write an integral that quantifies the change in the area of the surface of a cube when its side length quadruples from s unit to 4s units.

Answer:

5.2 hours

Step-by-step explanation:

To find the solution, you need to multiply Aretha's time by 1.6, since Neal takes 1.6 as long to run the marathon.

3.25 × 1.6 = 5.2

In other words, Neal takes 5.2 hours to run the marathon. Let me know if I can help you with anything else, 'kay?

Answer:

\(3 (1/3)^x\)

Step-by-step explanation:

i just graphed this in desmos graphing to verify. make sure when writing your answer you set 1/3 to the power of x and not just place the x next to the 1/3

Answer:

No

Step-by-step explanation:

2 = 3 inches

2x5=10

10 = 3x5 of 15 inches

so no and it would take 8 minutes to fill up the tub

The annual percentage yield (APY) to the nearest thousandth of a percent is approximately 4.642%.

To solve the given problem, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial investment)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

a. To find the amount after 4 years, we can substitute the values into the formula:

A = 28000(1 + 0.045/4)^(4*4)

Calculating inside the parentheses first:

A = 28000(1 + 0.01125)^(16)

Evaluate (1 + 0.01125)^(16):

A ≈ 28000(1.19235)

A ≈ $33,389.80

Therefore, the amount after 4 years is approximately $33,389.80.

b. To calculate the interest earned, we subtract the principal amount from the final amount:

Interest earned = A - P

Interest earned = $33,389.80 - $28,000

Interest earned = $5,389.80

The interest earned after 4 years is $5,389.80.

c. To find the amount after 1 year, we substitute the values into the formula:

A = 28000(1 + 0.045/4)^(4*1)

Calculating inside the parentheses first:

A = 28000(1 + 0.01125)^(4)

Evaluate (1 + 0.01125)^(4):

A ≈ 28000(1.045)

A ≈ $29,260

Therefore, the amount after 1 year is $29,260.

d. To calculate the interest earned after 1 year, we subtract the principal amount from the final amount:

Interest earned = A - P

Interest earned = $29,260 - $28,000

Interest earned = $1,260

The interest earned after 1 year is $1,260.

e. The annual percentage yield (APY) is a measure of the effective annual rate of return, taking into account the compounding of interest. To calculate the APY, we can use the formula:

APY = (1 + r/n)^n - 1

Where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, the annual interest rate is 4.50% (or 0.045) and the interest is compounded quarterly (n = 4).

Plugging in the values:

APY = (1 + 0.045/4)^4 - 1

Using a calculator or software to evaluate (1 + 0.045/4)^4:

APY ≈ (1.01125)^4 - 1

APY ≈ 0.046416 - 1

APY ≈ 0.046416

To convert to a percentage, we multiply by 100:

APY ≈ 4.6416%

The annual percentage yield (APY) to the nearest thousandth of a percent is approximately 4.642%.

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Answer:

x=4

Step-by-step explanation:

4(3x+3)=5(x+8) ------- Given

12x + 12 = 5x + 40

12x-5x= 40-12

7x = 28

x = 4

8x+8

Step-by-step explanation:

from the first you can see that there is a 3 in front of the x and if equal then 8 has to be in front of x as well

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Answer:

1) x = 30

2) x = 11.6

Step-by-step explanation:

1) 2x = 4x - 60   (vertical angles are equal)

subtract 4x from each side of the equation:

-2x = - 60

divide both sides by -2:

x = 30

2) 7x + 16 + 3x + 48 = 180°   (supplementary angles add up to 180°)

combine like terms:

10x + 64 = 180

subtract 64 from both sides of the equation:

10x = 116

divide both sides by 10:

x = 11.6

send a picture pls so I can help you

The difference between correlation and causation is that in causation one event is the cause of another, while in correlation the variables are just related.

These terms show the relationship between two variables; however, the type of relationship is different.

In causation, one variable is the cause and the other is the effect an example would be the number of lemonade cups sold and money collected.

On the other hand, in correlation, the variables are related but one does not cause the other. An example would be height and weight because they both refer to physical traits but ones do not cause the other.

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158.04$.

A discount is a decrease in the cost of a commodity or service. If the item is broken, you can ask the manager for a discount.

Given the Written price of the ski jacket is 213$ on that there is a discount of 30% and 6% of tax. Hence,

discounted price of jacket = 213 (1- 30%)

discounted price of jacket = 149 approx.

Total price of the jacket after-tax = 149 (1 + 6%)

The total price of the jacket after-tax = 158.04$

Therefore, the price of a $213 ski jacket with a 30% discount and a 6% tax is 158.04$.

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Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

3x=1+y is the ans submit it

Answer:

Lol i don't know.

Step-by-step explanation:

The given information states that AD is the angle bisector. An angle bisector is a line or ray that divides an angle into two congruent angles. In this case, AD divides the angle into two equal parts.

Angle bisectors have several properties. One important property is that they divide the opposite side of the triangle into segments that are proportional to the adjacent sides. This property is known as the Angle Bisector Theorem.

The Angle Bisector Theorem states that if AD is the angle bisector of angle A in triangle ABC, then the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the adjacent sides. In other words, AB/BD = AC/CD.

Another property of angle bisectors is that they are concurrent. This means that the three angle bisectors of a triangle intersect at a single point called the incenter. The incenter is the center of the circle that can be inscribed inside the triangle.

Angle bisectors also have geometric applications. For example, they can be used to find the length of a side or the measure of an angle in a triangle when certain other lengths or angles are known.

In summary, an angle bisector is a line or ray that divides an angle into two congruent angles. It has properties such as dividing the opposite side of a triangle proportionally and being concurrent at the incenter. Angle bisectors have applications in geometry and can be used to find unknown lengths or angles in a triangle.

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The below information displays common unit abbreviations for various physical quantities:

Mass: grams or kilograms (g or kg)

Length: meters or kilometres (m or km)

Time: seconds or minutes (s or min)

Electric Current: ampere (A or amps)

Temperature: Kelvin (K or °K)

Electricity/Electric Charge: coulomb (C or coulombs)

Luminous Intensity: candela (Cd or candelas)

Amount of Substance: mole (mol or moles)

Explanation:

- The unit abbreviation for length is "m."

- The unit abbreviation for mass is "g."

- The unit abbreviation for time is "s."

- The unit abbreviation for mass is "kg."

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Answer:

$2.50 for hotdog and $2 for soda

Answer: 1

Step-by-step explanation:

The prime factorisation of 14 and 1 is the product of 2 and 7, therefore Sarah's statement is correct for this particular example.

Prime factorisation is defined as the prime numbers of an integer that divides the number without a reminder.

The Lowest common multiple of a number is also known as the smallest positive number that is a multiple of two or more numbers.

You can find the LCM of a whole number by multiplying the two smallest numbers that can divide the integer without reminder.

The prime factorisation of 14 is the product of 2 and 7,therefore Sarah's statement is correct for this particular example.

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Answer:

x = 7

Step-by-step explanation:

The right angle is composed of the 2 given angles, so sum to 90°

4x + 40 + 6x - 20 = 90

10x + 20 = 90 ( subtract 20 from both sides )

10x = 70 ( divide both sides by 10 )

x = 7

The length of a side of the hexagon or square is - 16 units

The length of a side of the hexagon or square = x

The perimeter of the square = 4 × lengths of its side

                                               = 4x

The perimeter of the hexagon = 6 × lengths of its side

                                                  = 6x

According to the question,

                                           4x + 32 = 6x

                                       ⇒ 6x - 4x = 32

                                       ⇒  2x = 32

                                       ⇒  x = 16

So, the length of a side of the hexagon or square is - 16 units.

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Answer:

Actual tall building = 360 ft

Step-by-step explanation:

15 cm-----> 120ft

45 cm-----> x ft

x=(45*120)÷15=5400 ÷15 =360 ft

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Answer:

no solutions

Step-by-step explanation:

6n - 6n - 12 = 14 - 2 = 12 ( add 12 to both sides )

0 = 24 ← not possible

this indicates the equation has no solution

Answer:

3(3x-1)(3x+1)

Step-by-step explanation:

27x²-3

You can factor out a 3

3(9x²-1)

Now we can use the difference of perfect squares formula

x²-y²=(x+y)(x-y) which means that 9x²-1=

(3x-1)(3x+1)

put it all together and get

3(3x-1)(3x+1)

Answer:

b : 1/4

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

its b or d not c and not a

Step-by-step explanation:

The number of years that the balance in Isaac's account will be $9652 will be 3.97 years.

The amount in Isaac's account will increase at an exponential or a compound rate. This means that the amount that earns an interest is the amount deposited and the interest that has already been earned.

Number of years =  (In FV / PV)  / r

Where:

(In 9652 / 9500) / 0.004 = 3.97 years

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Answer:

?

Step-by-step explanation: