.5
56-65 _ 4 __ 55.5-65.5 ____ 10 _____ 60.5
66-75 _ 3 __ 65.5-75.5 _____10 _____ 70.5
76-85 _ 3 __ 75.5-85.5 _____ 10 _____ 80.5
Find the 7th term of the geometric sequence: 4, 14, 49, ...
Answer:
Step-by-step explanation:
[tex]a_2=a_1*r=>14=4*r=>r=\frac{7}{2}\\a_n=a_1*r^{n-1}=>a_7=a_1*r^{7-1}=4*(\frac{7}{2})^6=\frac{117649}{16}\\\\a_7=\frac{117649}{16}[/tex]
What is the volume of this figure?
Answer:
[tex]volume = 4 \times 4 \times 4 \\ = {4}^{3} \\ = 64 \: cubic \: ft[/tex]
Find the different
5-2
Answer:
3
Step-by-step explanation:
5-2=3 ¯\(◉‿◉)/¯
hope it may help you
mark as brainlist please!!
¯
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between and minutes. Find the probability that a randomly selected passenger has a waiting time minutes.
Answer:
Incomplete question, but I gave you a guide on the uniform distribution, and thus you just have to replace the values in these equations to find the desired probabilities.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{a - x}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Between a and b minutes.
Here you get a and b for the uniform distribution.
Find the probability that a randomly selected passenger has a waiting time minutes.
Here you will have the value of x.
The expression for ordering brushes for an art class is 5c - 1, where c is the class limit. Evaluate the expression when the class limit is 34. When the class limit is 34, the expression evaluates to
Answer: 169'
Step-by-step explanation:
Since the expression for ordering brushes for an art class is given as 5c - 1, where c is the class limit.
Therefore, when the class limit is 34, the expression evaluated will then be:
= 5c - 1
= 5(34) - 1
= 170 - 1
= 169
Therefore, 169 brushes were ordered.
Sets L and J are defined as follows: L = { g , h , i , j , k } J = { i , l , m , n , o } Find the intersection of L and J .
Answer:
Step-by-step explanation:a
Answer:
The answer is L∩J= {i}
Step-by-step explanation:
I just took a quiz and this was the correct answer
A line passes through the origin and has a slope of 1/2.
Which of the following points does the line pass through?
(1/2, 1)
(1, 2)
(2, 1)
(0, 1/2)
Answer:
(2, 1)
Step-by-step explanation:
A line that passes through the origin and has a slope of 1/2 can be best represented as y = 1/2x
it starts at the origin
goes 2 units to the right
1 unit above
2 units to the right + 1 unit above = (2, 1)
Final Answer: (2, 1)
Answer:
2,1
Step-by-step explanation:
trust
what is 5.7916 rounded to the nearest thousandth?
Answer:
5,792
Step-by-step explanation:
I'm pretty sure tell me if I'm wrong
Answer:
5.792
Step-by-step explanation:
To round to the nearest thousandth, look at the ten thousandths place.
If the number is greater than 5, we will round up. If it is 5 or less, we will keep the thousandths place the same.
There is a 6 in the ten thousandths place, so we will round up the thousandths place.
So, the rounded number will be 5.792
Suppose that E and F are points on the number line.
If EF=9 and E lies at 4, where could F be located?
If there are several locations, separate them with commas.
9514 1404 393
Answer:
-5 or 13
Step-by-step explanation:
A point that is 9 units from 4 on the number line ca be located at ...
4 - 9 = -5
4 + 9 = 13
F could be either of -5, 13.
play help me on this
Answer:
VTU T UTV all work
Give me brainiest answer please it helps a lot! :D
Step-by-step explanation:
Answer:
The answer is A <VTU, B <T and D <UTV
PLEASE HELP ME!!!!
QUESTION WILL BE WORTH 10 POINTS!!!
I WILL MARK BRAINLIEST!!!!
Please answer the 3 questions on the picture.
I would appreciate it so much.
Answer:
lol i dont know but yo dog smell like evolution and natural selection?
Step-by-step explanation:
Answer:
11.) 180-38=142 12.)24.5 13.)im not sure but want to say 10
Step-by-step explanation:
-2 (8p+2) -3(2-7p)=2(4+2p)
Answer:
p = 18
Step-by-step explanation:
Let's solve your equation step-by-step.
−2(8p+2)−3(2−7p)=2(4+2p)
Step 1: Simplify both sides of the equation.
−2(8p+2)−3(2−7p)=2(4+2p)
(−2)(8p)+(−2)(2)+(−3)(2)+(−3)(−7p)=(2)(4)+(2)(2p)(Distribute)
−16p+−4+−6+21p=8+4p
(−16p+21p)+(−4+−6)=4p+8(Combine Like Terms)
5p+−10=4p+8
5p−10=4p+8
Step 2: Subtract 4p from both sides.
5p−10−4p=4p+8−4p
p−10=8
Step 3: Add 10 to both sides.
p−10+10=8+10
p=18
Therefore, the final answer is 18, I hope this helps :D
Answer:
p=18
Step-by-step explanation:
See image below:)
Paul bakes raisin bars in a pan shaped like a rectangular prism. The volume of the pan is 480 cubic inches. The
HURRY PLEASE
length of the pan is
12 inches, and its width is 10 inches
V = 480 in^3
h = ?
12 in
10 in
What is the height of the pan?
Enter your answer in the box
in inches
Answer:
The height of the pan is 4 in.
Step-by-step explanation:
What is the GCF of the terms of 8c3 + 12c2 + 10c
Answer:
The GCF of the terms is 2c
Step-by-step explanation:
Greatest common factor:
To find the gcf of the expression, we find the gcf separately for the numbers and for the powers of c, and then multiply them.
Numbers:
8, 12 and 10.
Dividing them all by prime factors:
8 - 12 - 10|2
4 - 6 - 5
5 is not divisible by 2, so we stop there, and the gcf of the numbers is 2.
Powers of c:
Powers of c are 1, 2 and 3. The gcf of 1,2,3 is 1, as there is not a number that is divisible by all of 1,2,3 other than 1. So the gcf for the powers of c is c^1 = c.
GCF of the expression:
2*c = 2c
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
B..................................
Answer:
below
Step-by-step explanation:
v of sphere
v = 4/3 πr³
v= 4/3 *3.142*10³
v = 4188.8cm³
..... B is correct
Complete the following sentence to form a true statement. The expressions x2 - 14x + and (X - _)2 are equivalent. The e expressions x2 - 14x + [and (x-D) are equivalent (Simplify your answer. Type an integer or a fraction.)
52 words in 2minutes and 39 words in 90 seconds?
(Show your work)
Proportion form of the given problem is (52/120)=(39/90). They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.
When does two ratios form a proportion?Two ratios form a proportion if simplified form of both the ratios comes out as same ratio.
Using above method to find out whether the given ratios are forming proportion or not.
The question asks for an proportion.
So, 2 minutes = 120 seconds and set up the proportion
where it will be in the form of (words/seconds).
It is given that 52 words in 2minutes and 39 words in 90 seconds
Now, the proportion form will be;
(52/120) = (39/90).
They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.
Learn more about directly inversely proportional relationship variable here:
https://brainly.com/question/13082482
#SPJ2
Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April. The box shows her data for March. Select all true statements about the data.
Answer:
I think it's the first obtion
The sum of -5 + 6 and 7a - 8
7a-7
I hope you typed the question correctly because it was weird because -5+6=1
Answer:
1) 1
2) I'm getting no answer/ solution
Step-by-step explanation:
See image below:)
LCM of the given set of counting numbers 45,20,10
1. Jeremy has $12000 cash to invest in the bank compounded at 4% interest annually.
a.
What equation will calculate the value in x years? y =
Answer:
[tex]A(x) = 12000(1.04)^x[/tex]
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
$12000 cash
This means that [tex]P = 12000[/tex]
Compounded at 4% interest annually.
This means that [tex]r = 0.04, n = 1[/tex]
What equation will calculate the value in x years?
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(x) = P(1 + \frac{r}{n})^{nx}[/tex]
[tex]A(x) = 12000(1 + 0.04)^x[/tex]
[tex]A(x) = 12000(1.04)^x[/tex]
1. For each of 200 randomly selected cities, Gary recorded the number of churches
in the city (x) and the number of homicides in the past decade (y). He calculated
the linear correlation coefficient and was surprised to find a strong positive linear
correlation for the two variables. Does this suggest that building new churches
causes an increase in the number of homicides? Why do you think that a strong
positive linear correlation coefficient was obtained? Explain your answer with
reference to the term lurking variable.
Answer:
Kindly check explanation
Step-by-step explanation:
When certain variables are examined, there seems to be a sort of spurious relatuoshipnornassocuation between the two variables, this is evident in the relationship between churches and the number of homicide, when a strong positive correlation is observed between number of churches and number of homicides, this relationship is most likely to be due to the effect of a lurking or third variable which creeped into our analysis, a factor which has a posithe correlation on both number of churches and homicide level, Number of homicide and number of churches could have been correlated by the lncreasing population which may lead to overcrowding and competition Hence increasing rate of homicide, similarly, with high rise in population, the growth of church to accommodate the populees will also creep in.
Provide a formula that can be used to determine whether a point in a circle that is centered about (0,0) with a diameter of 12
Answer:
x² + y² = 36
Step-by-step explanation:
The formula for the circle is
x² + y² = 36
If the point is on the circle it will equal 36 when plugged into the formula
Point(6, 0)
6² + 0 = 36
36 = 36 on the circle
point (5, 1)
5² + 1² = ?
25 + 1 = 26
26 ≠ 36 not on the circle
Step-by-step explanation:
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which of the following points lies on the line 2x-y=12
Answer:
You forgot something
Step-by-step explanation:
"which of the following points "
no points follow?????
Summer School 2020 Math 8 NWLSD
TUWW
Oriya
Mr. Williamson bought 4 boxes of chewy granola bars and 5 boxes of crunchy granola bars. Each box contained the
same number of granola bars. He took all 72 granola bars to the class picnic. How many granola bars were in each
box?
Let x represent the number of granola bars in each box.
Step 1: Write an equation.
Step 2: Identify and combine like terms.
Step 3: Use the properties of equality and inverse operations to solve the equation.
Done
Intro
DODO
Answer:
8 granola bars in each box
Step-by-step explanation:
The equation is 4x+5x=72
4x and 5x are like terms, so combine those 9x=72
Use the division property of equality to solve for x, x=8
A number z is greater than 3 and is less than or equal to 8
Answer:
z > 3
z <_8
.......................
37% of what number is 72?
Answer:
26.64
Step-by-step explanation:
37% of x = 72
0.37x = 72
isolate x
x = 72*0.37
x = 26.64