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2 years ago

Fill in the boxes to complete each number chain.

Mathematics

1 answer:

docker41 [41]2 years ago

8 0

Answer:

Step-by-step explanation:

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How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

shepuryov [24]

$LHS\\ \\ =\frac { \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } }{ \tan { x } } \\ \\ =\frac { 1 }{ \tan { x } } \left( \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x } }{ \cos ^{ 2 }{ x } } -\frac { \sin ^{ 2 }{ x\cos ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \right) \\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x-\sin ^{ 2 }{ x\cos ^{ 2 }{ x } } } }{ \cos ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\left( 1-\cos ^{ 2 }{ x } \right) } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\cdot \sin ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } \sin ^{ 4 }{ x } }{ \sin { x\cos ^{ 2 }{ x } } } \\ \\ =\frac { \sin ^{ 3 }{ x } }{ \cos { x } }$

$\\ \\ =\sin ^{ 2 }{ x } \cdot \frac { \sin { x } }{ \cos { x } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \cot { x } } \\ \\ =\frac { \sin ^{ 2 }{ x } }{ \cot { x } } \\ \\ =RHS$

8 0

3 years ago

Priya is hosting a poetry club meeting this week and plans to have fruit punch and cheese for the meeting. She is preparing 8 ou

Sveta_85 [38]

Answer:

b= $3.99×2 + $2.50= $10.48

Step-by-step explanation:

We have the following unknowns:

p: number of people in the club

f: ounces of fruit punch

c: ounces of cheese

b: budget in dollars

We know that

p=12

Priya is preparing 8 ounces of fruit punch per person, so:

f= 8×p = 8×12 = 96

We need 96 ounces of fruit punch

Priya is preparing 2 ounces of cheese per person, so:

c= 2×p = 2×12 = 24

We need 24 ounces of cheese

A package of cheese contains 16 ounces and costs $3.99. In order to get all the cheese we need, Priya have to buy 2 packages of cheese.

2×16=32

32>24

A one-gallon jug of fruit punch contains 128 ounces and costs $2.50. Then, Priya have to buy only one gallon jug.

128>96

The budget would be:

b= $3.99×2 + $2.50×1

3 0

3 years ago

I don’t quite understand this problem could someone help me please

ale4655 [162]

Answer:

$\frac{7\sqrt{65}}{65}$

Step-by-step explanation:

Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.

$cos$ B = $\frac{7}{\sqrt{65}}$ = $\frac{7\sqrt{65}}{65}$

3 0

2 years ago