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alexandr1967 [171]
3 years ago
12

Is 8 a solution to 1/2x + 9 =13? Explain

Mathematics
1 answer:
elixir [45]3 years ago
7 0

Answer:

Yes.

Step-by-step explanation:

1/2 (8) + 9 = 13

1/2 x (8) equals 4

9 + 4 = 13

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(a) Use the Quotient Rule to differentiate the function f(x)=tan(x)-1/sec(x). f'(x)=
yKpoI14uk [10]

Answer:

(a) sin(x) + cos(x)

(b) sin(x) + cos(x)

(c) Both answers are equivalent

Step-by-step explanation:

(a) The given function is:

f(x) = \frac{tan(x)-1}{sec(x)}

According to the quotient rule:

f(x) = \frac{g(x)}{h(x)}\\f'(x)= \frac{g'(x)h(x)-g(x)h'(x)}{h(x)^2}

Applying the quotient rule:

f(x) = \frac{tan(x)-1}{sec(x)}\\f'(x)=\frac{sec^2(x)*sec(x)-(tan(x)-1)*sec(x)tan(x)}{sec(x)^2}\\f'(x)=\frac{sec^3(x)-sec(x)tan^2(x)+sec(x)tan(x)}{sec(x)^2}\\f'(x)=sec(x)+\frac{tan(x)-tan^2(x)}{sec(x)}\\ \frac{tan(x)}{sec(x)}=sin(x) \\f'(x)=sec(x)+sin(x)-sin(x)tan(x)\\

This can be simplified to:

f'(x)=sec(x)+sin(x)-sin(x)tan(x)\\f'(x) = \frac{1}{cos(x)}+sin(x)-\frac{sin^2(x)}{cos(x)}\\f'(x)=\frac{1+sin(x)cos(x)-sin^2(x)}{cos(x)}\\f'(x)=\frac{sin^2(x)+cos^2(x)+sin(x)cos(x)-sin^2(x)}{cos(x)}\\f'(x)=\frac{cos^2(x)+sin(x)cos(x)}{cos(x)}\\ f'(x)=sin(x) +cos(x)

(b) Simplifying in terms of sin(x) and cos(x):

f(x) = \frac{tan(x)-1}{sec(x)}\\f(x)=\frac{\frac{sin(x)}{cos(x)}-1 }{\frac{1}{cos(x)} } \\f(x)=sin(x)-cos(x)\\f'(x) = cos(x)+sin(x)

(c) As proven above, both answers are equivalent.

4 0
3 years ago
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Ede4ka [16]

Answer:

c and d are monomial because they have only one term

7 0
3 years ago
Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row. He sees 8 trombone players. How many f
sukhopar [10]
Twelve flute players.

Eight trombone players.

20 total of flute and trombone players.
6 0
3 years ago
What is 16/6 as a decimal?
Mars2501 [29]
To get 16/6 converted to decimal, you simply divide 16 by 6.
4 0
3 years ago
What effect does decreasing the temperature of a room have on a lifespan of a battery?
Leni [432]

This question is incomplete. There are options in the question (from reference) and no highlight in the red bolded text in the question.

What effect does decreasing the temperature of a room have on a lifespan of a battery?

Which variable is highlighted in red, bolded tex?  

a . Independent

b . Dependent

c . Control

d . None

But the answer to both the independent and dependent variables will be provided and explained in detail.

Answer:

Independent variable: decrease in temperature

Dependent variable: lifespan of battery

 Step-by-step explanation:

The independent variable in an experiment is defined as the variable that can be changed or manipulated in order to find an outcome while the dependent variable is defined as the variable that is influenced by the changes in the independent variable.

In the given example, a decrease in temperature  is the dependent variable as it is changing and the lifespan of battery  is the dependent variable as it is responding to the independent variable ?9decrease in temperature).

8 0
3 years ago
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