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3 years ago

5

Find the number of distinct arrangements of the 9 letters in SEVENTEEN. Two of the same letter are considered identical (not dis

tinct).

1 answer:

Bess [88]3 years ago

8 0

........54..............

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Multiple choice <br> a. 12 pie cm <br> b. 21 pie cm <br> c. 35 pie cm

Karolina [17]

Answer:

The correct option is;

a. 12 pie cm

Step-by-step explanation:

Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;

Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same

The volume of the square based prism = 452 cm³

Therefore, the volume of the cylinder (of equal base area) = 452 cm³

The formula for the volume of square based prism = Area of base × Height

∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm

Which gives;

Area of the base of the square based prism = 452/4 = 113 cm²

The area of the base of the cylinder $A_c$ = The area of the base of the square based prism = 113 cm²

The area of the base of the cylinder, $A_c$ is given by the following equation;

$A_c$ = π×r² = 113 cm²

r = √(113/π) = √35.97 ≈ √36 = 6 cm

The circumference of the base of the cylinder, $C_c$ is given by the following equation

$C_c$ = 2×π×r ≈ 2×π×6 = 12×π cm

The correct option is 12 pie cm.

7 0

2 years ago

Please Please help asap!!! Thank you

natali 33 [55]

Step-by-step explanation:

well, the starting equation and the target format have been given.

let's do the multiplications and compare the target with the starting information.

from there we see what is different or missing.

x² + 14x + 13 = 0

and

(x - p)² = q

x² - 2px + p² = q

x² - 2px + (p² - q) = 0

now let's compare the different parts :

x² = x²

-2px = 14x

-2p = 14

p = -7

p² - q = 13

-7² - q = 13

49 - q = 13

36 - q = 0

q = 36

so, the square (x - p)² = (x + 7)² is completed when

x² + 14x + 49 = 0

but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :

x² + 14x + 13 + 36 = 36

x² + 14x + 49 = 36

(x + 7)² = 36

just as we calculated already above.

and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)

x + 7 = ±6

x1 = 6 - 7 = -1

x2 = -6 - 7 = -13

3 0

1 year ago

Determine whether the relation shown in the table is a direct variation, and inverse, or neither.

Grace [21]

The table of values has an inverse relationship. An inverse relationship is a relationship in which changes in one set of values causes changes in another set of values in the other direction. Simply saying, if a set of values (x) increases, another set of values (y) decreases.

4 0

2 years ago

Find an equation of the tangent line to the bullet-nose curve y=|x|/sqrt(2−x^2) at the point (1,1) I think that square root is w

Mashcka [7]

$\bf y=\cfrac{|x|}{\sqrt{2-x^2}}\qquad \boxed{|x|=\pm\sqrt{x^2}}\qquad y=\cfrac{\sqrt{x^2}}{\sqrt{2-x^2}}\\\\
-------------------------------\\\\
\cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{\frac{1}{2}(x^2)^{-\frac{1}{2}}\cdot 2x\cdot \sqrt{2-x^2}~~-~~\sqrt{x^2}\cdot \frac{1}{2}(2-x^2)^{-\frac{1}{2}}\cdot -2x}{(\sqrt{2-x^2})^2}}$

$\bf \cfrac{dy}{dx}=\cfrac{\frac{x\sqrt{2-x^2}}{\sqrt{x^2}}~~+~~\frac{x\sqrt{x^2}}{\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{x(2-x^2)~~+~~x(x^2)}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\\\\\\
\cfrac{dy}{dx}=\cfrac{\frac{2x\underline{-x^3+x^3}}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{2x}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}$

$\bf \cfrac{dy}{dx}=\cfrac{2x}{\sqrt{x^2}\sqrt{2-x^2}(2-x^2)} \implies \boxed{\cfrac{dy}{dx}=\cfrac{2x}{|x|\sqrt{2-x^2}(2-x^2)}}
\\\\\\
\left. \cfrac{dy}{dx} \right|_{1,1}\implies \cfrac{2(1)}{|1|\cdot \sqrt{2-1^2}(2-1^2)}\implies 2\\\\
-------------------------------\\\\
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2(x-1)\implies y-1=2x-2
\\\\\\
y=2x-1$

5 0

3 years ago

How do you translate nine equals the quotient of a number and 54

NeX [460]

Answer:

9 = $\frac{n}{54}$ <em>or</em> n ÷ 54

Step-by-step explanation:

<u>nine equals</u> the quotient of a number and 54

/\

9 = <u>the quotient</u> of a number and 54

/\

9 = <u>will be division of a number and 54</u>

/\

9 = $\frac{n}{54}$ <em>or</em> n ÷ 54

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

5 0

2 years ago