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2 years ago

Can help me find area and perimeter step by step

Mathematics

1 answer:

Vera_Pavlovna [14]2 years ago

4 0

Answer:

area: 16.28 ft²
perimeter: 17.05 ft

Step-by-step explanation:

The figure is shown as being composed of a semicircle and a triangle. You know the formula for the area of a circle is ...

A = πr²

The radius of the semicircle is half its diameter, so is (4 ft)/2 = 2 ft. Then the area of a circle with radius 2 feet is ...

A = π(2 ft)² = 4π ft²

Our semicircle has half that area, so ...

area of semicircle = (4π ft²)/2 = 2π ft² ≈ 6.283 ft²

The area of the triangle is given by the formula ...

A = (1/2)bh

Here, the base is shown as 4 ft, and the height is shown as 5 ft. Then the triangle area is ...

triangle area = (1/2)(4 ft)(5 ft) = 10 ft²

So, the total area of the composite figure is ...

figure area = area of semicircle + triangle area

= 6.283 ft² + 10 ft² ≈ 16.283 ft² . . . . area of the figure

The perimeter of the curved portion of the semicircle is half the circumference of a circle of radius 2 ft. It will be ...

curved perimeter = (1/2)(2πr) = πr = π(2 ft) = 2π ft ≈ 6.283 ft

The length of each side of the triangle can be found from the Pythagorean theorem. Each side of the triangle is the hypotenuse of a right triangle with legs 2 ft and 5 ft. Then it will be ...

triangle side length = √(2² +5²) ft = √29 ft ≈ 5.385 ft

The total perimeter is ...

perimeter = 2 × triangle side length + semicircle length

= 2×(5.385 ft) + 6.283 ft = 17.054 ft

The perimeter of the figure is about 17.05 feet.

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Step-by-step explanation:

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2 years ago

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Answer:

y = 18 and x = -2

Step-by-step explanation:

y = x^2+bx+c To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0). Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically Plugging in (2,0) :

y=x2+bx+c

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2 years ago

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3 years ago

Read 2 more answers

If the distribution is really (5.43,0.54)

defon

Answer:

0.7486 = 74.86% observations would be less than 5.79

Step-by-step explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

N(mean, standard deviation)

Which means that:

$\mu = 5.43, \sigma = 0.54$

What proportion of observations would be less than 5.79?

This is the pvalue of Z when X = 5.79. So

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

$Z = \frac{5.79 - 5.43}{0.54}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486

0.7486 = 74.86% observations would be less than 5.79

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3 years ago