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4 years ago

10

The distance in inches around a toy flying disc with diameter 10 inches is given by the expression pie times 10. Evaluate this e

xpression. Round to the nearest tenth

1 answer:

boyakko [2]4 years ago

8 0

Answer:

pi*10 = 3.14*10 = 31.4 inches

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You have $14 and earn $0.75 for each cup of orange juice you sell. Write an equation in two variables that represents the total

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This would follow the $y = mx + b$ format
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A = 0.75j + 14
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Step-by-step explanation:

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3 years ago

The area (A) of a circle with a radius of r is given by the formula and its diameter (d) is given by . Arrange the equations in

ella [17]

Answer:

see explanation

Step-by-step explanation:

A = πr² ← r is the radius and r = $\frac{1}{2}$ d ← d is the diameter

Hence

π ( $\frac{1}{2}$ d)² = A, that is

$\frac{d^2\pi }{4}$ = A ( multiply both sides by 4 )

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4 years ago

A sine function had an amplitude of 3, period of 6pi, horizontal shift of 3pi/2, & vertical shift of -1.

Simora [160]

Answer: $\bold{y=\dfrac{1}{2}}$

<u>Step-by-step explanation:</u>

f(x) = A sin (Bx - C) + D

amplitude = |A|
period = $\dfrac{2\pi}{B}$
phase shift = $\dfrac{C}{B}$
vertical shift = D

<u>A</u>

amplitude of 3 is given so 3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

<u>B</u>

period of 6π is given so $6\pi=\dfrac{2\pi}{B}\quad \rightarrow \quad B=\dfrac{2\pi}{6\pi}\quad \rightarrow \quad B=\dfrac{1}{3}$

<u>C</u>

$\text{phase shift is given as}\ \dfrac{3\pi}{2}\ \text{so}\ \dfrac{3\pi}{2}=\dfrac{C}{\frac{1}{3}}\quad \rightarrow\quad \dfrac{(\frac{1}{3})3\pi}{2}=C\quad \rightarrow\quad \dfrac{\pi}{2}=C$

<u>D</u>

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

$f(x) = 3\ sin \bigg(\dfrac{1}{3}x - \dfrac{\pi}{2}\bigg) - 1$

Next, solve when x = 2π

$f(2\pi) = 3\ sin \bigg(\dfrac{1}{3}(2\pi) - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{2\pi}{3} - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{4\pi}{6} - \dfrac{3\pi}{6}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{\pi}{6}\bigg) - 1$

$= 3\ \bigg(\dfrac{1}{2}\bigg) - 1$

$=\dfrac{3}{2}-\dfrac{2}{2}$

$=\dfrac{1}{2}$

6 0

3 years ago