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3 years ago

Is 7/8 or 11/10 closer to 1

1 answer:

4 0

10. Find which one of the given fractions are value closer to 1. First = 7/8 Second = 11/10 Let’s start solving Let us start with the first value which is 7/8 => 7 needs to be divided with 8 => 7 / 8 = 0.875 Now, let’s solve the second value which is 11/10 => same with first solution., divide 11 by 10 => 11 / 10 => 1.1 Thus, 11/10 is the has the nearest value to 1.

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MATH HELP PLZ!!!

RoseWind [281]

Answer:

a) $tan (157.5) = \frac{1-cos 315}{sin315}$

$sin (165) =\sqrt{ \frac{1-cos (330) }{2}}$

$sin^{2} (157.5) = \frac{1-cos (315) }{2}$

cos 330° = 1- 2 sin² (165°)

Step-by-step explanation:

Step(i):-

By using trigonometry formulas

cos2∝ = 2 cos² ∝-1

cos∝ = 2 cos² ∝/2 -1

1+ cos∝ = 2 cos² ∝/2

$cos^{2} (\frac{\alpha }{2}) = \frac{1+cos\alpha }{2}$

cos2∝ = 1- 2 sin² ∝

cos∝ = 1- 2 sin² ∝/2

$sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}$

Step(i):-

Given

$tan\alpha = \frac{sin\alpha }{cos\alpha }$

we know that trigonometry formulas

$sin\alpha = 2sin(\frac{\alpha }{2} )cos(\frac{\alpha }{2} )$

1- cos∝ = 2 sin² ∝/2

Given

$tan(\frac{\alpha }{2} ) = \frac{sin(\frac{\alpha }{2} )}{cos(\frac{\alpha }{2}) }$

put ∝ = 315

$tan(\frac{315}{2} ) = \frac{sin(\frac{315 }{2} )}{cos(\frac{315 }{2}) }$

multiply with ' 2 sin (∝/2) both numerator and denominator

$tan (\frac{315}{2} )= \frac{2sin^{2}(\frac{315)}{2} }{2sin(\frac{315}{2} cos(\frac{315}{2}) }$

Apply formulas

$sin\alpha = 2sin(\frac{\alpha }{2} )cos(\frac{\alpha }{2} )$

1- cos∝ = 2 sin² ∝/2

now we get

$tan (157.5) = \frac{1-cos 315}{sin315}$

$sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}$

put ∝ = 330° above formula

$sin^{2} (\frac{330 }{2}) = \frac{1-cos (330) }{2}$

$sin^{2} (165) = \frac{1-cos (330) }{2}$

$sin (165) =\sqrt{ \frac{1-cos (330) }{2}}$

c )

$sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}$

put ∝ = 315° above formula

$sin^{2} (\frac{315 }{2}) = \frac{1-cos (315) }{2}$

$sin^{2} (157.5) = \frac{1-cos (315) }{2}$

cos∝ = 1- 2 sin² ∝/2

put ∝ = 330°

$cos 330 = 1 - 2sin^{2} (\frac{330}{2} )$

cos 330° = 1- 2 sin² (165°)

3 0

2 years ago

Perform the indicated operation & simplify. Express the answer as a complex number. ( 6 − 7 i ) ( − 8 + 3 i ) =___

slega [8]

( 6 − 7 i ) ( − 8 + 3 i )

First FOIL:

( 6 − 7 i ) ( − 8 + 3 i ) = -48 + 18i + 56i -21i^2

Combine like terms

= -48 + 74i -21i^2

Convert i^2 = -1

= -48 + 74i -21(-1)

And simplify

= -48 + 74i + 21

= -27 + 74i

6 0

1 year ago

The fish population of a lake is decreasing each year. A study is conducted. But, unfortunately some data was lost. The research

Solnce55 [7]

Answer:

$F(t) = 18000(0.6666)^{t}$

Step-by-step explanation:

The fish population after t years can be modeled by the following equation:

$F(t) = F(0)(1-r)^{t}$

In which F(0) is the initial population and r is the constant rate of decay.

Year one the fish population was 18000

This means that $F(0) = 18000$

In year three the fish population was 8000 fish.

Two years later, so $F(2) = 8000$

$F(t) = F(0)(1-r)^{t}$

$8000 = 18000(1-r)^{2}$

$(1-r)^{2} = 0.4444$

$\sqrt{(1-r)^{2}} = \sqrt{0.4444}$

$1 - r = 0.6666$

$r = 0.3334$

$F(t) = 18000(0.6666)^{t}$

4 0

2 years ago

Ax + c = R (solve for x)

sp2606 [1]

Ax + c = R (subtract c from each side)

Ax + c - c = R - c

Ax = R - c (divide A from each side)

Ax/A = (R-c)/A

x = $\frac{R-c}{A}$ <-answer

4 0

2 years ago

Read 2 more answers

10=2/3n+8 what is n ?

alexira [117]

The value of n in the given equation is -2.6

Step-by-step explanation:

Given,

10 = $\frac{2}{3n+8}$

To find the value of n

10 = $\frac{2}{3n+8}$

or, 10(3n+8) = 2 [ by cross multiplication]

or, 30n + 80 = 2

or, 30n = 2-80 [ taking the constant values in one side]

or, 30n = -78

or, n = $\frac{-78}{30}$

or, n = -2.6

8 0

2 years ago

Read 2 more answers