Answer:
1) dA/dt = -21 cm²/s and Area is decreasing
2)dP/dt = 0 and perimeter is constant
3) dD/dt = 21/13 cm/s and diagonal is increasing
Step-by-step explanation:
We are given that;
length l of a rectangle is decreasing at a rate of 3 cm/sec.
Thus, dl/dt = -3 cm/sec
Also, the width w is increasing at a rate of 3 cm/sec. Thus;
dw/dt = 3 cm/sec
When l=5 cm and w=12 cm;
A) Area is given by the formula;
A = lw
The rate at which area is increasing is;
dA/dt = l(dw/dt) + w(dl/dt)
Plugging in the relevant values;
dA/dt = 5(3) + 12(-3)
dA/dt = 15 - 36
dA/dt = -21 cm²/s
This is less than 0.thus, A is decreasing.
B) Formula for perimeter is;
P = 2l + 2w
rate of change of perimeter is;
dP/dt = 2(dw/dt) + 2(dl/dt)
Plugging in the relevant values, we have;
dP/dt = 2(-3) + 2(3)
dP/dt = 0
Thus,Perimeter is constant
C) the length of the diagonal of a rectangle is given by;
D = √(w² + l²)
Rate of change of diagonal is;
dD/dt = [2w(dw/dt) + 2l(dl/dt)]/(2√(w² + l²))
2 will cancel out in numerator and denominator to give;
dD/dt = [w(dw/dt) + l(dl/dt)]/(√(w² + l²))
Plugging in the relevant values gives;
dD/dt = [12(3) + 5(-3)]/(√(12² + 5²))
dD/dt = (36 - 15)/13
dD/dt = 21/13 cm/s
This is greater than 0.
Thus, diagonal is increasing.
What is the value of |5| - | -5| - (-5)? The solution is
Answer:
5
Step-by-step explanation:
when we simplify it we get 5-5+5 which equals 5
A family went to a baseball game. They spent $25 to park the car in a parking lot and $24 per ticket. Which equation represents x, the total number of people going to the baseball game if the family spends y, $145 total?
Profit is the amount of money that remains after all expenses of a project have been paid. The year has just ended, and Ajax Construction's owner is anxious to find out if the company had a profitable year. The company was awarded five contracts totaling $7,435,000. The costs associated with each project were: Project 1: $1,245,000 Project 2: $985,689 Project 3: $1,723,000 Project 4: $2,567,054 Project 5: $633,768 How much profit did the company earn?
Answer:
the Profit earned by the company is $280,489
Step-by-step explanation:
Total Cost of 5 projects awarded = $7,435,000
Cost of Project 1 = $1,245,000
Cost of Project 2 = $985,689
Cost of Project 3 = $1,723,000
Cost of Project 4 = $2,567,054
Cost of Project 5 = $633,768
We need to find the profit earned by the company.
First we need to find Total cost spent on all 5 projects.
It can be found by adding cost spent on all projects.
Total cost spent on all 5 projects = Cost of Project 1 + Cost of Project 2 + Cost of Project 3 + Cost of Project 4 + Cost of Project 5
Total cost spent on all 5 projects = $1,245,000+ $985,689 + $1,723,000+ $2,567,054 + $633,768
Total cost spent on all 5 projects = $7,154,511
Now we can calculate profit earned using formula:
Profit earned = Total Cost of 5 projects awarded - Total cost spent on all 5 projects
Profit earned = $7,435,000 - $7,154,511
Profit earned = $1,280,489
So, the Profit earned by the company is $280,489
-10x + 3y = 34
y = -8x
Answer
Step 1: Simplify both sides of the equation.
−10x + 3(−8x) = 34
−10x + −24x = 34
(−10x + −24x) = 34 (Combine Like Terms)
−34x=34
Step 2: Divide both sides by -34.
x=−1
Answer:
x=−1
So the pair of coordinates for your answer is (-1, 8)
Car Town
The cost of
renting a car
from us is just
$19.25 per day!
Write an equation for this situation.
y=9.75x
y=9.5x
y=19x
y=19.25x
Heeeeeeelp pleaaaaaaseeee
What’s is the slope?
Answer: 1/2
Step-by-step explanation:
y=1/2x-3
Identify a diameter of circle E.
Answer: B) HI
Step-by-step explanation:
х
(a) In the scale model, the length of the table is 9
centimeters. What is the length of the real table?
inches
Answer:Use the map of Maine to estimate the distance between the towns of China and New ... Since there are 4.5 centimeters between China and New Sweden, we can use a ... The scale model is a model of an object with dimensions that are in ... The child's picnic table is 22 inches tall, and the adult picnic table is 33 inches tall.
Step-by-step explanation:
Which number has a 3 that is 1/10 the value of the 3 in 14.37 ?
Answer:
0.3
Step-by-step explanation:
Hi if i have 8,000 saving for 12,000 how much more do i need?
Answer: 4,000
Step-by-step explanation: 12,000 - 8,000 = 4,000 Hope it helped!! :)
Jeff's father is planning to open a savings account to pay for Jeff's college education. He has found a bank that will pay 5 percent interest compounded daily. How much will he need to deposit initially so that in 14 years the balance will be $199,000?
Answer:
P = $183.14
Step-by-step explanation:
Given:
Rate of interest = 5% daily =0.05
Number of year = 14
Balance = $199,000
Computation:
Assume;
Number of days in a year = 365
199,000 = p[1+(0.05/365)]¹⁴⁽³⁶⁵⁾
199,000 = p[1+(0.001369)⁵¹¹⁰
199,000 = p[1086.59]
P = $183.14
Solve the following equation to determine the value of x: 3x + (x + 10) + 5x + (2x + 2) = 56
Answer:
I think x = 4.
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x + x +10 + 5x + 2x + 2 =56
(3x + x + 5x + 2x) + (10 + 2) = 56 (Combine Like Terms)
11x + 12 = 56
11x + 12 = 56
Step 2: Subtract 12 from both sides.
11x + 12 − 12 = 56 − 12
11x = 44
Step 3: Divide both sides by 11.
11x/11 = 44/11
x = 4
Which fraction and decimal forms match the long division problem? A. B. C. D.
Answer:
C 4/15 and 0.266 repeating
Step-by-step explanation:
I used a calculator
A taxi hurries with a constant speed of 38 miles per hour. How long will it take to travel a distance of 95 miles? O A. 40 minutes B. 13 minutes OC. 2.5 hours OD. 1.5 hours
Number 15. Solve for x
is 33 prime or composite Explain
Answer:
33 is composite
Step-by-step explanation:Because its factors are 1, 3, 11, 33
Help guys, I’m sure it’s easy for y’all
Answer:
(x, y) -------- ( -x,-y)
Rule : Rotation center (0,0) , angle of rotation 180° or -180°
Step-by-step explanation:
The vertices of the object and image have coordinates at ;
D(-4,2), --------D'( 4,-2 ),
E (-1,3), --------E'( 1,-3 ),
F (-1,-3),--------F'(1,3),
G (-3,-4),------G'( 3,4 ),
You notice that after the rotation ;
( x, y )-------change to (-x,-y),
This rule is rotation center origin angle 180°
Write an equation in slooe intercept form for the line that is parallel to y=-4x-3 and passes through the point (-2, 4).
Answer:
y=-4x-4
Step-by-step explanation:
m=-4
point(-2,4)
y-4 = -4 (x- (-2) )
y-4 = -4 (x+2)
y-4 = -4x -8
y = -4x -4
Step-by-step explanation:
we are going to use quadratic equation for this particular question . so now we are going to change the signs i.e from negative to positive or from positive to negative(-2 will turns to +2) nd +4 will turns to-4)
therefore, (x+2)(x-4) then we na expand the bracket x(x-4)+2(x-4)
x square -4x+2x-8
therefore the equation is nothing but x square-2x-8
Imagine that you are of traditional college age and you apply for a direct marketing position, and in the interview for the position, you are told that you look to young for the position. You have been discriminated against. This is a violation of:___________
Answer:
when grounds intersect.
Step-by-step explanation:
Analyzing the information related to the question above, it is possible to identify that the candidate for the direct marketing position suffered a violation when the grounds intersect.
It is correct to state this on the basis that the candidate was of traditional university age, but in the interview it is said that young people are sought for the position.
This type of discrimination can occur when the individual is discriminated against due to overlapping of several reasons, in the case of the candidate he was seen as a person older than he appeared to be, even though he was a requested age.
Does the point (8,0) lie on the line represented by 3x + 2y = 16?
O True
False
Answer:
false
Step-by-step explanation:
(0,8) is on the line, not (8,0) :)
A function is graphed below.
Which of the following represents the range of the function?
Answer:
el ranho de algo que esm ansgwne
What is the purpose of the periodic interest rate? (2 points)
a for borrowers to compare the rates between different loans
b for lenders to compare the interest rates between different investments
c to determine the amount of interest charged during a specific time frame
d to determine the minimum payment of a credit card
Answer:
The Answer is to determine the amount of interest charged during a specific time frame
Step-by-step explanation:
Choose the equation that represents the asymptote of the graph f(x) = 2^x +3.
y = 0
y = 3
x = 0
x = 3
Answer:
x = 0Step-by-step explanation:
The horizontal asymptote occurs at x = 0, Hence the equation that represents the asymptote of the graph is at x = 0
f(x) = 2^x +3.
0 = 2^x +3.
2^x +3. = 0
2^x = -3
log 2^ x = log(-3)
x log2 = log(-3)
x = log(-3)/log 2
Hence the required function is when x = 0
PLEASE HELPPPPP
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $208.34
Markdown: 72%
what is the sale price
There are 40 marbles in a bin and 25% of the marbles are red how many in the bin are red
Answer:
10 marbles
Step-by-step explanation:
25% * 40= 1000
1000/100=10
=10 marbles
y ≥ 12x – 1
y < 43x – 2
Answer:
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
Step-by-step explanation:
Use the equation and given point to answer the questions below. The equation of line a is y=12x−1, and it passes through point (6,2).
Quadrilateral CARD is similar to quadrilateral SNOW.
4 mm
13 mm
15 mm
6 mm
Sim
What is the length of SW in millimeters?
Answer:
13 I think if i´m right please mark me brainliest please thank you and have a great day
Step-by-step explanation:
PLZZZ HELP I NEED NOTE ABOUT UNDERSTANDING PERCENTS ON EDGE2020
50 POINTS AND BRAINLIEST FOR FIRST ANSWER
Answer:
A.
Step-by-step explanation:
^^^^::;:;;^^^^^^^^^^^^^^^^^^^^^^^^^^^^
How many moles are in 4.23 x 1024 formula
units of NaCl
Answer:
mol Fe3O4 6.022 x 1023 formula units Fe3O4 = 1.20 x 1024 formula units Fe3O4. 1 mol ... a-How many moles of sodium chloride does the can of salt contain?
Step-by-step explanation:
There are approximately 7.035 moles of NaCl in 4.23 x 10²⁴ formula units of NaCl.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
An expression is 4.23 x 10²⁴
To determine the number of moles of NaCl in 4.23 x 10²⁴ formula units of NaCl:
We need to use Avogadro's number, which is defined as the number of particles (such as atoms, molecules, or ions) in one mole of a substance. Avogadro's number is approximately 6.022 x 10²³ particles per mole.
To convert the given number of formula units of NaCl to moles, we divide by Avogadro's number:
Number of moles of NaCl = (4.23 x 10²⁴ formula units of NaCl) / (6.022 x 10²³ formula units/mol)
Number of moles of NaCl = 7.035 moles (rounded to three decimal places)
Therefore, the required value is 7.035 moles.
To learn more about multiplication;
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