Answer:
The length of the ladder is 7.21 feet
Step-by-step explanation:
Let
y = Height of the wall
x = Distance between the wall and the ladder (bottom)
L = Length of the ladder
So, the given parameters are:
[tex]\frac{dy}{dt} = -2ft/s[/tex]
When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:
[tex]L^2 = x^2 + y^2[/tex]
Differentiate with respect to time
[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
The length of the ladder does not change with time. So:
[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Rewrite as:
[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]
Divide both sides by 2
[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]
Recall that:
[tex]\frac{dy}{dt} = -2ft/s[/tex] and [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
So:
[tex]4 * 3 = -y * -2[/tex]
[tex]12 = 2y[/tex]
[tex]6 = y[/tex]
[tex]y = 6[/tex]
Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]
[tex]L^2 =4^2 + 6^2[/tex]
[tex]L^2 =52[/tex]
[tex]L = \sqrt{52[/tex]
[tex]L = 7.21ft[/tex]
HELPPPPPPPPP MATH PLEASE
Answer: 14
Step-by-step explanation:
Answer:
12 units^2
Step-by-step explanation:
The triangle on the left has an area of 2, the square has an area of 4 and the triangle on the right has an area of 6.
Add these up to get 2+4+6 = 12
A rectangle has a length of 18 11/12 ft and a width of 5 1/2 ft. What is the area?
Answer:
104.04 ft.²
Step-by-step explanation:
length times width
Answer:
104.042
Step-by-step explanation:
area of rectangle=length*width
1. Observa el siguiente conjunto de enteros (-1,0, 1)
A. ¿Cuál de las propiedades de los números reales son verdaderas
para el conjunto?
Answer:
no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas
Step-by-step explanation:
If the critic rates a total of 100 movies, what is the best prediction for the number of movies she gives exactly 3 stars?
А
27
B
47
50
D
35
Answer:
I think its gonna be 35 I'm not sure
The following expression represents the profit made by John as he mows
lawns: P = 20L - 100
Which description correctly interprets each part of the expression?
Answer:
P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.
Step-by-step explanation:
what is the perimeter write your solution
Answer: 88in
Step-by-step explanation:
As he has doubled the sides, the length would now be 24 and the width would be 20.
So then, to work out the perimeter you have to add up all of the sides.
24+24+20+20=88in
Hope this helps :)
three times the quotient of 3 and 5
Three times the quotient of 3 and 5 is equivalent to 1.8
The question asked us to convert the word problem to equation and solve.
The quotient of 3 and 5 is expressed as 3/5
Taking the product of the result and 3 will give;
Three times the quotient of 3 and 5 = 3 * 3/5
Three times the quotient of 3 and 5 = 9/5 = 1.8
Hence three times the quotient of 3 and 5 is equivalent to 1.8
Learn more on expressions here: https://brainly.com/question/723406
#SPJ6
Information collected from runner 3# is in the table below
The constant proportionality for runner 3 is..?
Answer:
the constant of proportionality would be 9
7+3 expressed as a difference
Answer:
7 - (-3)
Step-by-step explanation:
7 + 3 = 7 - (-3).
Zander found these coins in his Couch
Answer:
91 cents
Step-by-step explanation:
3 quarters+3 nickel+1 penny=91 cents
Answer:
91 cents
Step-by-step explanation:
3 quarters=75c
3 nickels=15c
1 penny=1c
75c+15c+1c=91 cents
PLS HELP ME!!! i’ll give you a brainliest answer :)
Answer:
B is the correct answer
What is the slope of the line ?(khan academy)
Answer:
The slope of the line is 2.
Step-by-step explanation:
Slope of a line:
Suppose that we have two points. The slope of the line is given by the change in y divided by the change in x.
In this question:
Points (0,0) and (1,2)
Change in y: 2 - 0 = 2
Change in x: 1 - 0 = 1
Slope: [tex]m = \frac{2}{1} = 2[/tex]
The slope of the line is 2.
Becky wants to eat 1/4 of a small pumpkin pie. which if the following statements are correct? select all that apply
a) If she cuts the pie into 8 pieces of the same size, she should eat 2 pieces
b) If she cuts the pie into 10 pieces of the same size, she would eat 4 pieces
c) If she cuts the pie into 12 pieces of the same size, she should eat 3 pieces
The local park has a circular pond with a radius of 9 feet. What is the pond's circumference?
Answer:
Using 3.14 as pi, the answer would be 56.52, and using just pi (as in the input on a calculator) would be 56.54867.
Step-by-step explanation:
The equation for circumference of a circle is C = πd, C representing the circumference and d representing the diameter. Since the equation shows the radius, the equation can also be C = 2πr, since the radius is half of the diameter. Multiply nine by two to get eighteen. 18 times 3.14 = 56.52.
5th grade math. Correct answer will be marked brainliest:
Answer:
(6,6)
Step-by-step explanation:
Answer:
(6,6)
Step-by-step explanation:
hope this helps have a great day.
Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant
Answer:
[tex]\mathbf{ \dfrac{128}{3}}[/tex]
Step-by-step explanation:
Given that:
[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]
[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]
[tex]Then;[/tex]
[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]
[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]
∴
[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]
[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]
∴
[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]
[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]
[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]
∴
[tex]\mathbf{V = \dfrac{128}{3}}[/tex]
help please i’ll give extra points
Answer:
P would be reflected into quadrant 4.
Step-by-step explanation:
Answer:
Quadrant 4
Step-by-step explanation:
The quadrant under P is quadrant 4. Imagine putting a mirror on the x-axis, where would P be? It would be on the fourth quadrant, the quadrant underneath P.
Have a nice day!
8+8+8=24 as multiplecation sentence
Answer
Hola la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
My work is down below.download the pdf and look at it.Please answer it!
what is -2 x 3 i do not understand this and this is my last problem
Answer:
-6
Step-by-step explanation:
if they were both positive numbers, it would be 6. But when you multiply a negative by a positive, the answer is negative.
Answer:
-6
Step-by-step explanation:
When you multiply a positive number by another positive number, you will always get a positive number as your answer. Same thing for negative. If you multiply a negative by a negative, you will always get a positive. However, when you multiply a negative by a positive, you will always get a negative number.
Since you know this, you can multiply 2 by 3, which is 6. Because 2 is negative and 3 is positive, you know that the answer must be negative. Therefore, you add the negative symbol to 6, giving you -6.
I hope this isn't too confusing. Please let me know if you have any more questions. Good luck!
Use the formula C = 5 over 9(F - 32) to write 126° F as degrees Celsius, round to the nearest tenth.
You are planning to take a group of friends to the movies for your birthday. The local movie theater charges $12.99 per
person. When you check the company's website, you find that they also offer a special group rate. The group rate is only $8.99
per person, but also includes a $20 reservation fee in addition.
What is the minimum number of people that would need to attend your party in order for the group rate to be a better deal?
A
4 people
B)
5 people
Eliminate
6 people
A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag
complete one column of the table with prices where popcorn is priced..... and to be continue
Answer:
The price for a 60-ounce bag of popcorn would be $16
Step-by-step explanation:
Answer:
The price for a 60-ounce bag of popcorn would be $16
Step-by-step explanation:
Function Modeling
The behavior of some parameters that depend on a set of variables can be modeled in several ways, like linear, quadratic, exponential, logarithmic, among many others.
The selection of the model is often a complex decision that involves statistics and data analysis.
The question provides us with four points where the volume of popcorn bags and the price in dollars. The easiest function that can be used is the line.
The equation of a line of the volume V and the price p can be found with the expression
We'll use the first two values (6,10) (8,20)
Simplifying and rearranging, we get the model
To test the accuracy of the model, we compute the values of p for V=35 and for V=48
Since the computed values are equal to those of the table, the model is accurate. We can now predict the price for V=60
The price for a 60-ounce bag of popcorn would be $16
Please help I need a quick answer
Answer:
the first one
Step-by-step explanation:
have a great day :D
what is the value of x ?
a. 10.4
b. 52
c. 61.6
d. 92
Marc and Anthony are pulling weeds. The can pull 25 weeds every three minutes. How many weeds can they pull in 15 minutes?
Answer:
125 weeds in 15 mins
Step-by-step explanation:
Help please plzzzzzzzz
Answer:
60
Step-by-step explanation:
120 + 90 + 90 + 60 = 360
18. State the slope and y-intercept of each linear equations.
a. 6(x + y) = 3(x - y)
b. 2(x + y) = 5(y + 1)
c. 5x + 10y - 20 = 0)
Answer:
a. m = -1, y-int = 0
b. m = 2/3, y-int = -5/3
c. m = -1/2, y-int = 2
Step-by-step explanation:
-Expand equations on both sides.
-Make 'y' the subject by collecting like terms and moving everything to the right, e.g. y = ...
-Slope is the number in front of x.
-Find y-intercept by letting x = 0 and solve the equation.
An experiment consists of spinning the spinner once. a: Find the probability of landing on a 2. b: find the probability of landing on a 1. c: Is landing in each section of the spinner equally likely to occur? Explain.
Answer:
points
Step-by-step explanation:
What is the area of the triangle?
Answer:
10
Step-by-step explanation:
1/2×(-2-(-7))×(6-(-4))