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3 years ago

Find the values of x and y. help please work has to be shown ..

Mathematics

1 answer:

Likurg_2 [28]3 years ago

5 0

Answer:

x = 7 and y = 17

Step-by-step explanation:

16x + 9x + 5 = 180 cuz they are supplementary

25x = 175

x = 7

We also know that 16x + 4y = 180

so 16(7) + 4y = 180, so 4y = 180 - 112, so 4y = 68. y = 17

hope this makes sense

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A sin^3theta+b cos^3theta=sintheta costheta and a sintheta-b costheta=0 then prove a^2+b^2=1

frozen [14]

Answer:

<em>Proof in explanation</em>

Step-by-step explanation:

<u>Trigonometric Identities</u>

The basic trigonometric identity is:

$\sin^2\theta+\cos^2\theta=1$

We'll use it and some basic algebra to prove that, given:

$a sin^3\theta+b cos^3\theta=sin\theta cos\theta$

And

$a\sin\theta-b\cos\theta=0$

Then

$a^2+b^2=1$

From the equation:

$a\sin\theta-b\cos\theta=0$

We have:

$a\sin\theta=b\cos\theta\qquad [1]$

The equation

$a sin^3\theta+b cos^3\theta=sin\theta cos\theta$

Can be rewritten as

$a\sin\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta$

Replacing [1]:

$b\cos\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta$

Taking the common factor:

$b\cos\theta (\sin^2\theta+ \cos^2\theta)=\sin\theta \cos\theta$

The expression in parentheses is 1, thus:

$b\cos\theta =\sin\theta \cos\theta$

Dividing by $\cos\theta$

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Replacing in

$a\sin\theta=b\cos\theta$

We have

$a\sin\theta=\sin\theta\cos\theta$

Dividing by $\sin\theta$

$a=\cos\theta$

Now:

$a^2+b^2=(\cos\theta)^2+(\sin\theta)^2$

This expression is 1, thus it's proven:

$\boxed{a^2+b^2=1}$

6 0

3 years ago

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AnnZ [28]

Answer:

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Step-by-step explanation:

We are given the following in the question:

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Discount given to Markel =

$=\dfrac{7}{100}\times c\\\\=0.07c$

Markel's bill =

= Cost price - Discount

$= c - 0.07x\\=c(1-0.07)\\=0.93c$

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4 years ago

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Simora [160]

Answer:

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3 years ago

Calculate, to four decimal places, the first ten terms of the sequence. an = 1 +(−4/9)^n

Lemur [1.5K]

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<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

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Find out more on equation at: brainly.com/question/2972832

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san4es73 [151]

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3 years ago

Read 2 more answers