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professor190 [17]

1 year ago

9

A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and a depth of 8 centime

ters. About how many cubic centimeters of soil are needed to plant the full tray? Round to the nearest cubic centimeter

2 answers:

olga_2 [115]1 year ago

7 0

I think 452cm^3
Voulme of one cylinder times 6

goldenfox [79]1 year ago

3 0

Answer:

Soil required = 453 cm³

Step-by-step explanation:

Volume of cone $=\frac{1}{3}\times \texttt{base area}\times \texttt{depth}$

Base area of cone $=\pi r^2=\pi \times 3^2=9\pi cm^2$

Depth of cone = 8 cm

Volume of one cone $=\frac{1}{3}\times 9\times \pi \times 8=75.39cm^3$

Volume of six cones = 6 x 75.39 = 452.39 cm³ = 453 cm³

Soil required = 453 cm³

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Let $f(x)$ be a function defined for all positive real numbers satisfying the conditions $f(x) > 0$ for all $x > 0$ and $f

algol [13]

Suppose we choose $x=1$ and $y=\dfrac12$ . Then

$f(x-y)=\sqrt{f(xy)+1}\implies f\left(\dfrac12\right)=\sqrt{f\left(\dfrac12\right)+1}\implies f\left(\dfrac12\right)=\dfrac{1+\sqrt5}2$

Now suppose we choose $x,y$ such that

$\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}$

where we pick the solution for this system such that $x>y>0$ . Then we find

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Note that you can always find a solution to the system above that satisfies $x>y>0$ as long as $x>\dfrac12$ . What this means is that you can always find the value of $f(x)$ as a (constant) function of $f\left(\dfrac12\right)$ .

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1 year ago

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Factor completely. 640-10x^2

Oxana [17]

Answer:

10 (8-x)(8+x)

Step-by-step explanation:

640-10x^2

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10 (64 - x^2)

Notice that inside the parentheses is the difference of squares

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1 year ago

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If m<3 =54°. find each measure.

weqwewe [10]

Answer/Step-by-step explanation:

Given:

m<3 = 54°

m<2 = right angle

a. m<1 + m<2 + m<3 = 180° (angles in a straight line)

m<1 + 90° + 54° = 180° (substitution)

m<1 + 144° = 180°

m<1 = 180° - 144°

m<1 = 36°

b. m<2 = 90° (right angle)

c. m<4 = m<1 (vertical angles)

m<4 = 36° (substitution)

d. m<5 = m<2 (vertical angles)

m<5 = 90°

e. m<6 = m<3 (vertical angles)

m<6 = 54°

f. m<7 + m<6 = 180° (same side interior angles)

m<7 + 54° = 180° (substitution)

m<7 = 180 - 54

m<7 = 126°

g. m<8 = m<6 (alternate interior angles are congruent)

m<8 = 54°

h. m<9 = m<7 (vertical angles)

m<9 = 126°

i. m<10 = m<8 (vertical angles)

m<10 = 54°

j. m<11 = m<4 (alternate interior angles are congruent)

m<11 = 36° (substitution)

k. m<12 + m<11 = 180° (linear pair)

m<12 + 36° = 180° (substitution)

m<12 = 180° - 36°

m<12 = 144°

l. m<13 = m<11 (vertical angles)

m<13 = 36°

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m<14 = 144° (substitution)

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1 year ago

Prove that. 1-sin2A=2sin^2(45-A)

Liula [17]

Answer:

Proved

Step-by-step explanation:

2 sin square( 45°-A)

(therefore;

by trigonometry ratios

sin45°=1)

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=2sin(1-A)

=1+sin2A

hence proved

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Tysm

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1 year ago

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xeze [42]

Answer:

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Step-by-step explanation:

We have the fraction $\frac{2m}{2m+3} -\frac{2m}{2m-3}$

Step 1. Use LCM of the fraction, (2m+3)(2m-3), to simplify the fraction:

$\frac{(2m-3)(2m)-(2m+3)(2m)}{(2m+3)(2m-3)} =\frac{2m^2-6m-[2m^2+6m]}{(2m+3)(2m-3)} =\frac{2m^2-6m-2m^2-6m}{(2m+3)(2m-3)} =\frac{-12m}{(2m+3)(2m-3)}$

Step 2. Equate the resulting fraction to zero and solve for $m$ :

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Step 3. Replace the value in the original equation and check if it holds:

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$-12m=0$

Since $m=0$ ,

$-12(0)=0$

$0=0$

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1 year ago

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