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evablogger [386]
3 years ago
13

Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants.

Mathematics
2 answers:
Mazyrski [523]3 years ago
3 0

Answer:

Step-by-step explanation:

sin x=a+b

cos x=a-b

sin²x+cos²x=(a+b)²+(a-b)²=2a²+2b²

or 2a²+2b²=1

a²+b²=1/2 which is constant for all values of x

(ii)

\frac{\sin x}{\cos x}=\frac{a+b}{a-b}\\\tan x=\frac{a+b}{a-b}=2\\a+b=2a-2b\\b+2b=2a-a\\or a=3b

trasher [3.6K]3 years ago
3 0

Answer:25

Step-by-step explanation:

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the length of a rectngle is 8/3 times as great as its widthwhat is the width if the length of a rectangle is 24 ft.
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L=(8/3)W = 24 ft.  Solving for W, we mult. both sides of this eqn by (3/8), obtaining

W = (3/8)(24 ft) = 9 ft (answer)
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A television weighs 7.4 kilograms how many grams does the television weigh
Pavlova-9 [17]
7400 grams is the answer.

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3 years ago
Here's a graph of a linear function. Write the
madam [21]

The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

<h3>What is a straight line?</h3>

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\

As we can see in the graph the line goes from (-6, 0) and (0, 3)

Finding the slope:

\rm m =\dfrac{3-0}{0-(-6)}\\

m = 3/6 = 1/2

y = mx + c

y = (1/2)x + c

c is the y-intercept

c = 3

The equation:

y = (1/2)x + 3

Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

Learn more about the straight line here:

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5 0
2 years ago
Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south. He is not sure where to point hi
GrogVix [38]

Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south, the heading he should have and the velocity of the broom with respect to the ground are mathematically given as

VR = 20, 699 m/s South

<h3>What is the heading he should have and the velocity of the broom with respect to the ground?</h3>

Divide horizontal and vertical components of Vs and Vw vectors

For Vs

Vs = Vs cos∅ [s] + Vs Sin∅ [w]

Vs = 18 Co58 [s] + 18 sin∅ [w]

For Vw

Vw = Vw Cos 55' [s] + Vw Sin 55 [E]

5.8333 x Cos 55 (s) + 5-8333 Sin 55 [E]

Vw = 3.3458 [s] + 4.7783 [E]

Resultant velocity VR = Vs + Vw

VR= 18 Coso (s) + 18 sine [w] +3.3458 (5) +42783 (E)

VR = (186030 +3.3458) [5] + (18sing - 4.7183)6]

(Harry Potter) flies south

18sin∅ - 4.7783 18=0

Hence

Sin∅ = 4.7783 18/18

∅ =sin{-1}(4.7783 18/18)

∅  = 15.3943

Harry Potter flies in the direction south to ∅ = $15.3943w]

Hence  velocity

VR = (18 cos∅   + 35452) s + 0

VR = (17.3541 +3-3458) s

VR = 20, 69999 m/s South

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1 year ago
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