When the wheels of a bicycle rotate 30 times the bicycle moves a distance of 175 feet what is the rate

Evaluate for x=2 and y=3: x^2y^-3/x^-1y

Artemon [7]

Answer:

8/81

Step-by-step explanation:

It's most efficient to simplify the quotient algebraically before inserting the values of the variables x and y.

The given expression reduces to x³ / y^4.

Substituting 2 for x and 3 for y, we get:

(2)³ 8

--------- = ---------- (Agrees with first given possible answer)

(3)^4 81

4 0

3 years ago

What is x for the following: |x-1/x-1|=1 and... x-1/x-1

Natalija [7]

Answer:

2, or any negative number

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

At an annual salary of $55,000 per year, what is the amount of semimonthly paychecks?

Amiraneli [1.4K]

Semi monthly means 2 times per month
assume that pay is at beginning and middle of month (doesn't matter, but makes it easier for me)

so 12 months
2 times per month
12 times 2=24
divide 55000 by number of months
55,000/24=2291.67

so the amount per paycheck, assuming equally distributed amounts throughout the paychecks, is $2291.67

4 0

3 years ago

I need help on this 2 problems please help

Digiron [165]

Answer:

3. 294 m²

4. 185,856 mm²

Step-by-step explanation:

To find the surface area of any figure, you can simply find the sum of the areas of all the sides. In question 3, the figure is a triangular prism that has two triangular bases and three rectangular sides. The measurements for the triangles are b = 9m and h = 6m. The formula for the area of a triangle is base times height divided by 2, or 9 x 6 = 54/2 = 27 m². However, since there are two triangular bases, the area for both is 54 m². The measurements for the other three rectangles are given:

7(10) + 8(10) + 9(10) = 240 m² + 54 m² = 294 m²

The surface area of a cube is much easier since all sides are equal and can be found using the formula:

SA = 6s², where 's' represents the measure of a side.

SA = 6(176)² = 185,856 mm²

6 0

3 years ago