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3 years ago

Solve 2 cos theta + 2 = 3 in the interval from 0 to 2pi. Round to the nearest hundredth.

1 answer:

4 0

2cos theta = 1 -> cos theta = 1/2

Then theta = pi/3 + 2npi or -pi/3 + 2npi, where n is random interger

And the domain is restricted in [0,2pi]

So answer will be pi/3 or 5pi/3

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Zach has an above-ground pool that has a radius of 5.5 feet. He wants to put a new wall liner around his pool and needs to know

Tems11 [23]

Answer: 34.54feet

Step-by-step explanation:

Thw circumference of the pool will be calculated by using the formula:

= 2πr

where

π = 3.14

r = 5.5

Therefore, circumference = 2πr

= 2 × 3.14 × 5.5

= 34.54feet

Therefore, the circumference of the pool to the nearest hundredth is 34.54feet.

7 0

3 years ago

A metal conduit will be used as a pathway for wiring through a concrete block. The conduit is a 5 foot long rod with an outer di

kolbaska11 [484]

Answer: 586.59 cubic centimeters .

Step-by-step explanation:

As per given . we have

Inner diameter = 1.8 inches

⇒Inner radius :r = 0.9 in. (radius is half of diameter)

= 0.9 x (2.54) = 2.286 cm [∵ 1 in . = 2.54 cm]

Outer diameter = 2 inches

⇒Outer radius : R = 1 inch = 2.54 cm

Height : h = 5 feet = 5 x(30.48) = 152.4 cm [∵ 1 foot = 30.48 cm]

The formula to find the volume of a hollow cylinder :

$V=\pi(R^2-r^2)h$ , where R= outer radius , r= inner radius and h= height.

Now , the volume of metal in the conduit :

$V=(3.14)(( 2.54)^2-(2.286)^2)(152.4)$

$V=(3.14)(6.4516-5.225796)(152.4)$

$V=(3.14)(1.225804)(152.4)$

$V=586.591342944\approx586.59\ cm^3$

Hence, the volume of metal in the conduit is 586.59 cubic centimeters .

5 0

3 years ago

Mackenzie spent a total of $17.50 on Saturday afternoon.She bought a movie ticket for $7.25 and snacks for $4.95.She spent the r

Helga [31]

17.50-7.25-4.95=5.30/2=2.65

5 0

2 years ago

Simplify the expression. 5g – 7g + 4 + 2g

Marina86 [1]

Answer:

Step-by-step explanation:

there is no quantity for g and 4 is all that is left

4 0

3 years ago

Please help me ! Reduced to lowest terms

Mandarinka [93]

Answer:

Step-by-step explanation:

7) 2ab + 4ac = 2*a*b + 2 *2 *a*c

= 2a(b + 2c)

$\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}$

8) ac - a²c² = c( a - a²c)

bc - abc = c(b - ab)

$\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\$

$=\dfrac{a-a^{2}c}{b-abc}$

9) b²+ 4b - 5 = b² + 5b - 1b - 5

= b(b + 5) - 1(b + 5)

= (b +5)(b - 1)

b² + 8b + 15 = b² + 5b + 3b + 15

= b(b + 5) + 3(b + 5)

= (b + 5 )(b + 3)

$\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\$

$=\dfrac{b-1}{b+3}$

8 0

2 years ago