7. A 10 foot ladder slides down a wall at a rate of 3 ft/sec. At what rate is the (acute) angle between the ladder and the wall changing when the foot of the ladder is 5 feet from the wall? How fast is the base of the ladder sliding away from the wall at this instant?
Answers
The rate at which the angle between the ladder and the wall changes is 30√75 ft/sec and the rate at which the base of the ladder slides away from the wall at this instant is 13.2 ft/sec.
When a 10-foot ladder slides down a wall at a rate of 3 ft/sec, the rate at which the (acute) angle between the ladder and the wall changes when the foot of the ladder is 5 feet from the wall and the rate at which the base of the ladder slides away from the wall are required to be calculated.
Let's mark the length of the ladder as ‘l’ and the distance of the ladder from the wall as ‘x’.If the ladder has slid x feet down the wall at time t, the triangle formed by the ladder, the wall, and the ground is such that l² = x² + y². The angle is θ, then sin θ = y/l, cos θ = x/l, and tan θ = y/x.
Thus, we have the following equation:(l)² = (x)² + (y)²Differentiate with respect to t.2(l)(dl/dt) = 2(x)(dx/dt) + 2(y)(dy/dt)
Solve for dy/dt when x = 5ft and dx/dt = 3 ft/sec.dy/dt = (l/x)(dx/dt)√[l² - x²]dy/dt = (10/5)(3)√[10² - 5²]dy/dt = 30√75 ft/sec
Now, let's differentiate the equation l² = x² + y² with respect to time:2l(dl/dt) = 2x(dx/dt) + 2y(dy/dt)
We have already calculated the value of dy/dt from the previous step. Substituting, l = 10, x = 5 and dx/dt = 3, we get: 20(dl/dt) = 10(3) + 2(5)(30√75)dl/dt = 13.2 ft/sec
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Related Questions
If the circumference of a right cylinder is tripled, the volume will increase by a factor of _____.
Answers
Answer:the answer is 9
Step-by-step explanation:
Thomas bought a pair of blue jeans at the mall. The original price was $27.00, but the jeans were on sale at a 25% discount. How much money did Thomas save buying the jeans at the discounted price?
A. $6.75
B. $33.75
C. $5.40
D. $20.25
Answers
27*0.25=6.75
take a deck of playing cards form following sets out of those
A=Set of playing cards
B=SET OF RED COLOURED FACE CARD
Answers
The information given about the probability shows that the cardinality of D is 18.
How to calculate the probability?From the complete information, the number of red-colored cards is 26.
Also, the number of red-colored number cards will be 18.
The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.
Here, the cardinality of set D is 18.
Here is the complete question:
Take a deck of playing cards. Form following sets out of those:
A = Set of Face Cards
B = Set of Red Coloured Face cards
C = Set of Black Coloured Face Cards
D = Set of Red Coloured Number Cards
Find the Cardinality of set D
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if a child is confronted about stealing cookies from a cookie jar and when the parent asks who took the cookies, the child simply frowns and tucks their head into their chest and says nothing. the child is utilizing what function of non-verbal communication? question 1 options: contradicting function substituting function regulating function complementing function
Answers
When a child is confronted in front of his parents about stealing cookies from Jar, the function used is substituting function.
The substituting function replaces verbal communication. The primary role of bodily structure in substituting function is Nonverbal communication includes substituting.
Thus, the above statement is a example of nonverbal communication's replacing function, as the child is confronted by his body language in front of a parent when he steals the cookies.
Communication is a continual process that consists primarily of three components: sender, message, and recipient.
verbal communication:
Oral communication is communication that occurs by verbal, verbal, or written communication that delivers or conveys a message to others. The use of language to convey information vocally or in sign language is known as verbal communication.
non- verbal communication:
It can happen with signs, symbols, colors, touches, body parts, or face features. Insignificant communication is the use of body language, facial expressions, and body language to send information to another. It can be used both purposefully and unintentionally. For example, when you hear an idea or a piece of new or exciting information, you may smile.
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Two sailboats are traveling along the same path away from a dock, beginning from different locations at the same time. John’s boat beings 30 miles from the dock and is 50 miles from the dock after 5 hours. The distance of Roberta’s boat from the dock is represented by the function y = 5x + 25, where x represents time and y represents the distance from the dock.
Which boat was farther from the dock at the beginning, and which traveled more quickly?
A. John’s boat was farther from the dock at the beginning, but Roberta’s boat traveled more quickly.
B. Roberta’s boat was farther from the dock at the beginning, and it traveled more quickly.
C. John’s boat was farther from the dock at the beginning, and it traveled more quickly.
D. Roberta’s boat was farther from the dock at the beginning, but John’s boat traveled more quickly.
Please Help!!!!
Answers
Answer:
c
Step-by-step explanation:
The correct statement is John’s boat was farther from the dock at the beginning, and it traveled more quickly option (C) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Two sailboats are traveling along the same path away from a dock, beginning from different locations at the same time.
y = 5x+25
at starting x=0
y = 25 miles away from the dock
x = 5
y = 5×5+25
y = 50 miles
= (50 - 25)/5
= 5
Thus, the correct statement is John’s boat was farther from the dock at the beginning, and it traveled more quickly option (C) is correct.
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I REALLY NEED THE ANSWER PLEASE THANK YOU
Answers
Note that in the arithmetic prompt above, the largest possible result Rachel can get is 4383.
What is the explanation for the above response?
We want to find the largest possible result for the expression BADF - KCCC + EGA, where each letter is replaced by a different number from 0 to 9. Since we want the largest result, we should try to make the leftmost digit of each number as large as possible. One way to do this is:
B = 9 (largest possible digit)
A = 8 (second largest digit)
D = 7 (third largest digit)
F = 6 (fourth largest digit)
K = 5 (largest possible digit different from B, A, D, F)
C = 4 (largest possible digit different from K, B, A, D, F)
E = 3 (largest possible digit different from K, B, A, D, F, C)
G = 2 (largest possible digit different from K, B, A, D, F, C, E)
Substituting these values, we get:
BADF - KCCC + EGA = 9876 - 5444 + 321
= 4383
Therefore, the largest possible result Rachel can get is 4383.
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Why the following hypotheses are not constructed correctly.H0: μ ≤ 10; HA: μ ≥ 10A. The alternative hypothesis HA should not have the equality sign.B. The hypothesized value is not the same under the null and alternative hypotheses.C. Hypothesis testing is about a sample statistic.
Answers
The reason why the following hypotheses are not constructed correctly is because of option B. The hypothesized value is not the same under the null and alternative hypotheses.
In hypothesis testing, the null hypothesis (H0) and the alternative hypothesis (HA) should have the same hypothesized value, but with opposite signs. In this case, the hypothesized value is 10, but the signs are not opposite. The null hypothesis has a less than or equal to sign (≤) and the alternative hypothesis has a greater than or equal to sign (≥). This means that there is overlap between the two hypotheses, which is not correct.
The correct way to construct the hypotheses would be:
H0: μ ≤ 10; HA: μ > 10
or
H0: μ ≥ 10; HA: μ < 10
Option A is incorrect because the alternative hypothesis can have the equality sign if the null hypothesis does not have it. Option C is also incorrect because hypothesis testing is about a population parameter, not a sample statistic.
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Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas? $
Answers
Answer: The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.
Step-by-step explanation: Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.
We are to find the price per pound of apples and bananas.
The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.
Then, according to the given information, the system of equations describing the situation is as follows:
Multiplying equation (i) by 2, we have
and multiplying equation (ii) by 3, we have
To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at
From equation (i), we get
Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.
Answer:Bro the answer is price per pound of apples is $1.25
and the price per pound of bannanas is $0.75
Class 10 cbse
Q) Four years ago George was four times older than his daughter. After four years, George will be 2 years more than two times the age of his daughter. Find the present age of George and his daughter.
Please answer asap
Answers
Answer:
George Washington 67 and sister 63
Answer: 28
Step-by-step explanation:
Let the present age of George be = x years
and present age of her daughter is = y years
4 years ago,
George age be = x - 4
Daughter age be = y - 4
After four years,
George age be = x +4
Daughter age be = y+ 4
Substitute the value of x in equation 2
➡
Value of y put in equation 1
➡x= 28
So, the present age of George is 28 years and his daughter's age is 4 years.
if f(x) = mx +c, f(4) = 11 and f(5) = 13, find the value of f(2).
Answers
Answer:
7
Step-by-step explanation:
\(f(4)=4m+c=11 \\ \\ f(5)=5m+c=13\)
Subtracting the equations yields that m=2, and thus c=3.
\(\implies f(2)=2(2)+3=7\)
Solve the Magic Square
Answers
The missing numbers for the respective rows are:
row 1: 4/5
row 2: -4/5 and -2/5
row 3: -3/5 and 6/5
How to evaluate for the missing numbersMissing number for row 1(top row):
1 - 1/5 = 4/5
Missing number for row 2 (2nd number for last column):
3/5 - 1 = -2/5
Missing number for row 2 (1st number for first column):
-2/5 - 2/5 = -4/5
Missing number for row 3 (1st number for first column):
1/5 + (-4/5) = -3/5
Missing number for row 3 (2nd number for second column):
4/5 + 2/5 = 6/5
Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5
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Possible question:
If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.
write a recursive algorithm to multiply two positive integers, m and n, using repeated addition. specify the base case and the recursive case.
Answers
The recursive algorithm to multiply two positive integers m and n using repeated addition is :
Algorithm Multiply(m, n):
1. Base case: if m or n is 0, return 0.
2. Recursive case: if m is odd, return n + Multiply(m-1, n).
if m is even, return Multiply(m/2, n) + Multiply(m/2, n).
The base case is when either m or n is 0, in which case the product is 0.
In the recursive case, we use repeated addition to compute the product of m and n. If m is odd, we add n to the product of (m-1) and n.
This can be seen as adding n to itself (m-1) times. If m is even, we split it into two equal halves and recursively compute the product of each half, and then add the two products together.
This is essentially a divide-and-conquer approach.
For example, to compute the product of 5 and 7 using this algorithm:
Multiply(5, 7) -> 7 + Multiply(4, 7) -> 7 + (Multiply(2, 7) + Multiply(2, 7)) -> 7 + ((Multiply(1, 7) + Multiply(1, 7)) + (Multiply(1, 7) + Multiply(1, 7))) -> 7 + ((7 + 7) + (7 + 7)) -> 35
So the product of 5 and 7 is 35.
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In 2015 the viewership of a particular show was 5.6 million. A year later the viewership was 3.7 million. What was the percent of increase or decrease?
Answers
Answer:
The percentage decrease is -33.93%
Step-by-step explanation:
Firstly we check if there is an increase or decrease
Since we went from 5.5 million to 3.7 million, that is a decrease
Percentage decrease = (3.7 - 5.6)/5.6 * 100%
= -1.9/5.6 * 100% = -33.93%
If 15 actuators have failed today, what is the probability that a) at least 10 are repairable? b) from 3 to 8 are repairable? c) exactly 5 are repairable?
Answers
The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
According to the statement
we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.
we know that the formula of probabilities is
probability = possible outcomes / total outcomes
So,
at least 10 are repairable = 1 - (10 are not repairable)at least 10 are repairable = 1 - 10/15
at least 10 are repairable = (15 - 10)/15
at least 10 are repairable = (5)/15
at least 10 are repairable = 1/3
from 3 to 8 are repairable = 3/15 *8/15from 3 to 8 are repairable = 1/5 *8/15
exactly 5 are repairable = 5/15exactly 5 are repairable = 1/3
These are the probabilities of the given conditions.
So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
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Which expression is equivalent to 9(5s)?
Answers
Answer:
\(9*5\)
Step-by-step explanation:
9(5s) are 9*5.
A clothing manufacturer is examining the efficiency of its factories. All of its factories produce an average of 1,250 pairs of jeans each month, with a standard deviation of 125 pairs of jeans, normally distributed. How many pairs of jeans produced separates the lowest 33% of the means of jean production from the highest 67% in a sampling distribution of 12 factories
Answers
Using the normal distribution, it is found that 1234 pairs of jeans produced separates the lowest 33% of the means of jean production from the highest 67% in a sampling distribution of 12 factories.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).For this problem, the parameters are given by:
\(\mu = 1250, \sigma = 125, n = 12, s = \frac{125}{\sqrt{12}} = 36.08\)
The desired amount is the 33rd percentile, which is X when Z = -0.44, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
-0.44 = (X - 1250)/36.08
X - 1250 = -0.44 x 36.08
X = 1234.
1234 pairs of jeans produced separates the lowest 33% of the means of jean production from the highest 67% in a sampling distribution of 12 factories.
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The figure below is divided into 100 squares of equal size.
What percent of the figure is shaded?
Answers
Answer:
36%
Step-by-step explanation:
If there are 100 squares of equal size
There are 36 squares that are shaded
36 out of 100 as a percentage is 36%
Answer:
36%
Step-by-step explanation:
First, count how many squares there are. There are 36 shaded squares according to my count.
Then, since we are trying to find what percent 36 is out of 100, we divide the part (P) by the total (T).
36/100= 0.36
Multiply that number by 100 and you have your percentage!
If x is an even number then what’s the next even number ?
Answers
Answer:
2x
Step-by-step explanation:
an even number is a number EXACTLY divisible by 2
therefore if x is an even number the next is X times 2 which is 2x
Answer:
x+2
Step-by-step explanation:
what type of mathematical law is this (6+4)+100=6+(4+100)
Answers
Answer:
Associative Property of Addition
Step-by-step explanation:
According to the Associative Property of Addition: when three real numbers are added, it makes no difference which two are added first.
a + (b + c) = (a + b) + c
Therefore, in the given equality statement: (6 + 4) + 100 = 6 + (4 + 100), the sum of the numbers on either side of the equation will have the same results.
(6 + 4) + 100 = 6 + (4 + 100)
(10) + 100 = 6 + (104)
110 = 110
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If you deposit or put in $1550 into a savings account earning 7.2% simple interest for 2 years, how much money total will you have in your account? Show the equation you use and solve.
Answers
Answer:
22320
Step-by-step explanation:
simple interest= p (deposit) × r (rate) × t (time)
=1550×7.2×2
=22320
which equation represents a parabola opening to the right with a vertex at the origin and a focus at (9,0)?
Answers
Answer:
y² = 36x
Step-by-step explanation:
Parabola opens right.
Thus equation is from; y² = 4ax
And focus is at (a, 0)
Since we are given focus at (9, 0),it implies that a = 9
Thus, equation of parabola is;
y² = 4 × 9 × x
y² = 36x
Mrs. Martinez and Ms. Jones' classes are competing for best average homework completion over the course of the semester.
Answers
According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.
How do average and mean differ?The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.
Comparing the median and average.By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.
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The graph below represents the proportional relationship between the weight of objects on Earth versus their weight on the Moon. What is the constant of proportionality? (Hint: it equals the slope of the line.)
Answers
Answer:
\( \frac{1}{6} \)
Step-by-step explanation:
let constant = k, then the proportional equation must be
y=kx
as the graph we get random point through (12, 2) so x=12 and y=2, substitute to y=kx we get
2=k.12
2/12=k
1/6 = k
An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
Answers
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
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11 + 16 + 4 = ????????????
Answers
Answer:
31! :D
Step-by-step explanation:
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If you want to join you can,
Good luck!!
God Bless!!
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find the value of - |3.4|
Answers
Answer: 3.4
Answer:
-3.4
Step-by-step explanation:
"| |" are absolute value which means |-4| is actually 4. However, if there is a negative outside of the lines, than the answer is negative.
What is the numerical value of mswithin when sswithin= 70, the sample size = 17 and the number of groups = 3? group of answer choices mswithin = 70
Answers
The numeric value of ms within is = 19.
What is a numeric value?A real number, regardless of its sign, has a numerical value. A definite quantity is a defined amount measurement.To find the numeric value of ms within:
Given: Swithin = 70, sample size = 17 and number of groups = 3.
So, 17 × 3 = 51
70 - 51 = 19
Therefore, the numeric value of ms within is = 19.
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Betty babysat for 3 hours each night for 12 nights. She earned a total of $288 babysitting. Betty wants to calculate her hourly rate. How much did Betty earn per hour babysitting?
Answers
Answer:Betty earned $8 per hour babysitting
Step-by-step explanation:
Number of hours worked per day =3
Number pf nights worked =12
Number of hours wored for 12 nghts =3x12=36hours
Now if 36 hours earned her $288
1 hour will earn her=( 288 x 1) / 36 = 8 hours
Can someone help me pls and determine if this is no solution, one solution, or infinte solutions
−2x−6y=−4
2x+6y=4
ILl give brainly
Answers
Answer:
There is one solution, x = 2 - 3y
Step-by-step explanation:
Yes
No
34. Toby and three of his friends ate lunch together at a deli.
Each person ordered a sandwich and a drink.
No
kem
Fill in each box to write an expression to represent the
amount they spent altogether
Sandwich
Cost (5
275
125
Drink
х
How much did Toby and his friends spend altogether?
1.25
1.50
2
2.75
3
4
Answers
The amount that Tony and his friend's will spend at the dell can be found by
writing an expression for the total cost.
Response;The amount that they spent at the dell is $16Method used in finding the amount that was spent;Given;The number of Toby's friends = 3
Number of people that ate lunch, n = Toby + His friends = 1 + 3 = 4
The cost of the sandwiches and drinks
\(\begin{tabular}{|c|c|c}Item&Cost(\$)\\Sandwich&2.75\\Drink &1.25\end{array}\right]\)
Solution;The expression that gives the amount Toby and his friends spend altogether is therefore;
Amount spent = n × (Cost of a sandwich + cost of a drink)
Which gives;
4 × (2.75 + 1.25) = 16
The amount Tony and his friends spent is $16.
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