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3 years ago

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A piece of land is 20cm by 5cm. A portion of the land by size 10cm by 2cm was used to cultivate tomatoes. what is the area of th

e land?

1 answer:

Sergio039 [100]3 years ago

8 0

Answer:

80cm^2

Step-by-step explanation:

20*5=100

10*2=20

100-20=80

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Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio

lina2011 [118]

Answer:

The point of intersection is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

$y=0.5x+5$

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

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

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:

$(x-0)^2+(y-5)^2=(3)^2$

Simplify:

$x^2+(y-5)^2=9$

At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:

$x^2+((0.5x+5)-5)^2=9$

Simplify:

$x^2+(0.5x)^2=9$

Square:

$x^2+0.25x^2=9$

Combine like terms:

$\displaystyle 1.25x^2=\frac{5}{4}x^2=9$

Solve for <em>x: </em>

<em /> $\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}$ <em />

Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.

To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:

$\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34$

So, the point of intersection in QI is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

6 0

2 years ago

2. Calculate the amount of gallons needed to fill the pool shown below. (3 points)

hammer [34]

Answer:

52,322 gal

Step-by-step explanation:

will make it simple and short.

vol = ( a + b ) * h/2 times the depth

vol = (10 + 4) x (40/2) x 30 = 8400 cu. ft. ---------->>> then convert to gal.

6.2288 gal

vol = 8400cu.ft. x ----------------- = 52,322 gal

1 cu.ft.

8 0

3 years ago

Sean has 5 1/2 cups of grape tomatoes, if each serving is 3/4 of a cup, how many servings of grape tomatoes does Sean have

ollegr [7]

Answer:

7 servings

Step-by-step explanation:

first make 5 1/2 unsimplified, to 11/2. then multiple it by 2 so the denominator is the same as 3/4, making it 22/4. 22/3 is 7 1/4, so he has 7 full servings and 1/4th of a serving.

6 0

3 years ago

333 = 5230(0.95) - 217

rjkz [21]

Answer:

333 = 4751.5

you have to evaluate

5 0

3 years ago

You are given that a wheel has a radius of 2 feet and a spin rate of 10 revolutions per minute. Describe how you would determine

ss7ja [257]

Answer:

About 126 ft/min

Step-by-step explanation:

We know r = 2 feet, and that the wheel has an angular speed of 10 rpms, or 10 revolutions per minute. Our goal is to get the speed in ft/sec.

10 rev 1 minute 2π radians 2 feet

----------- × ---------------- × ------------------ × ------------

1 minute 60 seconds 1 revolution 1 radian

= 10 * 2π * 2 = 126 ft/minute

The answer is reasonable. Another, simple approach to this would be using the formula 2π * r * rpm. If so, 2π * 2 * 10 which would be 126 ft/minute.

6 0

3 years ago