Let vector a = 3i + j - k.

Find the vector b in the direction of vector a such that |b| = 5

For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)

But if you've been introduced to L'Hopital's rule: we have

[tex]\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0[/tex]

9514 1404 393

Answer:

  7.56 cm

Step-by-step explanation:

The volume is given by the formula ...

  V = 1/3b²h . . . . where b is the base edge length, and h is the height.

Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...

  144 cm³ = 1/3h³

  432 cm³ = h³

  h = ∛432 cm ≈ 7.55953 cm

The height of the pyramid is about 7.56 cm.

Answer:

[tex]7.56cm[/tex]

Step-by-step explanation:

Given that,

base length = Height

so,

[tex]volume = \frac{1}{3} {b}^{2} h \\ [/tex]

We can also write this as( according to this question)

[tex]v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} [/tex]

let's solve

[tex]v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55[/tex]

[tex]base = height = 7.55cm \\ [/tex]

= 7.56cm

Answer:

Nicholas can order up to 3 toppings.

Step-by-step explanation:

Solve for the tip:

15% of the total cost = 15% × $7.50

Convert percentage into a decimal:

0.15 × 7.50 = 1.125

Variable x = number of toppings

Set up an equation:

7.50 + 1.125 + 1.25x = 13

Combine like terms:

8.625 + 1.25x = 13

1.25x = 4.375

x = 3.5

Since it is impossible to order "half" of a topping (0.5), Nicholas can only order up to 3 toppings.

Answer:

Mr Mohapi is selling cheaper chairs

Step-by-step explanation:

Find the cost per chair from both prices by dividing the total price by the number of chairs:

22500/500

= 45

9600/200

= 48

So, Mr Mohapi is selling at a price of $45 per chair and Mr Shuma is selling at a price of $48 per chair.

Since 45 is smaller than 48, Mr Mohapi's chairs are a better deal.

Mr Mohapi is selling cheaper chairs.

Answer:

(1,2) is ordered pair to (-4,2).

Step-by-step explanation:

(1,2)

hora khoi thaha vayena hai

Answer:

8%

Step-by-step explanation:

APR means annual percentage rate.

To convert the daily rate to an APR, multiply the daily rate by the number of days in a year

365 days = 1 year

0.02192% x 365 = 8.0008%

To round off to the nearest percent, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

The tenth digit is 0, so the number would be rounded off to 8%

Answer:

Step-by-step explanation:

let the height of the room(h) = x

Length(l) = 3*x = 3x

length = 2 * breadth

breadth(b) = length /2 = 3x/2

Cost of whitewashing the 4  walls = ₹ 7200

Area of 4 walls = 7200 ÷ 50 = 144 m²   ------(I)

Area of walls = 2lh + 2bh

                      = 2*3x*x + 2  *[tex]\frac{3x}{2}[/tex] * x

                       = 6x² + 3x²

                        = 9x²

9x² = 144    {From (I)}

x²  = 144/9

x²  = 16

x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]

x = 4 m

height = 4 m

length = 3*4 = 12m

Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]

Area of floor = l*b

                    = 12 * 6

                    = 72 m²

Cost of carpeting the floor = 72 * 325 = ₹ 23400

Answer:

A. 45%

Step-by-step explanation:

34/75=45 = 45%

Answer:

y = 10 between 0 and 1

AND

y=15x for x>=1

Step-by-step explanation:

This has 2 segments. One when 0 < x < 1 (y=$10), and one when x >= 1 (y=$15x)

So

y = 10 between 0 and 1

AND

y=15x for x>=1

-2a(a - d) + 2a(2a - 3d)

(-2a * a) + (-d * -2a) + (2a * 2a) + (2a * -3d)

-2a^2 + 2ad + 4a^2 - 6ad

(4a^2 - 2a^2) + (2ad - 6ad)

2a^2 - 4ad

---The above expression is simplified, though not fully. The below expression is fully simplified.

2a(a - 2d)

Hope this helps!

Answer:

70 days

Step-by-step explanation:

that is the procedure above

Answer:

62

Step-by-step explanation:

Of means multiply and is means equals

.03 * n = 1.86

Divide each side by .03

.03n/.03 = 1.86/.03

n =62

Answer:

27, 18

Step-by-step explanation:

Here's why

Answer:

C. 30

Step-by-step explanation:

We have a list of names that need to be sorted in a specific order. For this, we will use a permutation. This can be found on a scientific calculator, however, I'll be using the equation.

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

n = total number of objects

r = number of objects selected

In this instance, n will equal 6 since we have 6 different names to choose from and r will equal 2 since we are picking two names. Enter the values into the equation and evaluate.

[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]

Therefore, there are 30 possible two-part names.

Answer:

-2/5

Step-by-step explanation:

Answer:

198 KM

Step-by-step explanation:

82.5KM/5.5L= 15KM per liter

13.2 x 15 = 198 KM

Answer:

12 minutes

Step-by-step explanation:

Given

[tex]s_1 = 10mi/h[/tex] --- walk speed

[tex]s_2 = 20mi/h[/tex] --- jog speed

[tex]d = 2\ miles[/tex] --- distance

Required

The time to walk the given distance

Time is calculated as:

[tex]Time = \frac{distance}{speed}[/tex]

In this case, the speed is the speed at which she walks.

So, we have:

[tex]Time = \frac{d}{s_1}[/tex]

Substitute known values

[tex]Time = \frac{2mi}{10mi/h}[/tex]

[tex]Time = 0.2hr[/tex]

Convert to minutes

[tex]Time = 0.2 * 60mins[/tex]

[tex]Time =12mins[/tex]

Answer:

The answer is 7.5

Let the cost of a lamp = x

6 lamps would cost 6x

He bought 3 lamps at 3x plus Thad 950 left.

3 lamps plus the 950

Would be the same amount as 6 lamps:

Set up an equation and solve for x:

3x + 950 = 6x

Subtract 3x from both sides:

950 = 3x

Divide both sides by 3:

X = 316.67

Each lamp was $316.67

Multiply the price of a lamp by 6:

316.67 x 6 = 1900

He had $1900

Answer: $1900

Step-by-step explanation:

Mr Lim had enough money to buy 6 similar lamps. However he only bought 3 such lamps. That means he had only spent half of his money (6-3=3).

So, if he take money remaining with him = x = $950

Amount of money he first had = 2x =$950×2 = $1900

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Answer:

  see attached

Step-by-step explanation:

Short answer: to solve this problem, follow directions.

Let c and p represent numbers of cakes and pies produced daily. Then the constraints are ...

  2c +3p ≤ 108 . . . . . . . . available hours of preparation time

  1c +0.5p ≤ 20 . . . . . . . available hours of decoration time

  p ≥ 0, c ≥ 0 . . . . . . . . . negative numbers of cakes or pies cannot be produced

__

It works well to let a graphing calculator do this.

The feasible region is the doubly-shaded area with vertices ...

  (0, 0), (0, 36), (3, 34), (20, 0)

__

Profit is $25 per cake and $12 per pie, so is ...

  p = 25c +12p

__

The attached table shows the profit for the various mixes of cakes and pies in the feasible region. The most profit is had by production of cakes only.

The maximum profit is $500 per day for production of 20 cakes.

_____

Additional comment

We have used x for cakes and y for pies in the attachment, because those are variables that the Desmos calculator prefers.

As is sometimes the case, the production point giving maximum profit leaves one of the resources (preparation time) only partially utilized.

Answer:

$19.68

Step-by-step explanation:

this is not really clearly defined.

I assume it means that they are buying the item, no matter how much it costs, and that the split ratio between them also remains the same no matter the actual cost.

x = what Marcia is paying

and 132 - 18% = 132 × (100 - 18) / 100 = 132×0.82 = 108.24

so,

x + x/2 + x/3 = 108.24

6x + 3x + 2x = 649.44

11x = 649.44

x = $59.04

Mario's part is x/3 = 59.04/3 = $19.68

Step-by-step explanation:

hơi khó hiểu thông cảm UwU

Answer:

The answer is 12

Step-by-step explanation:

You see its because.

Answer:

?=12

Step-by-step explanation:

Using the Thalès's theorem:

[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]

Answer:

40*8.5=340

6*90=540

total=880/2.5=352bags

Answer:

x=0

x=6

x=-1

Step-by-step explanation:

x(x^2-5x-6)

x(x-6)(x+1)

x=0

x=6

x=-1

Answer:

Maybe length iss= 27 cm.

Answer:

4w = -5-19

4w=-24

w=-6

hope that answers your question

good luck