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3 years ago

5

Simplify sin(180-theater).cos(90°-theater)-1/cos(-theater)

1 answer:

Harman [31]3 years ago

3 0

[sin(180-a) x cos(90-a) - 1]/cos(-a)
= [sin(a) x sin(a) - 1]/(-cos(a))
= [sin^2(a) -1]/(-cos(a))
= [-cos^2(a)]/(-cos(a))
= cos(a)

formula used
sin(180-a) = sin(a)
cos(90-a) = sin(a)
cos(-a) = -cos(a)
sin^2(a) + cos^2(a) = 1
all of these are easily proved by the unit circle. you might find someone to explain this. it will be very handy.

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Given f(x)=3x^2+5 and g(x)=x−2 . What is (fg)(x) ? 3x^2−x+7 3x^3−6x2+5x−10 −3x^2+x−7 3x^3−10

wolverine [178]

For this case we have that by definition:

$(fg) (x) = f (x) * g (x)$

So:

$(fg) (x) = (3x ^ 2 + 5) (x-2)$

We apply distributive property that states that:

$(a + b) (c + d) = ac + ad + bc + bd$

In addition, we take into account that:

$+ * - = -$

$(fg) (x) = 3x ^ 3-6x ^ 2 + 5x-10$

Answer:

$3x ^ 3-6x ^ 2 + 5x-10$

Option B

6 0

2 years ago

Read 2 more answers

Find the area of the polygon defined by the coordinates (0,-5),(-5,0),(-15,-20),and(-20,-15)

alekssr [168]

Area of the polygon defined by the given points is 62.5 sq units

Step-by-step explanation:

Step 1 :

Let P be the point (-5,0) Q = (0,-5), R = (-15,-20) and S = (20,-15)

We have to to find the area of the polygon PQRS

Step 2 :

The area of polygon given the vertices (x $(x_{1} ,y_{1} ), (x_{2} ,y_{2}) ... (x_{n} ,y_{n} )$ is given by

Area = mod ( $(x_{1} y_{2} - y_{1}x_{2}) + (x_{2} y_{3} - y_{2}x_{3}) + ... (x_{n} y_{1} - y_{n}x_{1})$ ) ÷ 2

Where $x_{n}$ is the vertex n's x coordinate , $y_{n}$ is the vertex n's y coordinate

Substituting the corresponding values ,

Area of PQRS = mod ( (25 - 0)+ (0-75) +(300-300) +( 0-75) ) ÷ 2

= mod (25-75+0-75) ÷ 2

= mod (-125) ÷ 2 = 125 ÷ 2 = 62.5 sq units

Step 3 :

Answer :

Area of the polygon defined by the given points is 62.5 sq units

4 0

2 years ago

X* square root of 3 =34

disa [49]

Answer:

17.49286

Step-by-step explanation:

Photomath :)

4 0

2 years ago

Read 2 more answers

Evaluate a(4b + c2) if a = 2, b = 5, and c = 1.

Maksim231197 [3]

Answer:

42

Step-by-step explanation:

a = 2, b = 5, and c = 1

a*(4b + c²) = ⇒ plug in values
2*(4*5 + 1²) = ⇒ solving exponents
2*(20 + 1) = ⇒ parenthesis
2*21 = ⇒ multiplication
42 ⇒ answer

3 0

3 years ago

Read 2 more answers

4. k/6 = 8/16 5. 5.4/7 = 27/h 6. 8/11 = 4/y+2

kupik [55]

Answer:

4. $k=3\\$

5. $h=35$

6. $\frac{7}{2}$ or 3.5

Step-by-step explanation:

$\frac{k}{6}=\frac{8}{16}$

Multiply those 2 values whose diagonal has both terms and divide by the term whose diagonal has the variable.

$k=\frac{8*6}{16}\\ k=\frac{48}{16}\\ k=3$

-----------------------------------------------------------------------

$\frac{5.4}{7}=\frac{27}{h}$

$h=\frac{7*27}{5.4} \\h=\frac{189}{5.4}\\ h=35$

-------------------------------------------------------------------------

$\frac{8}{11}=\frac{4}{y+2}$

$y+2=\frac{11*4}{8}\\ y=\frac{11*4}{8}-2\\y=\frac{44}{8}-2 \\y=\frac{11}{2}-2\\ y=\frac{11-2*2}{2}\\ y=\frac{11-4}{2}\\ y=\frac{7}{2}=3.5$

7 0

2 years ago