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PIT_PIT [208]
2 years ago
12

Trigonometric equations 5sinx = 3sinx + square root of 2

Mathematics
1 answer:
Lera25 [3.4K]2 years ago
4 0

\qquad\qquad\huge\underline{{\sf Answer}}♪

Let's solve for x ~

\qquad \sf  \dashrightarrow \:5 \sin(x)  = 3 \sin(x)   +  \sqrt{2}

\qquad \sf  \dashrightarrow \:5 \sin(x)  - 3 \sin(x)  =  \sqrt{2}

\qquad \sf  \dashrightarrow \:2 \sin(x)  =  \sqrt{2}

\qquad \sf  \dashrightarrow \: \sin(x)  =  \sqrt{2}  \div 2

\qquad \sf  \dashrightarrow \: \sin(x) =  \frac{1}{ \sqrt{2} }

\qquad \sf  \dashrightarrow \:x = 45 \degree \:  \: or \:  \:  \frac{\pi}{4}  \: rad

・ .━━━━━━━†━━━━━━━━━.・

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Please answer with clear instructions so that i can apply this to other questions
marishachu [46]

Answer:

1 and - 1

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope ( gradient ) )

y = x ← is in this form

with gradient m = 1

Parallel lines have equal gradients

Then the gradients of lines parallel to the given line is 1

Given a line with gradient m then the gradient of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{1} = - 1

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2 years ago
Suppose that during one period extreme cold,the average daily temperature decreased 1 1/2 F each day. How many days did it take
Alenkasestr [34]

We have been given that during one period extreme cold, the average daily temperature decreased 1\frac{1}{2} degree F each day. We are asked to find number of days it will take for the temperature to decrease by 9 degree F.

First of all we will convert our mixed fraction into improper fraction.

1\frac{1}{2}=\frac{3}{2}

Now we will divide total temperature change (9) by average daily temperature change (\frac{3}{2}) to find number of days.

9\div\frac{3}{2}

Dividing a number by a fraction is same as multiplying the number by reciprocal of the fraction.

9\cdot\frac{2}{3}

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Therefore, it will take 6 days for the temperature to decrease by 9 degree F.

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2 years ago
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UkoKoshka [18]

Answer:

The point of intersection is (0,-2).

Step-by-step explanation:

Equation 1: y=-4x-2

Equation 2 : -2x+y=-2

Plot the lines on the graph

Refer the attached figure

Equation 1: y=-4x-2 ---- Red

Equation 2 : -2x+y=-2 ---- Blue

Point of intersection : A point where both the lines intersect is called point of intersection.

So, Both lines intersect at point (0,-2)

So, Point of intersection is (0,-2)

Hence The point of intersection is (0,-2).

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3 years ago
Please help me on this question
Alina [70]

Answer:

DE = 13.4 cm  (to 1 decimal place)

Step-by-step explanation:

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E is midpoint of BC   (given)

BE = EC  = 12/2 = 6 cm

CD = AB = 12 cm   (opposite sides of a square are congruent)

angle ECD is a right angle (interior angles of a square are 90 deg.)

Consider right triangle ECD

DE = sqrt(EC^2+CD^2)    ............. pythagorean theorem

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alina1380 [7]

Answer:

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