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3 years ago

Which sum or difference identity could be used to prove that sin(π + q) = -sin q

Mathematics

2 answers:

blondinia [14]3 years ago

8 0

Answer:

sinπcosq + cosπsinq

Step-by-step explanation:

This was the answer on edg

i'm just as clueless so I'm trying to help from my mistakes

yan [13]3 years ago

4 0

Answer:

we should know that :

sin ( a + b ) = sin a * cos b + sin b cos a

For the given equation :

sin (π + q) = sin π * cos q + sin q * cos π

sin π = zero and cos π = -1

∴ sin (π + q) = 0 * cos q + sin q * (-1) = - sin q

Another solution:

The angle (π + q) lies in the third quarter ⇒ (1)

(π + q) and (-q) are supplementary angles ⇒ (2)

From (1) and (2)

sin(π + q) = -sin q

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I need help fast what is 9m−(3+7m) simplified?

iogann1982 [59]

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

4 0

3 years ago

(a) The function k is defined by k(x)=f(x)g(x). Find k′(0).

Brut [27]

Answer:

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) = $\frac{f'(5)g(5) - f(5)g'(5)}{2g^{2}(5) }$

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use product rule,i.e., $\frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}$

this will give k'(x)=f'(x)g(x) + f(x)g'(x)

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ $m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)}$ ]. Since m(x) has a function g(x) in the denominator so we need to use division rule to differentiate m(x). Division rule is as follows : $\frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}$

this will give $m'(x) = \frac{1}{2}\times\frac{f'(x)g(x) - f(x)g'(x)}{g^{2}(x) }$

on substituting the value x=5, we will get the value of m'(5).

{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : $\frac{\mathrm{d} f(x)}{\mathrm{d} x}=f'(x)$ }

4 0

3 years ago

A grocery store sells and 8 ounce bottle of juice for $1.76 What is the cost of the juice per ounce?

Marat540 [252]

Answer:

$0.22

Step-by-step explanation:

Now we know that 8 ounces total to $1.76. That means that in order to find how much 1 ounce costs, we will end up dividing both sides by 8

8 oz = $1.76

8 oz / 8 = $1.76 / 8

1 oz = $0.22

So, we now know that 1 oz is equal to 22 cents. You can also confirm your answer by multiple 0.22 by 8, and you'll see that you'll get 1.76

6 0

3 years ago

Given: F(x)=x+2 and G(x)=3x+5 (F - G) (x) = ? 4 -3x-3 -3x-3

lakkis [162]

What’s the x your trying to find

4 0

3 years ago

Name this polynomial by its degree: 3x² + 5x-3

Stella [2.4K]

Answer:

$\boxed{\textsf {The given polynomial is a quadratic polynomial. }}$

Step-by-step explanation:

A polynomial is given to us and we need to make the polynomial by its degree . Here the given polynomial is 3x² + 5x -3 .

$\sf\implies p(x)= 3x^2+5x-3$

So here we can see that the highest power of the variable in the given polynomial is 2 . So the polynomial is a quadratic polynomial .

★ More to Know :-

When we equate this quadratic polynomial with 0 , it becomes a quadratic equation.

That is ,

$\sf\implies p(x)= 3x^2+5x-3=0$

This is done in order to find the zeroes of the polynomial. The zeroes of the polynomial are the values for which the polynomial becomes 0 .

4 0

3 years ago

Read 2 more answers