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3 years ago

15 divided by 6 2/3 = A. 100 B. 2/14 C. 100 1/4 D. 2 3/4

Mathematics

2 answers:

Ket [755]3 years ago

5 0

The answer is D. 2 2/3

satela [25.4K]3 years ago

3 0

The answer is 2 1/4.

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Find the derivative of ln(secx+tanx)

Sliva [168]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3000160

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Find the derivative of

$\mathsf{y=\ell n(sec\,x+tan\,x)}\\\\\\ \mathsf{y=\ell n\!\left(\dfrac{1}{cos\,x}+\dfrac{sin\,x}{cos\,x} \right )}\\\\\\ \mathsf{y=\ell n\!\left(\dfrac{1+sin\,x}{cos\,x} \right )}$

You can treat y as a composite function of x:

$\left\{\! \begin{array}{l} \mathsf{y=\ell n\,u}\\\\ \mathsf{u=\dfrac{1+sin\,x}{cos\,x}} \end{array} \right.$

so use the chain rule to differentiate y:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(\ell n\,u)\cdot \dfrac{d}{dx}\!\left(\dfrac{1+sin\,x}{cos\,x}\right)}$

The first derivative is 1/u, and the second one can be evaluated by applying the quotient rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{\frac{d}{dx}(1+sin\,x)\cdot cos\,x-(1+sin\,x)\cdot \frac{d}{dx}(cos\,x)}{(cos\,x)^2}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{(0+cos\,x)\cdot cos\,x-(1+sin\,x)\cdot (-\,sin\,x)}{(cos\,x)^2}}$

Multiply out those terms in parentheses:

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{cos\,x\cdot cos\,x+(sin\,x+sin\,x\cdot sin\,x)}{(cos\,x)^2}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{cos^2\,x+sin\,x+sin^2\,x}{(cos\,x)^2}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{(cos^2\,x+sin^2\,x)+sin\,x}{(cos\,x)^2}\qquad\quad (but~~cos^2\,x+sin^2\,x=1)}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{1}{u}\cdot \dfrac{1+sin\,x}{(cos\,x)^2}}$

Substitute back for $\mathsf{u=\dfrac{1+sin\,x}{cos\,x}:}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{~\frac{1+sin\,x}{cos\,x}~}\cdot \dfrac{1+sin\,x}{(cos\,x)^2}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{cos\,x}{1+sin\,x}\cdot \dfrac{1+sin\,x}{(cos\,x)^2}}$

Simplifying that product, you get

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{1+sin\,x}\cdot \dfrac{1+sin\,x}{cos\,x}}\\\\\\ \mathsf{\dfrac{dy}{dx}=\dfrac{1}{cos\,x}}$

∴ $\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=sec\,x} \end{array}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: derivative composite function logarithmic logarithm log trigonometric trig secant tangent sec tan chain rule quotient rule differential integral calculus

3 0

3 years ago

How to combine fractions 5b/4a+b/3a-3b/a

Step2247 [10]

Most importantly, while including divisions with various denominators, the initial step says that we should change these portions so they have "a similar denominator" .Here are the means for including divisions with various denominators .Construct each portion with the goal that the two denominators are equivalent. Keep in mind, while including divisions with various denominators, the denominators must be the same. So we should finish this progression first. a. Re-compose every proportionate division utilizing this new denominator b. Now you can include the numerators, and keep the denominator of the proportionate divisions. c. Re-compose your answer as a streamlined or decreased division, if necessary. We know this sound like a great deal of work, and it is, yet once you see completely how to locate the Common Denominator or the LCD, and manufacture proportional parts, everything else will begin to become all-good. Thus, how about we set aside our opportunity to do it. Solution: 5b/4a + b/3a -3b/a =15b/12a + 4b/12a – 36b/12a = -17b/12 a Or = - 1 5b/12a in lowest term.

8 0

3 years ago

What is the quotient of 5 1/2 and 1/8

Stels [109]

Answer:

Step-by-step explanation:

5 1/2 / 1/8

turn into improper fraction

11/2 then change to multiplication

11/2*8/1(have to flip)

88/2(multiply across)

simplify=44

4 0

3 years ago

In your pattern which shape covers more of the plane blue rhombus red trapezoid or green triangles? Explain how you know.

mixas84 [53]

Answer:

Which shapes cover more of the plane" means that we are comparing the areas covered by the different types of shapes. In these patterns, two triangles match up to one rhombus, and three triangles match up to one trapezoid.

In both Pattern A and Pattern B, the first hexagonal part is made up of 7 triangles, 4 rhombuses, and 3 trapezoids.

The first hexagonal part is repeated across the pattern, so whichever type of shape covers the most area of this first part also covers the most area in the whole pattern.

hope it helps

3 0

3 years ago

Last month Kim trained 3 times as many dogs as cats.

Lisa [10]

Answer:

Step-by-step explanation:

dog=3x

cat=x

3x+x=32

4x=32

4/4

32/4

x=8

3(8)=24

x=8

So she trained 24 dogs and 8 cats

6 0

3 years ago