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2 years ago

- 7.42 as a mixed number in simplest form.

1 answer:

5 0

Well first, the fraction is written 7 42/100, but 42 divided by 2 and 50 divided by 2 equal 21/50. You cannot simplify it anymore, therefore the answer in <span>simplest form is 7 21/50.</span>

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8. The length of an actual road is

Natasha_Volkova [10]

Answer:

It's A.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

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

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

2 years ago

your kitchen is in your house is being remolded. it takes 2 workers , 12 days to finish the job. Each worker works 7 hours a day

uranmaximum [27]

I think it is $4284 b/c you would do $25.5*7 hours*12 days*2 workers=$4284 total

3 0

2 years ago

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

Klio2033 [76]

The firs term
A(1)=-6+(1-1)(6)
A(1)=-6+(0)(6)
A(1)=-6

The fourh term
A(n)=-6+(n-1)(6)
A(4)=-6+(4-1)(6)
A(4)=-6+(3)(6)
A(4)=-6+18
A(4)=12

The tenth term
A(10)=-6+(10-1)(6)
A(10)=-6+(9)(6)
A(10)=-6+54
A(10)=48

Answer:
D. -6,12,48

6 0

2 years ago

a carpenter has been asked to build an open box with a sqaure base. the sides of the box will cost $3 per m^2 and the base will

slamgirl [31]

<h2>Dimension of box is 2 m x 2 m x 1.33 m</h2>

Step-by-step explanation:

Let a be base side and h be the height.

Volume of box, V = a²h

The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.

That is

4a² + 3 x 4 x a x h = 48

4a² + 12 a x h = 48

a² + 3 ah = 12

$h=\frac{12-a^2}{3a}$

So volume is

$V=a^2\times \frac{12-a^2}{3a}=4a-\frac{a^3}{3}$

At maximum volume we have derivative is zero,

$dV=4da-3\times \frac{a^2}{3}da\\\\0=4-a^2\\\\a=\pm 2$

Negative side is not possible, hence side of square base is 2m.

Substituting in a² + 3 ah = 12

2² + 3 x 2 x h = 12

h = 1.33 m

Dimension of box is 2 m x 2 m x 1.33 m

5 0

3 years ago