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3 years ago

15

Solve the equation:

" title="2 {x}^{2} + 7x - 3 = 0" alt="2 {x}^{2} + 7x - 3 = 0" align="absmiddle" class="latex-formula">

1 answer:

Genrish500 [490]3 years ago

3 0

Answer:

$delta = {7}^{2} - 4 \times 2 \times ( - 3) \\ = 49 + 24 = 73 \\ x 1= \frac{ - 7 + \sqrt{73} }{4} \\ x 2= \frac{ - 7 - \sqrt{73} }{4}$

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A regulation baseball field measures 90 feet between each base. What is the distance around the bases in yards?

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Home to 1st base = 90 ft
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2nd base to 3rd base = 90 ft
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The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the

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Let r represent the radius of cylinder.

We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be $1.5r$ .

We will use lateral surface area of pyramid to solve our given problem.

$LSA=2\pi r h$ , where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

$LSA=2\pi r\cdot (1.5)r$

Now we will find the total surface area of cylinder.

$TSA=2\pi r(r+h)$

$TSA=2\pi r(r+1.5r)$

$TSA=2\pi r(2.5r)$

$\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}$

$\frac{TSA}{LSA}=\frac{2.5r}{1.5r}$

$\frac{TSA}{LSA}=\frac{25}{15}$

$\frac{TSA}{LSA}=\frac{5}{3}$

Therefore, the ratio of total surface area to lateral surface area is $5:3$ .

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3 years ago