the length of a rectangle is given by 2t+1 and its height is t^(1/2), where t is time in sec. Find the rate of change of the area with respect to time

Answers

Answer 1
A=(2t+1)t^1/2 differentiate both sides w.r.t t to get the solution

Related Questions

Choose the method of pay that would result in the most earnings for one month on sales of $73,620. a. Straight commission of 6% on all sales. b. Monthly salary of $3,000 plus 2% commission on all sales. c. Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that. d. Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.

Answers

a. 0.06(73,620) = 4417.20 pay on straight commission of 6%
b. 3000 + 0.02(73,620) = 3000 + 1472.40 = 4472.40 (salary + 2% com)
c. 0.04(50,000) + 0.09(73620 - 50,000) = 2000 + 2125.80 = 4125.80
d. 0.05(35,000) + 0.07(73620 - 35,000) = 1750 + 2703.40 = 4453.40

most earnings would be : B. monthly salary + 2% commission

The method of pay that results in the most earnings is the second method of pay

In order to determine which method of pay would result in the most earnings ,  the value of each method would be determined

Value of the first option

6% commission on all sales = 6% x  $73,620.

0.06 x  $73,620. = $4,417.20

Value of the second option

Monthly salary of $3,000 plus 2% commission on all sales =  $3,000 + (2% x  $73,620)

$3,000 + (0.02% x  $73,620)

= $3000 + $1472.40

= $4472.40

Value of the third option

Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that.

= (4% x $50,000) + (9% x $23,620)

= $2000 + $2125.80

= $4125.80

Value of the fourth option

Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.

= (5% x$35,000) + (7% x $38,620)

= $1750 + $2703.40

= $4,453.40

A similar question is solved here: https://brainly.com/question/17181309?referrer=searchResults

If Zelda has a 300 inch roll of binding for a quilt and the quilt must be 84 inches long how wide can she make it

Answers

So first you would want to multiply 84 by 2 because that would let you know how many inches you are using right now. 84 x2 = 168 now that you know you are already using 168 inches you must subtract that from 300 to find out how much you have left 168 - 300 = 132 you now have to divide that by 2 to get how long one side is 132 divided by 2 is 66. She can make it 66 inches wide.

what is 14 9/100 as a decimal

Answers

.09 or 0.09

The place after the decimal is the tenths place, the next place is the hundredths place
.9 = 9/10
.09 = 9/100
.009 = 9/1000

generate the first five terms in the sequence using the explicit formula. yn=-5n-5

Answers

For this you need to note that "n" represents position of sequence.
y1 is y on position 1 and so on. Sequence goes: y1,y2,y3,y4... and so on

So all you have to do is to implement values 1,2,3,4,5 for n and get 5 members of sequence. (start from 0 if your n starts from 0)

y0 = -5
y1 = -5-5 = -10
y2 = -15
y3 = -20
y4 = -25
y5 = -5*5 - 5 = -30

The first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are: -10, -15, -20, -25, -30.

To generate the first five terms in the sequence using the explicit formula [tex]y_n[/tex]  = -5n - 5,

we substitute the values of n from 1 to 5 into the formula.

For n = 1:

[tex]y_1[/tex]= -5(1) - 5 = -10

For n = 2:

[tex]y_2[/tex] = -5(2) - 5 = -15

For n = 3:

[tex]y_3[/tex] = -5(3) - 5 = -20

For n = 4:

[tex]y_4[/tex] = -5(4) - 5 = -25

For n = 5:

[tex]y_5[/tex] = -5(5) - 5 = -30

Therefore, the first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are:

-10, -15, -20, -25, -30.

Learn more about Sequence here:

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what is 1626 divided by 12 as a mixed number

Answers

It would be: 1626 / 12 = 135.5 = 135 1/2

So, your final answer is 135 1/2

Hope this helps!

Answer:

1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Step-by-step explanation:

To find : What is 1626 divided by 12 as a mixed number ?

Solution :

Writing 1626 divided by 12 in a fraction from,

[tex]\frac{1626}{12}[/tex]

Writing fraction in simpler form by reducing with common factors,

[tex]\frac{1626}{12}=\frac{2\times 3\times 271}{2\times 2\times 3}[/tex]

[tex]\frac{1626}{12}=\frac{271}{2}[/tex]

Writing [tex]\frac{271}{2}[/tex] in mixed fraction by dividing 271 by 2,

[tex]271=135\times 2+1[/tex]

i.e. [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Therefore, 1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

A bag of chips contains 145 calories per serving. Each bag of chips contain 3 servings.

How many calories are in 2 bags of chips?

A.145 calories

B.150 calories

C.435 calories

D.870 calories

Answers

it says that 1 bag contains 3 servings of 145 calories. you need to multiply 145 times 3, which equals to 435. then since it two bags containing 435 calories in 3 servings you add the 435 + 435 which equal 870

Answer:

870 calories Option D.

Step-by-step explanation:

A bag of chips contains calories per serving = 145

If each bag contains servings = 3

so total calories per bag = 3 × 145

                                         = 435

Now we have to calculate the total servings in 2 bags.

Number of calories in 1 bag = 435

Therefore, number of calories in 2 bags = 435 × 2

                                                                   = 870 calories

Option D. 870 calories is the answer.

which is bigger 40% of 210 or 1/4 of 320

Answers

Final answer:

To find out which is bigger, we calculate 40% of 210 and 1/4 of 320. 40% of 210 is greater than 1/4 of 320.

Explanation:

To find out which is bigger, 40% of 210 or 1/4 of 320, we need to calculate both values.

First, 40% of 210 can be calculated by multiplying 210 by 0.4. This gives us 84.

Next, 1/4 of 320 can be calculated by dividing 320 by 4. This gives us 80.

Therefore, 40% of 210 is greater than 1/4 of 320.

Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and x are related by the equation.

What is the change in the total cost for each book printed?

What is the cost to get started (before any books are printed)?

Equation: y=1250+25x

Answers

What is the change in the total cost for each book printed?
$25
What is the cost to get started (before any books are printed)?
$1250

Find f if f"(theta)=sin (theta) + cos (theta), f(0)=3, and f'(0)=4

Answers

replace the x with theta :

f''x = sin x + cos x

f'x  = - cos x  + sin x + c

f'0 = -1 + 0 + c =4

c = 5

f'x = -cos x + sin x + 5
fx = -cos x  - sin x  + c
f0  = -1  + c = 3

c = 4

fx = -cos x - sin x + 4

Hope this helps

Elsie pays $21.75 for 5 student tickets to the fair what is the cost of each student ticket

Answers

I believe your answer would be 4.35
If it's 21.75 in total, then to find 1 ticket you'd divide by 5:
2 ÷ 5 = 0
21 ÷ 5 = 4 (remainder 1)
17 ÷ 5 = 3 (remainder 2)
25 ÷ 5 = 5
So it would cost $4.35 each, hope this helps!

An object with a mass of 6.3 kg has a mass of 7.1newtons applied to it, what is the resulting acceleration of the object

Answers

Since, a = F (net) / m (net)
Therefore a = 7.1 / 6.3 = 1.13 m/sec^2

The resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

To find the resulting acceleration of an object when a force is applied to it, you can use Newton's second law of motion, which states:

F = ma

Given that the force F = 7.1 Newtons and the mass m = 6.3 kg, we can rearrange the formula to solve for acceleration:

[tex]\[ a = \frac{F}{m} \]Substitute the given values:\[ a = \frac{7.1 \, \text{N}}{6.3 \, \text{kg}} \]Now, divide to find the acceleration:\[ a = \frac{7.1}{6.3} \, \text{m/s}^2 \]\[ a = 1.127 \, \text{m/s}^2 \][/tex]

So, the resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

Complete question:

An object with a mass of 6.3 kg has a force of 7.1 Newtons applied to it. What is the resulting acceleration of the object?​

What is the determinant of an identity matrix?

Answers

Answer:

The determinant of an identity matrix is always 1.

Step-by-step explanation:

Given : An identity matrix.

We have to find the determinant of an identity matrix.

Consider an identity matrix,

Identity matrix is a matrix having entry one in its diagonal and  rest all entries are zero.

Let us consider a 2 × 2 identity matrix,

[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

We know determinant of a  2 × 2 matrix

[tex]I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

is given by

D = ad - bc

Thus, here a = 1 , b = 0 , c= 0 d= 1

Thus, D = 1 - 0 = 1

Thus, The determinant of an identity matrix is always 1.

Which of these statements is punctuated properly?


"You're kidding she said". You are not going in there.

"You're kidding" she said "You are not going in there."

"You're kidding," she said. "You are not going in there."

"You're kidding, she said. You are not going in there."

Answers

the third one "you're kidding," she said. "you are not going in there ."

Find the product.

(-2x ^2) ^3 -3x

Answers

Final answer:

To find the product of (-2x^2)^3 and -3x, first calculate the cube of -2x^2 (-8x^6), then multiply it by -3x to obtain 24x^7.

Explanation:

The student has asked to find the product of two expressions, (-2x^2)^3 and -3x. To solve this, we first calculate the cube of -2x^2, which is -8x^6, then we multiply this result by -3x to find the final product.

So, let's perform these two steps:

Cube of -2x^2: (-2x^2)^3 = (-2)^3 × (x^2)^3 = -8 × x^6 = -8x^6

Multiplication by -3x: -8x^6 × -3x = 24x^7

Therefore, the product is 24x^7.

The polynomial given below has _____ root(s).

3x2 - 8x + 4

A. two positive
B. two negative
C. two complex
D. one positive and one negative

Answers

3x²-8x+4=0
(3x-2) (x-2)=0
x=2/3 ,  x = 2
Hence, the polynomial has two positive roots.
Option A is the correct choice.

2 times the sum of a number and 4 is no more than three times the sum of a number and 7 decreased by 4

Answers

[tex]2(x+4) \geq 3((x+7)-4) \\ 2x+8 \geq 3(x+7)-12 \\ 2x+8 \geq 3x+21-12 \\ 2x+8 \geq 3x+9 \\ 2x \geq 3x+1 \\ -x \geq 1 \\ x \leq -1[/tex]

Find the amount of simple interest earned after 2 years on $480 invested at a 7% annual interest rate?

Answers

Formula for the simple interest is:
I = P · r · t,
where:  P = $480,  r = 7% = 0.07, t = 2 years;
I = 480 · 0.07 · 2 = $67.20
Answer:
The amount of simple interest is $67.20

Using the simple interest formula, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

Finding Simple Interest on an Investment

To calculate the simple interest earned after 2 years on a $480 investment at a 7% annual interest rate, you can use the simple interest formula: Interest = Principal times Rate times Time.

The principal (P) is the initial amount of money, which in this case is $480. The rate (R) is the annual interest rate expressed as a decimal, so 7% becomes 0.07. The time (T) is the number of years the money is invested or borrowed, which is 2 years in this scenario.

Using the simple interest formula:

Interest = 480 times 0.07 times 2

Interest = 33.6 times 2

Interest = $67.20

Therefore, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

Amounts of trade discounts are not fixed? True or False ...?

Answers

True. A trade discount is the amount by which a manufacturer reduces the retail price of a product when it sells to a reseller, rather than to the end customer. The trade discount is determined by quantity and market and is set at a rate by the manufacturer. 

Trade discounts are not fixed; they are true to vary based on several factors including order volume, buyer-seller relationships, and industry norms. They are a dynamic component of economic transactions within the complex trade environment and are influenced by market interactions and broader economic principles.

The statement "Amounts of trade discounts are not fixed" is true. Trade discounts can vary greatly and are typically influenced by a variety of factors including the volume of the goods ordered, the relationship between the buyer and seller, and the industry standards.

For instance, when businesses deliver larger lots, volume discounts may be offered, which reflect the lower costs of providing goods in bulk rather than differences in willingness to pay. This variation in trade discounts ensures that each transaction is adjusted to meet the precise needs of both the buyer and seller, depending on the specific circumstances of the trade.

Moreover, the trade environment is complex and the interactions between buyers and sellers determine the gains from trade in an economy. These interactions depend on market structure, negotiation possibilities, and the mode of sale, such as retail or auction.

Consequently, trade discounts are part of a dynamic economic system where various elements such as free trade agreements, industry adjustments, transaction costs, and the unmeasured benefits of competition and product variety all play a role in shaping the final outcome.

3 out of 4 students surveyed in a school said they will vote for nuncio for class president predict how many of the 340 students in the school would vote for nuncio

Answers

340 * 3/4 because that's what the kids agreed to do

To predict the number of votes for Nuncio for class president, multiply 3/4 (or 0.75) by the total number of students (340), resulting in a prediction that 255 students would vote for Nuncio.

To predict how many of the 340 students in the school would vote for Nuncio for class president, we need to understand the proportion that we got from the survey. Since 3 out of 4 students said they would vote for Nuncio, this is the same as 75% or 0.75 when expressed as a decimal.

We then apply this proportion to the total number of students in the school:

Convert the fraction 3/4 to a decimal: 3 ÷ 4 = 0.75.

Multiply the total number of students by the decimal: 340 students × 0.75 = 255 students.

Therefore, we predict that 255 of the 340 students would vote for Nuncio for class president.


Select all situations that could be represented by a constant rate.
A) the number of cars manufactured per day at a factory
B) the speed of a toy rocket as it is launched straight into the air the number of
C) rotations per minute made by a fan
D) the population increase of a bacteria colony in a petri dish

Answers

C is the answer because rotations is the amount of times that can be calculated by 1 min since nothing can be change in 1 min and we can find the constant rate of rotations 100 % easy because of 1 min constant and no change
A and c can be right

Suppose that ln 2=a and ln3=b. Use properties of logarithms to write each logarithm in terms of a and b

ln0.5 ...?

Answers

The solution to the problem is as follows:

ln(0.5) could be written as ln(2) - ln(2) - ln(2) = a - a - a = -a 

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Use the stem and leaf plot shown to answer the following question.

Answers

16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46

37 is the upper quartile value

A comic book costs $3.99, including tax. It is marked up 45%. What is the final price of the comic book after it is marked up? $1.80 $4.44 $5.79 $6.15

Answers

$1.80

3.99 x 0.04 = 1.79
and you get 1.80 when you round it

the real answer is 5.79, the other person had had miscalculation

7/8,0.98,8/9 least to greatest

Answers

7/8

8/9

.98

hope this helps good luck

The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:

F = 9 over 5C + 32

Which of the following formulas correctly solves for C?

C = 5F − 32 over 9
C = 5 F over 9 − 32
C = 9 over 5(F − 32)
C = 5 over 9(F − 32)

Answers

The correct answer is ) C = 5 over 9(F − 32)

Answer:

The correct option is 4.

Step-by-step explanation:

The relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F is defined by the given equation.

[tex]F=\frac{9}{5}C+32[/tex]

We need to find the formula for C.

Subtract 32 from both the sides.

[tex]F-32=\frac{9}{5}C+32-32[/tex]

[tex]F-32=\frac{9}{5}C[/tex]

Multiply both sides by 5.

[tex]5(F-32)=9C[/tex]

Divide both sides by 9.

[tex]\frac{5(F-32)}{9}=\frac{9C}{9}[/tex]

[tex]\frac{5}{9}(F-32)=C[/tex]

The formula for C is [tex]C=\frac{5}{9}(F-32)[/tex].

Therefore the correct option is 4.

Find two consecutive whole numbers that /76 lies between.

Answers

76 lies between ,<  35 and 41 >

The cost of 5 dresses and 2 belts is $48. The cost of 3 dresses and 2 belts is $32. Find the cost of a dress and a belt. Let x denote the cost of a dress and y denote the cost of a belt.

Answers

For this Question use the substitution method.

5x+2y = $48 ------First Equation.
3x+2y = $32 ------ Second Equation

x= 48-2y/ 5 ( 48-2y divided by 5)

Put the value of x in the second equation.

3(48-2y/5)+2y = $32
 (144-6y/5) + 2y = $32
Take L.C.M 
144-6y+10y/5 = $32
144+4y = 32*5
144+4y = 160
4y = 160-144
4y = 16
y = 4
Now put the value of y in any equation.
5x+2(4) = $48
5x+8 = $48
5x = 48-8
5x = 40
x = 8
-------------------------
A Dress costs $8 and a belt costs $ 4.
Final answer:

By setting up a system of linear equations and solving for x and y, we find that the cost of a dress is $8 and the cost of a belt is $4.

Explanation:

To find the cost of a dress and a belt, we can set up a system of linear equations using the information given. Let x denote the cost of a dress and y denote the cost of a belt. We then have two equations:

5x + 2y = $48  (1)3x + 2y = $32  (2)

Subtract equation (2) from equation (1) to eliminate y:

5x + 2y - (3x + 2y) = $48 - $32

2x = $16

Now we can solve for x:

x = $16 / 2

x = $8

Now that we know the cost of a dress (x), we can substitute this value into equation (2) to find the cost of a belt (y):

3(8) + 2y = $32

24 + 2y = $32

2y = $32 - $24

2y = $8

y = $8 / 2

y = $4

Therefore, the cost of a dress is $8 and the cost of a belt is $4.

During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 132 ° F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T = -0.005x^2 + 0.45x + 125. Will the temperature of the part ever reach or exceed 132 ° F? Use the discriminant of a quadratic equation to decide.

A. no
B. yes

Answers

Answer: The answer saying YES, is WRONG, the CORRECT ANSWER IS NO.

Answer:

The answer is no

0.45^2-4(-.005)(125)=2.7025

so no it do not exceed

Step-by-step explanation:

The product of twenty-one negative integers is negative.
True

False

Answers

Answer: TRUE:
_____________________
It is TRUE that the product of 21 (twenty-one) negative integer is a negative number; because you are multiplying an ODD NUMBER of NEGATIVE INTEGERS.
________________________
The correct answer for the given statement above would be TRUE. It is true that the product of twenty-one negative integers is negative. Analyze this. If you multiply 2 negative integers, it gives you a positive integer. So, every 2 negative integers you multiply, the product will always be positive, and since the given is 21 negative integers, this would also give you a negative result. Hope this answer helps.

WILL UPVOTE!
Factor the expression.
36c^2 −121

Answers

Free yet powerful Solver Simplifier that Shows Work ... ... Step 2 : Trying to factor as a Difference of Squares : 2.1 Factoring: 36c2-121 ... Note : - AB + AB equals zero and is therefore eliminated from the expression....
the answer would be 2.1 according to this
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