Ajay spends 6 hours at school. It takes him 35 min to travel from home to school and the same amount of time to return . He retu

Answer:

Here is the solution to the entire assessment: https://school.ckseattle.org/documents/2019/2/8_2_The_Pythagorean_Theorem_and_Its_Converse.pdf

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refer to the attached digram.

The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.

The perimeter of a rectangle can be expressed as 2(x+r) where:

x is the length

2r represents the rectangle's width, equivalent to the semicircle's diameter.

The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.

Thus, the total perimeter contributed by the two semicircles is 2πr.

Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr

where r indicates the semicircle's radius.

Expanding this gives us

Perimeter of the track = 2x + 4r + 2πr

which can also be represented as Perimeter of the track = 2(x + 2r + πr)

b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.

P = 2x + 4r + 2πr

By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x

Next, we divide each side by 2.

(P - 4r - 2πr) / 2 = 2x

Thus, x = (P - 4r - 2πr) / 2

c) Given

P = 600ft

r = 50ft

x = (600 - 4(50) - 2π(50)) / 2

x = (600 - 200 - 100(3.14)) / 2

x = 400 - 314 / 2

x = 86 / 2

x = 43ft

Therefore, rounding to the nearest foot, the value of x is 43ft

Answer:

1.0 gram (rounded from.98)

Step-by-step explanation:

This is an exponential equation represented as , where a denotes the initial quantity and b represents the rate of decay (or growth). The initial amount a is straightforward, being 430, but for b, ensure it's expressed in decimal form. To convert the percentage (like 27.4%) to decimal, simply move the decimal point two places to the left, yielding.274.

Next, with the equation , we can apply the value of x as 19.

Also, be aware that if different units are involved, like if t represented a decay over 19 hours, those would need to be converted as well. I'm here to help if you require further clarification.

Distributions from owners refer to payments that business owners take out from profits the firm earns, commonly issued as dividends. An ADR, or American Depositary Receipt, is a type of stock bought and sold within the U.S. market that represents a specific number of shares in a foreign company. Therefore, the owner’s payments do not originate from the ADR shares.

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

The population of the barangay can be modeled using the exponential function;

P(t) = P0e^kt

P(t) reflects the population after t years

P0 denotes the initial population

t indicates the time

With an initial population of 1000, we set P0 = 1000

Given that the population doubles every 60 years, at t = 60, it holds that P(t) = 2P0

Inserting that into the equation yields

2P0 = P0e^k(60)

2 = e^60k

Taking the natural logarithm of both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Inserting the determined k value and P0 into the function gives

P(t) = 1000e^(0.01155)t

Thus, the exponential model for the population of the barangay is

P(t) = 1000e^(0.01155)t