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3 years ago

If the circumference of a circle is 12, and the angle measure of an arc is 60o, which is the length of the arc?

1 answer:

3 0

We can get the measurement of the arc by determining first the radius of the circle. The circumference of a circle is equal to 2 * pi * radius. Hence from a 12 unit2 circumferenced circle, the radius is 1.91 units.Length of the arc is equal to radius times the angle in radians. 60 deg is equal to pi over 3. The length of the arc is equal to 2 units.

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I built a storage shed in the shape of a rectangular box on a square base. The material that I used for the base cost $4 per squ

Dmitrij [34]

Answer:

$V = \frac{450L - 6 L^{3} }{10}$

Step-by-step explanation:

The volume of a cuboid can be determined simply by the formula: V= LWH

(where: L is length, H is height and W is width).

In this particular case the base is a square, which means the length and width are equal. Hence we can modify the equation of volume:

$V = L^{2} H$

Now we need to find the value of H in terms of L. For this we can develop the equation for cost incurred in building the storage shed. We find the area of each side of the cuboid, and then we multiply it by cost per square feet to find the total cost incurred; as shown below:

Area:

Base: $L$ × $L = L^{2}$

Roof: $L$ × $L = L^{2}$

Side: $4 H$ × $L = 4HL$ (we have considered all four sides)

Cost:

Base: 4 $L^{2}$

Roof: 2 $L^{2}$

Side: $2.50 * 4HL = 10 HL$

Total cost:

4 $L^{2}$ + 2 $L^{2}$ + 10 $HL$ = 450

We simplify this equation further:

6 $L^2$ + 10HL = 450

10HL = 450 - 6 $L^2$

$H = \frac{450- 6 L^2}{10L}$

We now have the value of H, which we can substitute in the formula of Volume we deduced earlier:

substituting $H = \frac{450-6L}{10L}$ in $V = L^{2} H$ :

$V = L^2$ × $\frac{450 - 6L }{10L}$

Simplifying it further:

$V = L$ × $\frac{450 - 6L}{10}$

$V= \frac{450L - 6L^3}{10}$ is the final answer.

3 0

3 years ago

The expression 7z-9p+9z-z

nika2105 [10]

Answer:

15z - 9p

Step-by-step explanation:

7z - 9p + 9z - z

=7z - 9p +8z

= -9p + 15z or 15z - 9p Answer

Hope this helps!

4 0

4 years ago

I really don't understand this I need help

Salsk061 [2.6K]

In looking at it I would guess it is asking which of the points is on the line? To answer that you would have to take each point an plug it into the equation and see if it is true.

3x - 7 = y

A(9,20)
3(9) - 7 = 20
27 - 7 = 20
20 = 20 True - this point is on the line

B(5,0)
3(5) - 7 = 0
15 - 7 = 0
8 = 0 False - this point is not on the line

C(3,2)
3(3) - 7 = 2
9 - 7 = 2
2 = 2 True - this point is on the line

I hope this helps

7 0

3 years ago

Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equat

Nina [5.8K]

Answer:

Correct choice is D

Step-by-step explanation:

Given the system of two equations:

$\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..$