Complete question
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)
Answer:
[tex]\frac{dx}{dt}=11.94m/min[/tex]
Step-by-step explanation:
From the question we are told that
Slant height [tex]z=29m[/tex]
Change in Vertical height [tex]\triangle y=7m/s[/tex]
Horizontal length [tex]x=21[/tex]
Generally in finding the distance form the top to the bottom of the wall it is mathematically given by
[tex]x^2+y^2=z^2[/tex]
[tex]21^2+y^2=29^2[/tex]
[tex]y^2=29^2+21^2[/tex]
[tex]y=35.81[/tex]
Generally solving for the differential equation is mathematically represented as
[tex]x^2+y^2=29^2[/tex]
[tex]2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0[/tex]
[tex]x*\frac{dx}{dt} +y*\frac{dy}{dt} =0[/tex]
[tex](21)*\frac{dx}{dt} +(35.81)*(-7) =0[/tex]
[tex](21)*\frac{dx}{dt} -250.64 =0[/tex]
[tex]\frac{dx}{dt}=\frac{250.64}{21}[/tex]
[tex]\frac{dx}{dt}=11.94m/min[/tex]
The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.
So, A right angle triangle is formed.
Since, the bottom of the ladder is 21 meters from the wall.
So, [tex]y=21[/tex]
Applying Pythagoras theorem,
[tex]x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20[/tex]
Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.
[tex]\frac{dx}{dt}=-7meter/min[/tex]
Differentiate below equation with respect to time.
[tex]x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.[/tex]
Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Learn more about Differentiation here:
https://brainly.com/question/14023950
f(x)=9/x , g(x) = x / x + 1
Answer
f(x)=9/x , g(x) = x / x + 1 = 9/2
Step-by-step explanation:
Need help asap please on these two
Answer: first one is a. (v = 1 2/3) the second on is c. (line up numbers at the decimal point)
Step-by-step explanation:
4. The length of a rectangle is one more than twice the width. The area is 105 in?.
Find the WIDTH of the rectangle. *
9514 1404 393
Answer:
7 in
Step-by-step explanation:
For width w in inches, the length is given as 2w+1. The area is the product of length and width, so we have ...
A = LW
105 = (2w +1)w
2w^2 +w -105 = 0
To factor this, we're looking for factors of -210 that have a difference of 1.
-210 = -1(210) = -2(105) = -3(70) = -5(42) = -6(35) = -7(30) = -10(21) = -14(15)
So, the factorization is ...
(2w +15)(w -7) = 0
Solutions are values of w that make the factors zero:
w = -15/2, +7 . . . . . negative dimensions are irrelevant
The width of the rectangle is 7 inches.
The circumference of a circle is 64. What is the radius of the circle?
please help me with this thankyou
Answer:
Area of the Rectangle is (length×breadth)
[tex]5 {x}^{5} {y}^{3} \times {(7 {x}^{3}y) }^{4} = 5 {x}^{5} {y}^{3} \times 2401 {x}^{12} {y}^{4} \\ = 12005 {x}^{17} {y}^{7} [/tex]
Third option is the right answer.
3 49 2
- + - x -
8 14 7
Show your working clearly
—————
(Fractions)
anyone please help asap!!! The theater holds 250 people last last nights performance was sold out, students under the age of 16 paid $2.50 per ticket, but everyone else in the theater paid four dollars. Last night show brought in $910 how many people were under the age of 16 and how many were older than 16 that went to the show?
Answer:
there were 60 people that are under 16 and 190 people above 16.
A baker used 48 cups of almond flour for a recipe. The ratio of cups of almond flour to cups of whole wheat flour that she used was 3 to 5. How many cups of whole wheat flour did the baker use?
Answer:
I have made it in above picture
Six rolls of fabric are used for making five dresses equally.
How much fabric is used for each dress?
Answer:
1.2 rolls
Step-by-step explanation:
6 rolls=5 dresses
1.2 rolls =1 dress
hope i helped:)
help please! due today!
If ,
[tex]\tt{z=-3+5i }[/tex] ⠀
so,
[tex]\overline{z}[/tex]=[tex]\tt{ -3-5i }[/tex]
Because,
In the argand plane ,[tex]\overline{z}[/tex] is the reflection of z in x-axis
Substitute y=-2x+5 into 2y=2x-8 and solve for x
(help me asap please)!!
Answer:
x = 3
Step-by-step explanation:
2y = 2x - 8
2(-2x + 5) = 2x -8
-4x + 10 = 2x - 8
+4x +4x
10 = 6x - 8
+8 +8
18 = 6x
divide both sides by 6
x = 3
Hope this Helps!!!
f (x) = -x2 + 164x - 64, f(x) = -4x2 - 10x + 84, f(x) = 3x² + 24.
Answer:
You need to ask a question for someone to answer it.
Are you looking for their derivatives?
-x² + 164x - 64 => -2x + 164
-4x² - 10x + 84 => -4x - 10
3x² + 24 => 6x
Indefinite Integrals?
-x² + 164x - 64 => -x³/3 + 82x² - 64x + C
-4x² - 10x + 84 => -4x³/3 - 5x² + 84x + C
3x² + 24 => x³ + 24x + C
Want them factored?
-x² + 164x - 64 => has no factors
-4x² - 10x + 84 => 2(2x - 7)(x + 6)
3x² + 24 => 3(x² + 8)
We can't ensure a proper answer if you don't ask the question.
What is the final amount if 588 is decreased by 3% followed by a 6% increase?
Give your answer rounded to 2 DP.
Answer:
604.58
Step-by-step explanation:
because hegarty says its 604.58
The expression 20a + 13c is the cost (in dollars) for adults and students to enter a science center. Find the total cost for 4 adults and 24 students.
Answer:
$392
Step-by-step explanation:
Given the expression :
Total cost = 20a + 13c
a = adult
c = student
The total cost for 4 adults and 24 students
a = 4 ; c = 24
Total cost :
20(4) + 13(24)
80 + 312
= $392
LOOK AT PICTURE look at picture
Answer:
-25.776
Step-by-step explanation:
-7.2
x 3.58
Multiply to get the sums and add them together to get your answer.
day 2 on still being stuck on this... this is due on Friday lol so please help 3
Answer:
It's 17
Step-by-step explanation:
1. 15 squared is 225
2. 8 squared is 64
3. 225+64=289
4. find the square root of 289
5. 17 is because when you square 17, you get 289.
P.S mark ar brainliest, rate 5 stars and hit that thanks button.
Could someone help me with 7-10
On Match each function with its graph
Answer:
c
Step-by-step explanation:
3 1/4 - 4 1/2 show your work
If I did the math correct, the answer is -1 1/4, i'll attach a ss in a second.
Algerba 1 (polynomials) plss help
Answer:
Step-by-step explanation:
the coefficient is the number that is multiplied by x² so is 17
the constant term is the one without any x ( it does not change when x changes) so is -13
Which is not a representation of the equation y = 0.5x - 2?
Select one: just look at the picture.
Answer:
D is incorrect so ur answer is D
Compare Marcella's possible earnings of Office Essentials t o her possible earning at Everything Office. If her goal is to earn $ 4,000, which company Marcella should choose ? Explain your reasoning. Show your /work
(DUE SOON I NEED HELP ASAP)
Answer:
Correct answers: Part A: Moe = 2500 + 125n and Meo = 2000 + 150n. Part B: oe: 12 machines; eo: 14 machines. Part C: 20 machines or higher.
PARCC evidence statement(s) tested: HS.D.1-1:
Solve multi-step contextual problems with degree of difficulty appropriate to the course, requiring application of knowledge and skills articulated in 7.RP.A, 7.NS.3, 7.EE, and/or 8.EE.
The evidence statement above references mainly Math Practice 4 in the Common Core:
[MP.4] Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. … By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
It may also reference other standards of mathematical practice, including MP.1 (make sense of problems and persevere in solving them), MP.2 (reason abstractly and quantitatively), and MP.5 (use appropriate tools strategically).
The question requires students’ prior understanding of the eighth-grade Common Core standard 8.EE.C, found under Expressions and Equations (analyze and solve linear equations and pairs of simultaneous linear equations), which states that they should be able to [EE.C.7] “solve linear equations in one variable” and [EE.C.8] “analyze and solve pairs of simultaneous linear equations.”
Note that the PARCC question referenced here simply uses understanding of these standards from eighth grade, considering this understanding to be securely-held knowledge. The PARCC question in Algebra 1 tests students’ ability to model with mathematics, as referenced in Math Practice 4.
Step-by-step explanation:
Help pls!! Find the value of x and m
Answer:
The answer's the third one listed.
Step-by-step explanation:
The equation to solve for x is:
6x + 16 + 10x - 6 + 90 = 180
16x + 100 = 180
16x = 80
x = 5
To solve for angle BCD, just substitute 5 for x
m = 10(5) - 6
m = 50 - 6
m = 44
A grocery store sells tangerines in 25kg bags. A customer bought 4 kg of tangerines for a school party. How many bags did he buy?1.Select allequations that represent the situation.
a.4⋅25=?
b.?⋅25=4
c.25÷4=?
d.4÷25=?
e.?÷25=
a parallelogram has a size of 8ft and 6ft with an area of 54 ft squared. what is the length of the altitude to the 8ft base
A. 6.75
B.9
C.24
D.27
Answer: may i see a picture then I can help
Step-by-step explanation:
please answer and fast i will mark brainliest
Answer:
B
Step-by-step explanation:
To get from 1 to 5, add 4.
To get from 3 to 7, add 4.
To get from 4 to 8, add 4.
Hope this helps!
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9, the length of T Q is 16, and the length of R Q is x.
What is the value of x?
12 units
15 units
20 units
24 units
Answer:
the actual answer is 20 units
Step-by-step explanation:
The value of x which is equal to length RQ is 20 units.
The given parameters;
Length of ST = 9 Length of TQ = 16Length of RQ = xFrom the given triangle we can apply similar triangle property as follows;
[tex]\frac{base \ of \ triangle \ SRQ}{hypotenuse \ of \ triangle \ SRQ} = \frac{base \ of \ triangle \ RTQ}{hypotenuse \ of \ triangle \ RTQ} \\\\\frac{RQ}{SQ} = \frac{TQ}{RQ} \\\\\frac{x}{(9 + 16)} = \frac{16}{x} \\\\x^2 = 25 \times 16\\\\x = \sqrt{25 \times 16} \\\\x = 5 \times 4\\\\x = 20 \ units[/tex]
Thus, the value of x which is equal to length RQ is 20 units.
Learn more about similar triangles here: https://brainly.com/question/11899908
If you know the answer could you please help me out I would really appreciate it thank you!!
Answer:
X=4 ; X minus two equals zero
Step-by-step explanation:
X minus two equals zero:
x-2=2
Add two to both sides:
x=4
0.110 is _____ than 0.450?
A. less
B. greater
C. equal
D. greatest
Which graph represents f(x) and the inverse f^-1(x)
Answer:
D
Step-by-step explanation:
The inverse or f⁻¹(x) of a function f(x) is the graph being reflected over the line y = x.
For A, f(x) is reflected over the x-axis.
For B, f(x) is rotated about a point.
For C, f(x) reflected over the y-axis.
And for D, f(x) is reflected over the line y = x.
So, the graph that represents f(x) and its inverse f⁻¹(x) is choice D.
Lucas bought some black socks and white socks each package of black socks contains six pairs each package of white socks contains four pairs Lucas but W packages of white socks and eight packages of black socks for a total a 56 pair of socks which equation could use also determine the number of packages of White Sox W Lucas bought?
Answer:
w = 2 He bought 2 packages of white socks
Step-by-step explanation:
6(8) + 4w = 56
48 + 4w = 56
4w = 8
w = 2
Check your work
6(8) + 4(2) = 56
48 + 8 = 56
56 = 56