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1 year ago

Let f(r) = 42 - 5, find f(3).

Mathematics

1 answer:

liberstina [14]1 year ago

5 0

F (x) = 4x - 5
F (3) just means substituting x with 3
For further please ask in question

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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

What happens to the value of the expression 70 - 3g as g increases

exis [7]

Answer:

It decreases

Step-by-step explanation:

Given the expression: 70-3g

When g=1, 70-3g=70-3(1)=70-3=67
When g=2, 70-3g=70-3(2)=70-6=64
When g=3, 70-3g=70-3(3)=70-9=61
When g=4, 70-3g=70-3(4)=70-12=58
When g=5, 70-3g=70-3(5)=70-3=55

From the above, notice that as g increases, the value of the expression decreases.

6 0

3 years ago

Can anyone help with expanding this?

Readme [11.4K]

Answer:

is this collage mathz

Step-by-step explanation:

7 0

2 years ago

40 POINTS is (4,7) a solution of equations? Explain your answer 2x+4y=36 3x-4y=-6

dsp73

2x + 4y = 36
3x - 4y = -6
--------------add
5x = 30
x = 6

2x+4y=36
2(6)+4y=36
12 + 4y = 36
4y = 24
y = 6

answer
(6, 6) is a solution of equations
(4,7) is NOT a solution of equations

6 0

2 years ago

Read 2 more answers

The expression 3 × n can be written without the multiplication sign as 3n. For each expression in parts (a)–(c), Use n = 1, 2, 3

baherus [9]

You can because you already know the number is 3 and the blank number is n

7 0

2 years ago