27. Dylan bought 3 identical shirts online for a total cost of $71.83 including a flat rate of $7.99 for shipping. Write

It took 4 hours for Nancy

Ghella [55]

Answer:

for what lol

Step-by-step explanation:

5 0

2 years ago

Evaluate the limit with either L'Hôpital's rule or previously learned methods.lim Sin(x)- Tan(x)/ x^3x → 0

Vsevolod [243]

Answer:

$\dfrac{-1}{6}$

Step-by-step explanation:

Given the limit of a function expressed as $\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}$ , to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

$= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)$

Step 2: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the function

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\$

Step 3: substitute x = 0 into the resulting function

$= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)$

Step 4: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\$

$= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)$

Step 6: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\$

Step 7: substitute x = 0 into the resulting function in step 6

$= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}$

<em>Hence the limit of the function </em> $\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}$ .

3 0

3 years ago

You begin with $90 in your savings account and your friend begins

Colt1911 [192]

Answer:

F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.

F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.

When you graph the equations, plugging in different values for t, you can see that the graphs intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200. They will not have the same amount of money in 10 weeks.

7 0

3 years ago

Read 2 more answers

Solve with the law of sine

Zinaida [17]

1) Triangle QRT, where q = 32.4 ft, r = 29.8 ft, t = 42.1 ft

No this cannot make a second triangle

2) Triangle ABC, where B = 62°, a = 11.52 m, c = 19.34 m

No this cannot make a second triangle

3) Both of the triangles cannot make a second triangle

The following is a detailed explanation of the sine law: In a triangle, side "a" divided by angle sine "a" equals side "b" divided by angle sine "b" equals side "c" divided by angle sine "c."

The formula for law of sine is written as

Sine A a = Sine B/ b = Sine C / c

These law helps in determining the given angles and sides

For the situation given; both cannot be used to make a second triangle

Learn more about conditions Infinite number of triangles at:

brainly.com/question/29637739

#SPJ1

5 0

2 years ago

Mr. Ruarks evergreen trees grow 10 inches per year. His customer would like to purchase the trees when they reach 2 meters in he

djyliett [7]

Isn't it 5?

I think it's 5 , I may be wrong idk.

5 0

4 years ago