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2 years ago

7

Jason will use a 1/3 gallon pitcher to fill an empty three-quarter gallon water jug. How much water will he need in order to com

pletely fill the water jug

2 answers:

kolbaska11 [484]2 years ago

6 0

He'll need 3/4 gallons of water

Inessa05 [86]2 years ago

6 0

Answer:

half of a full pitcher

Step-by-step explanation:

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What is the value of x in this equation? 2x + 2 = -46

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x = -24

Step-by-step explanation:

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3 years ago

Simplify csc θ(1−cos^2 θ)/sinθ cos θ to a single trigonometric function

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Answer:

<u><em></em></u> $\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha$ <u><em></em></u>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the trigonometric function

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

we know that sin²∝ + cos²∝ = 1

⇒ sin²∝ = 1- cos²∝

Now we have to simplify the given trigonometric function

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

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

<u><em>Step(ii)</em></u>

we know that cosec∝ = 1/ sin∝

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

After cancellation sine function, we get

= $\frac{1 }{ cos\alpha } = sec\alpha$

<u><em>Final answer:-</em></u>

<u><em></em></u> $\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha$ <u><em></em></u>

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2 years ago

Prove that ----1/2 (cos :2 theta-cos 8theta)=sin 5theta.sin 3theta

cupoosta [38]

Prove that:

$cos(2\alpha )-cos(8\alpha )=sin(5\alpha )sin(3\alpha )$

Remember that:

$cos(A+B)=cos(A)cos(B)-sin(A)sin(B)\\cos(A-B)=cos(A)cos(B)+sin(A)sin(B)\\\\\\cos(A+B)-cos(A-B)=-2sin(A)sin(B)$

We wish to remove this add (A+B).

$\left \{ {{A+B=p} \atop {A-B=q}} \right. \\\\2A=p+q$

$A=\frac{p+q}{2} \\\\B=\frac{p-q}{2}$

Then we de identity:

$cos(p)-cos(q)=-2sin(\frac{p+q}{2}) sin(\frac{p-q}{2})$

Let p=2α and q=8α

$cos(2\alpha )-cos(8\alpha )=-2sin(\frac{2\alpha +8\alpha }{2})sin(\frac{2\alpha -8\alpha }{2}) \\\\cos(2\alpha )-cos(8\alpha )=-2sin(5\alpha )sin(-3\alpha )\\\\*sin(-\alpha )=-sin(\alpha )\\\\cos(2\alpha )-cos(8\alpha )=2sin(5\alpha )sin(3\alpha )$

3 0

2 years ago