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2 years ago

What is the derivative of y=3tan(x)y=3 tan (x) ?

Mathematics

2 answers:

maw [93]2 years ago

6 0

$y=3tanx\\\\tanx=\frac{sinx}{cosx}\Rightarrow y=\frac{3sinx}{cosx}\\\\\\y'=\frac{(3sinx)'cosx-3sinx(cosx)'}{(cosx)^2}=\frac{3cosxcosx-3sinx(-sinx)}{cos^2x}=\frac{3cos^2x+3sin^2x}{cos^2x}\\\\=\frac{3(cos^2x+sin^2x)}{cos^2x}=\frac{3(1)}{cos^2x}=\frac{3}{cos^2x}\\\\-------------------\\\\sin^2x+cos^2x=1$

viva [34]2 years ago

6 0

Answer is in the attachment below. Use the "product rule".

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Solve 15 ≥ -3x or 2/3 x ≥ -2.

hjlf

Solve each of the equations independently, then determine if the are continuous or discontinuous.
15≥-3x [start here]
-5≤x [divide both sides by (-3). *Dividing by a negative number means the direction of the sign changes!]
x≥-5 [just turned around for analysis]

Next equation:
2/3x≥-2 [start here]
x≥-2(3/2) [multiply both sides of the equation by the reciprocal, 3/2)
x≥-3

So, (according to the first equation) all values of x must be greater than, or equal to -5.

(According to the second equation) all values of x must be greater than, or equal to -3.
So, when graphed on a number line, both equations graph in the same direction, so they are continuous.

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2 years ago

Read 2 more answers

A line with a negative slope intersects a horizontal line 3 units above the x-axis. Select each point that can not be the inters

AnnyKZ [126]

Step-by-step explanation:

Since both lines intersect each other 3 units above the x-axis, the y-value of the point of intersection must be 3.

Looking at the options, (-3, 5), (3, -2) and (0, -3) are all invalid points.

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2 years ago

Question 3

Crank

Step-by-step explanation:

Given that,

The mass of a patient = 70 kg

A 70kg patient has approximately 8 pints of blood.

The patient donates 470mL of blood.

We know that,

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8 pints = 4544 mL

Required fraction,

$\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}$

So, the required fraction is approximately $\dfrac{1}{10}$ .

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2 years ago

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Harrizon [31]

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Reil [10]

By the knowledge and application of <em>algebraic</em> definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)

<h3>How to solve an algebraic equation</h3>

In this question we have an equation that can be solved by <em>algebraic</em> definitions and theorems, whose objective consists in clearing the variable x. Now we proceed to solve the equation for x:

- 10 · x + 1 + 7 · x = 37 Given
(- 10 · x + 7 · x) + 1 = 37 Associative property
-3 · x + 1 = 37 Distributive property/Definition of subtraction
- 3 · x = 36 Compatibility with addition/Definition of subtraction
x = 12 Compatibility with multiplication/a/(-b) = -a/b/Definition of division/Result

By the knowledge and application of <em>algebraic</em> definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)

To learn more on linear equations: brainly.com/question/2263981

#SPJ1

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