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2 years ago

The diameter of a circular placemat is 42 centimeters. What is the approximate area of the circular placemat

Mathematics

1 answer:

Inga [223]2 years ago

4 0

<em><u> $area \: of \: a \: circle \: or \: circular \: object \: = \pir^{2} \\ \:$ </u></em>

Answer:

1386cm^2.

Step-by-step explanation:

Radius of a circle = diameter / 2

= 42cm /2

= 21cm.

Area = (3.142 *21*21)cm^2

= 1386cm^2

To convert into metres:

=1386/100

=13.86m^2

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Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

slavikrds [6]

$f'(x)=2x-\dfrac3{x^4}$
$\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx$
$f(x)=x^2+\dfrac1{x^3}+C$

Given that $f(1)=2$ , we get

$2=1^2+\dfrac1{1^3}+C$
$2=2+C$
$\implies C=2$

so that

$f(x)=x^2+\dfrac1{x^3}$

8 0

3 years ago

Find the smallest solution to the equation 2/3 X² equals 24

iren [92.7K]

Answer:

The smallest solution is -6

Step-by-step explanation:

2/3 x^2 = 24

Multiply each side by 3/2

3/2 *2/3 x^2 = 24*3/2

x^2 = 36

Take the square root of each side

sqrt(x^2) = sqrt(36)

x = ±6

The smallest solution is -6

The largest solution is 6

4 0

3 years ago

Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points. Rachel scored 78 p

Artemon [7]

Answer:

Keenan's z-score was of 0.61.

Rachel's z-score was of 0.81.

Step-by-step explanation:

Z-score:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points.

This means that $X = 80, \mu = 77, \sigma = 4.9$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{80 - 77}{4.9}$

$Z = 0.61$

Keenan's z-score was of 0.61.

Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3.7 points.

This means that $X = 78, \mu = 75, \sigma = 3.7$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{75 - 78}{3.7}$

$Z = 0.81$

Rachel's z-score was of 0.81.

6 0

2 years ago

Find the zeros of y=x^3-x^2-9x+9

notsponge [240]

The zeros are at -3, 1 and 3

7 0

3 years ago

Why0.6 is ten time as much as 0.06

weeeeeb [17]

The numbers after the decimal place are represented as 10ths, hundredths, thousandths, and so on. 0.6 is said as "Zero point six tenths." Or "Zero and six tenths."
0.06 is said as "Zero point zero six hundredths." Or "Zero and six hundredths."

5 0

3 years ago