I need help with this Algebra

7. Which dimensions result in the minimum perimeter for a rectangle with area 42.0 cm2?

natali 33 [55]

9514 1404 393

Answer:

7. d. l = 6.48 cm, w = 6.48 cm

8. d. square

Step-by-step explanation:

For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.

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7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.

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8. In light of the above, the shape is a square.

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The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.

8 0

2 years ago

What type of probability uses a knowledge of sample spaces as opposed to observations to determine the numerical probability of

Aneli [31]

Answer:

Classical probability

Step-by-step explanation:

Classical property is that type of probability or statistical concept that deals with the measurement of the odds or likelihood of some event.

It is that form of probability that is simplest in approach and includes the equal likelihood of happening or occurrence of an event.

In order to determine the numerical probability of an event, it makes use of the knowledge of sample spaces in contrast with the observations.
It takes a proper note of an event in order to calculate its probability and also it deals with the likelihood of a certain event rather than making observations.

5 0

2 years ago

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Stacey filled her 1/2 cup measuring cup seven times to have enough flour for a cake recipe. How much flour does the cake recipe

adoni [48]

First you would do 1/2 * 7 and you would get your answer which would be 3 1/2 cups of flour.

xXRebekahXx Please rank brainliest if this was helpful!!

3 0

2 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

1 year ago

PLEASE HELP WILL MARK BRAINLIEST Determine the value of h. Round your answer to the nearest hundredth if necessary.

jarptica [38.1K]

Answer:

<h2><u>Answer</u><u> </u><u>:</u><u>-</u></h2>

Here,

At first we know that parallel line cut transversal lines. They make them in a proportion.

h/10 = 9/13

h = 10 × 9/13

h = 90/13

h = 6.92

$\\$

5 0

2 years ago

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