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3 years ago

Solve for a! 264=π×a×(20-a) Thank you!

Mathematics

1 answer:

jasenka [17]3 years ago

4 0

Answer:

a ≈ 14 or 6

Step-by-step explanation:

264 = π × a × (20 - a)

a(20 - a) = $\frac{264}{Pi}$ ≈ 84 (rounded off to nearest whole number)

Opening the brackets we get;

a² - 20a + 84 = 0

Applying the quadratic formula we get:

a ≈ 14 or 6

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The combined height of one for tree and one pine tree is 21 meters. The height of 4 for trees stacked on top of each other is 24

slamgirl [31]

Answer:

The height of the fir tree is 9 meters tall and the pine tree is 12 meters.

Step-by-step explanation:

Given:

Note :→ there is a mistake it is fir tree not for tree.

The combined height of one fir tree and one pine tree is 21 meters.

The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.

Now, to find how tall are the types of trees.

Let the height of one fir tree be $x$ .

And the height of one pine tree be $y$ .

So, the combined height of one fir tree and one pine tree:

$x+y=21.$

$y=21-x.$ .........( 1 )

Now, as given the height of 4 for trees stacked on top of each other is 24 meters taller than one pine tree:

$4x=y+24.$

Putting the value of equation (1) in the place of $y$ :

$4x=21-x+24$

Adding both the sides $x$ we get:

$5x=21+24.$

$5x=45.$

Dividing both the sides by 5 we get:

$x=9\ meters.$

So, the height of one fir tree = 9 meters.

Now, putting the value of $x$ in equation (1) we get:

$y=21-9$

$y=12\ meters.$

Thus, the height of one pine tree = 12 meters.

Therefore, the fir tree is 9 meters tall and the pine tree is 12 meters tall.

6 0

3 years ago

When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance

bekas [8.4K]

a) $v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

The average speed is equal to the ratio between the total distance ( $d_{tot}$ and the total time taken ( $t_{tot}$ ):

$v=\frac{d_{tot}}{t_{tot}}$

the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:

$d_1 = (3 h)(60 mph)=180 mi$

So the total distance is

$d_{tot}=d_1 +d_2 = 180 mi+20 mi=200 mi$

The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:

$t_{tot}=3 h +t_2$

So, the equation can be rewritten as:

$v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

b) 0.50 h (half a hour)

Since we know the value of the average speed, $v=57.14 mph$ , we can substitute it into the previous equation to find the value of $t_2$ , the time the trucker drove in the city:

$v=\frac{200 mi}{3h +t_2}\\3h+t_2 = \frac{200 mi}{v}\\t_2 = \frac{200 mi}{v}-3h=\frac{200 mi}{57.14 mph}-3 h=0.50 h$

3 0

3 years ago

What is the center or a circle represented by the equation (x+9)2 + (y-6)2 = 10 to the power of 2

m_a_m_a [10]

Answer:

(-9,6)

Step-by-step explanation:

The general equation of a circle is given as:

x²+y²+2gx+2fy+c = 0

The centre of the circle is (-g,-f)

Given the equation of the circle

(x+9)² + (y-6)² = 10²

First we need to expand and write it in the general form. On expansion:

x²+18x+81+y²-12y+36 = 100

Collecting like terms

x²+y²+18x-12y+81+36-100 = 0

x²+y²+18x-12y+17 = 0

Comparing to the general equation

2gx = 18x

g = 9

2fy = -12

f = -6

The center of the circle = (-g, -f)

= (-9,-(-6))

= (-9, 6)

4 0

3 years ago

Select the correct answer from each drop-down menu.

ruslelena [56]

The independent variable in the relationship is the Number of Months and should be placed on the x-axis

The dependent variable in the relationship is the Number of Fish and should be placed on the y-axis

Step-by-step explanation:

Let us explain the independent and dependent variables of a relation

The independent variable is the input of the relation

The dependent variable is the output of the relation
The values of dependent variables depend on the values of independent variables
When the relation represented graphically the independent variable placed on the x-axis and the dependent variable placed on the y-axis

The table:

→ Number of Months: 0 : 1 : 2 : 3 : 4

→ Number of Fish : 1,024 : 1,280 : 1600 : 2,000 : 2,500

Let us check is their any constant ratio between the consecutive values of the number of fish

∵ 1,280 ÷ 1,024 = 1.25

∵ 1,600 ÷ 1.280 = 1.25

∵ 2,000 ÷ 1,600 = 1.25

∵ 2,500 ÷ 2,000 = 1.25

∴ The table represent an exponential function, where the input

is the number of months and the output is the number of fish

∵ The input is independent variable

∴ The independent variable is the number of months

∵ The output is the dependent variable

∴ The dependent variable is the number of fish

∵ The independent variable is placed on the x-axis

∴ The number of months should be place on the x-axis

∵ The dependent variable is placed on the y-axis

∴ The number of fish should be place on the y-axis

The independent variable in the relationship is the Number of Months and should be placed on the x-axis

The dependent variable in the relationship is the Number of Fish and should be placed on the y-axis

Learn more:

You can learn more about the relation in brainly.com/question/10708697

#LearnwithBrainly

6 0

3 years ago

MrRissso [65]

Answer:

Step-by-step explanation:

4 0

3 years ago