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3 years ago

15 pts

Mathematics

1 answer:

zhenek [66]3 years ago

8 0

Answer:

The total volume of juice in a six-pack is $254.3\ in^{2}$

Step-by-step explanation:

step 1

Find the volume of one can

The volume of the cylinder (can of juice) is

$V=\pi r^{2} h$

we have

$r=3/2=1.5\ in$ ----> the radius is half the diameter

$h=6\ in$

assume

$\pi =3.14$

substitute

$V=(3.14)(1.5)^{2} (6)$

$V=42.39\ in^{2}$

step 2

Find the total volume of juice in a six-pack

Multiply the volume of one can by 6

$42.39*(6)=254.3\ in^{2}$

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A farmer plans to fence a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five

garik1379 [7]

Answer:

Length of diagonal is 7.3 yards.

Step-by-step explanation:

Given: The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width.

To find: The length of the diagonal of the corral.

Solution: Let the width of the rectangular garden be <em>x</em> yards.

So, the length of the diagonal is $x+5$

width of the rectangular corral is $3x$

We know that the square of the diagonal is sum of the squares of the length and width.

So,

$(3x)^{2} +x^{2} =(x+5)^{2}$

$9x^{2} +x^{2} =x^{2}+10x+25$

$9x^{2}-10x-25=0$

$x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a}$

$x=\frac{10\pm\sqrt{(-10)^{2} -4(9)(-25)} }{2(9)}$

$x=\frac{10\pm\sqrt{100}}{18}$

Since, side can't be negative.

$x=\frac{5}{9}+\frac{5}{9}\sqrt{10}$

Now, length of the diagonal is

$5+\frac{5}{9}+\frac{5}{9}\sqrt{10}$

Hence, length of diagonal is 7.3 yards.

4 0

3 years ago

the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle?

miss Akunina [59]

The equation of a circle in standard form is

$(x - h)^2 + (y - k)^2 = r^2$

where (h, k) is the center of the circle, and r is the radius if the circle.

We need to find the radius and center of the circle.
We are given a diameter, so to find the center, we need the midpoint of the diameter.

M = ((-6 + 6)/2, (6 + (-2))/2) = (0, 2)
The center is (0, 2).

To find the radius, we find the length of the given diameter and divided by 2.

$d = \sqrt{(-6 - 6)^2 + (6 - (-2))^2)}$

$d = \sqrt{144 + 64}$

$d = \sqrt{208}$

$r = \dfrac{d}{2} = \dfrac{\sqrt{208}}{2} = \dfrac{\sqrt{208}}{\sqrt{4}} = \sqrt{52}$

$(x - 0)^2 + (y - 2)^2 = (\sqrt{52})^2$

$x^2 + (y - 2)^2 = 52$

7 0

3 years ago

Slope intercept form that passes though the point (-2,-3) and has a slope of 5/2

olganol [36]

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8 0

3 years ago

Read 2 more answers

Select the correct answer.

andrew-mc [135]

Answer:

$v=\sqrt{\frac{E}{m}}$

Step-by-step explanation:

The formula is given as:

$E=mv^2$

We need to solve this formula for v, that means that v to one side and let it be solved in terms of the other variables (E and m). First, we isolate v:

$E=mv^2\\\frac{E}{m}=\frac{mv^2}{m}\\\frac{E}{m}=v^2$