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.
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6. In Rectangle DEFG DE=7. EF=3 FG = 7, and DG = 3
6
In Rectangle MNOP, MN=7, NO = 3. OP=7, and MP=3
Can Rectangles DEFG and MNOP be classified as similar, congruent
both or neither? Explain
Answer:
5
Step-by-step explanation:
5x+y=7
20x+2=y
What does x=?
What doesy=?
Answer: y = 6 x = 0.2
Step-by-step explanation:
5x+y=7
20x+2=y
re-write one
5x + y = 7 OR y = 7 - 5x
substitution
20x + 2 = 7 - 5x
20x + 5x = 7 - 2
25 x = 5
x = 5/25
x = 0.2
now for finding y
y = 7 - 5x
y = 7 - 5(0.2)
y = 7 - 1
y = 6
A square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches. The area of the resulting rectangle is 6o in 2 what was the area of the
Answer:
area of the original square = 36 in²
Step-by-step explanation:
given data
one side is increased = 9 inches
other side is decreased = 2 inches
area of the resulting rectangle = 60 in²
solution
we consider here x as the length of any one side
and
longer side of the resulting rectangle = x + 9
and
the shorter side x - 2
so that area of this rectangle is (s+9) × (s-2) = 60 in²
standard form of equation is x² + 7x - 18 = 60 .....................1
it will be
x² + 7x - 78 = 0
(s+13) (s-6) = 0
so that here x = -13
and x = 6
here we Discard x = -13 because the side length cannot be negative.
so x = 6
and area of the original square = 36 in²
What is the solution to the system of equations below?
X+ 3y = 15
and 4x+ 2y = 30
O (6,3)
O (3,6)
O (7,-6)
O (-6, 7)
Answer:
(6,3)
Step-by-step explanation:
Here is the system of equations:
x+3y=15
4x+2y=30
Since we have x with a coefficient of 1 in the first equation, let's use substitution to solve this system.
In the first equation, subtract 3y from both sides
x=-3y+15
now substitute -3y+15 as x in the second equation, and solve for y
4(-3y+15)+2y=30
do distributive property
-12y+60+2y=30
combine like terms
-10y+60=30
subtract 60 from both sides
-10y=-30
divide by -10
y=3
Now, substitute y as 3 into either one of the equations to solve for x.
For example, let's use x=-3y+15
x=-3(3)+15
multiply
x=-9+15
x=6
The answer is x=6 and y=3. As a point it's (6,3)
Hope this helps!
Romeo paid 380.75 in car repairs the sales tax is 7.5%. What is the total that Romeo has to pay
Step-by-step explanation:
Answer: $380.75x0.075%=28.55625 28.55625+380.75%-D409.30625 $409.30625 $409.31 Answer: $409.31
Toshеlle wants to take strength training classes at the
community center. She has to pay a one-time enrollment fee of $25 to join the
community center, and then $45 for each class she wants to take. Write an
equation in slope-intercept form for the cost of taking x classes.
Answer:
I would say y=45x+25
I’m doing the same workbook page
(If this is wrong I’m sorry)
Hope this helps
Have a great day/night
I need help, I don't quite understand
Answer:
1
Step-by-step explanation:
so we have:
f+2>5 2 goes the other side, so
f>5-2
f>3
f+4<9 4 goes to the other side, so
f<9-4
f<5
we have two inequality
f>3
f<5
f belongs (3,5), we have only one value for this, it is 4
Helpppp pllzzz & thx
In circle B, find x if m A = 3x + 9 and m B = 8x – 4.
The value of x is 11.
Central Angle Theorem :It states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points.
From given figure, [tex]A=3x+9,B=8x-4[/tex]
[tex]\angle B=2\angle A\\\\8x-4=2(3x+9)\\\\8x-4=6x+18\\\\8x-6x=18+4\\\\2x=22\\\\x=22/2=11[/tex]
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Simplify the following.
–(32)2
Answer:
-64
Step-by-step explanation:
If i'm not mistaken and this is times then it is just
-32 times 2
which is -64.
-
Have a wonderful day and best of luck!
PLEASE HELP FAST ( i will give brainliest)
Answer:
Step-by-step explanation:
60+30=90
180-90=90
60+30+90=180
so the x is 90
Answer:
x=3.5 if rounded if not than 3.4
Step-by-step explanation:
The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?
It could be 190 because its a half measure
 this one is really hard
Answer:
142
Step-by-step explanation:
opposite angle theorem
Answer:
D. 142
Step-by-step explanation:
They are vertical angles which are always equal
please help me almost done
Answer:
x = -8
<XCE = 30
Step-by-step explanation:
Remark
In any question like this, there are 8 possible answers. Of the 8, 4 are acute angles and 4 are obtuse. So any pair are either equal to each other, or they are supplementary. In this case the two given angles are equal.
We have a little bit of both in this question.
Solution
3x + 174 = - 7x + 94 Alternate exterior angles. Add 7x to both sides.
3x+7x +174 = 94 Combine
10x + 174 = 94 Subtract 174 from both sides
10x = 94 - 174
10x = - 80 Divide by 10
x = - 80/10
x = - 8
===================
Check
3x + 174 = -24 + 174 = 150
-7x + 94 = -7*-8 + 94
-7x + 94 = 56 + 94 = 150
<XCE
<XCE = 180 - (3x + 174)
<XCE = 180 - (-24 + 174)
<XCE = 180 - (150)
<XCE = 30
While on a business trip to Brookfield, Haley treated her co-workers to a meal that cost $50. Haley knew that when the bill came, she would need to pay Brookfield sales tax of 14% and would want to leave an 18% tip on the original $50. Including tax and tip, how much did Haley's meal cost?
Answer:
$66
Step-by-step explanation:
The meal cost $50 without taxes.
The cost of tax:
$50*%14= $7
so she will pay a $7 tax
Also, she wants to tip %18 of the original $50 so:
$50*%18= $9
so she will tip $9
$50 + $7 + $9 = $66
Twenty years ago, James made a deposit of $13,000.00 into an account. After twenty years, the account had earned $10,400.00 in interest. What simple
interest rate did the account earn?
Answer:
Use the information given to write an equation in standard form.
Slope is -3, and (0, -4) is on the line.
Step-by-step explanation:
Which of the following is not a geometric tool?
A.Compass
B.Pen
C.Protractor
D.Set Squares
Answer:
C. Protractor
Answer:
A
Step-by-step explanation:
A compass is for directions.
Help me please. I'll give Brainliest.
Please helpoppplllll mei need to complete this I will give brainly
Answer:
(5,-6) I think
Step-by-step explanation:
A publishing company creates a book for young children. To find the number of pictures on the page, the book says to multiply the page number by 3 and add 1. She discovers this pattern:
Which would best complete the pattern?
A. 4 x 3 = 12, 4 + 12 = 16, 16
B. 4 x 3 = 12, 12 + 1 = 13, 13
C. 4 x 3 = 12, 12 = 3, 3
D. 4 + 3 = 7, 7 x 3 = 21, 21
Answer:
B
Step-by-step explanation:
B is the only choice that has both all of the steps, and all of the steps in the right order.
Answer:
21
Step-by-step explanation:
Which equation represents the pattern in the table?
La Vasha noticed that she caught six pigeons for every turtle when she played Pocket Monster
Walk. If LaVasha caught 102 pigeons, how many turtles did she catch?
Answer:
She has 17 turtles
Step-by-step explanation:
You have to divide 102 by 6 which equals 17.
The system of equations has .
Answer:
A System of Equations has two or more equations in one or more variables Many Variables So a System of Equations could have many equations and many variables.
Step-by-step explanation:
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.
HELP ASAP PLEASE!!
what is the distance (in units) between points C and D? round your answer to the nearest hundredth.
1) 4.54 units
2) 5.00 units
3) 5.83 units
4) 34.00 units
Answer:
2
Step-by-step explanation:
Plzz help me to find coefficient in binomial theorem (25 points)
Denote x2 by y.
(x2-3)7=(y-3)7
This is a binomial expansion in y, and you want the coefficient of y4 because y4=x8
You have 7 terms of (y-3) in (y-3)7. To get the fourth power of y, you need to choose y from four of the terms. The number of ways you can do this is the combinations of 7 things taken 4 at a time. This is:
7!/(4!3!)=35
So, the coefficient of x8 in the given expansion will be 210.
HOPE IT HELPS
THANK YOU
The base of a parallelogram is 6 ft more than the height. If the area of the parallelogram is 55 ft^2, what are the measures of the base and the height?
Answer:
Height = 5 ft
Base = 11 ft
Step-by-step explanation:
The area of a parallelogram is
Base × Height
From the question:
The base of a parallelogram is 6 ft more than the height.
Base = 6ft + h
If the area of the parallelogram is 55 ft^2,
what are the measures of the base and the height?
This is calculated as:
55 ft² =( 6 + h ) × h
55 = 6h + h²
h² + 6h - 55 = 0
h² +5h - 11h - 55 = 0
h(h + 5) - 11(h + 5) = 0
(h + 5)(h - 11) = 0
h - 11 = 0
height = 5ft
Base = 6 + h = 6 + 5
Base = 11ft
The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?
Answer:
The inequality =
106 - 4x ≥ 70
The number of weeks =
9 weeks
Step-by-step explanation:
The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?
Let the number of weeks for Casey's dog to lose for 4 pounds be represented as: x
The goal weight = 70 Ibs
Hence:
70 Ibs = 106Ibs - 4Ibs ×x
106 - 4x ≥ 70
4x ≥ 106 - 70
4x ≥ 36
x ≥ 36/4
x ≥ 9 weeks
It would take 9 weeks for Casey's dog to lose 4 pounds per week and weigh 70 Ibs
Therefore:
The inequality =
106 - 4x ≥ 70
The number of weeks =
9 weeks
The expression (2x^2)^3 is equivalent to _____. ^this is for to remind that the 2 and 3 are exponents
a.6x2
b.6x5
c.8x6
Answer:
c
Step-by-step explanation:
(2x²)³ = 2³(x^(2×3))
=2³x⁶
=8x⁶
I need help on this question
Answer:
X^2+13x+40=area
Step-by-step explanation:
So its
(x+8)*(x+5)
Now solve
Use FOIL
x^2+5x+8x+40
Now combine
x^2+13x+40
There you have it
question:
solve the first equation for Y
2x+y=5
2y=2x-8
answer choices:
a) y=-2x+5
b) y=2x+5
c) y=2x-5
d) y=x-4
e) y=2x-8
(i dont understand it help)
Answer:
(c) y = 2x - 5
Step-by-step explanation:
y=2x+y=5
subtract 2x from both sides of the equation
the answer is C
i don’t understand help
Answer:
rational as it can be expressed as the quotient of two integers
Answer:
that is a rational number
Step-by-step explanation:
A rational number is a number that can be express as the ratio of two integers. ... Likewise, any integer can be expressed as the ratio of two integers, thus all integers are rational.
Example: 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.) All integers are rational numbers.
An irrational number is real number that cannot be expressed as a ratio of two integers. ... The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. Many square roots are also irrational since they cannot be reduced to fractio
