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3 years ago

Y - 6 = 4(1 - 4)

Mathematics

1 answer:

klasskru [66]3 years ago

4 0

y - 6 = 4(1 - 4)

y - 6 = 4 - 16

y - 6 = -12

y = -12 + 6

y = -6

This is a horizontal line through the point (0, -6). See below.

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What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for x.)

marshall27 [118]

The volume of the composite figure is the third option 385.17 cubic centimeters.

Step-by-step explanation:

Step 1:

The composite figure consists of a cone and a half-sphere on top.

We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.

The radius is 4 cm and the height is 15 cm.

The volume of the cone :

$V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32$ cubic cm.

Step 3:

The area of a half-sphere is half of a full sphere.

The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 4 cm. We take π as 3.1415.

The volume of a full sphere $\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07$ cubic cm.

The volume of the half-sphere $=\frac{1}{2} (268.07) = 134.037$ cubic cm.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume $251.32+134.037 = 385.357$ cub cm. This is closest to the third option 385.17 cubic centimeters.

5 0

3 years ago

The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so th

Reptile [31]

Answer:

The least number of items to produce is 41

Step-by-step explanation:

Average Cost

Given C(x) as the cost function to produce x items. The average cost is:

$\displaystyle \bar C(X)=\frac{C(x)}{x}$

The cost function is:

$C(x) = -20x+1681$

And the average cost function is:

$\displaystyle \bar C(X)=\frac{-20x+1681}{x}$

We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

We set the inequality:

$\displaystyle \frac{-20x+1681}{x}\le 21$

Multiplying by x:

$-20x+1681 \le 21x$

Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

Adding 20x:

$1681 \le 21x+20x$

$1681 \le 41x$

Swapping sides and changing the sign:

$41x \ge 1681$

Dividing by 41:

$x\ge 41$

The least number of items to produce is 41

8 0

2 years ago

1. A group of workers is harvesting berries at a constant rate. An equation that represents the number of baskets of berries the

lbvjy [14]

Answer: (a) The slope of the line is 5 and the y-intercept is (0,10). (b) The rate of change is 5 and the initial amount is 10.

Explanation:

The given equation is,

$y=5x+10$ .... (1)

(a)

The slope intercept form of the a line is,

$y=mx+b$ .... (2)

Where, m is slope and (0,b) is y-intercept.

On comparing (1) and (2) we get,

$m=5, b=10$

Therefore, the slope is 5 and the y-intercept is (0,10).

(b)

The rate of change is also known as slope therefore the rate of change is 5.

To find the initial amount put x=0 in the given equation.

$y=5(0)+10=10$

Therefore, the initial value is 10.

The rate of change represents the number of baskets of berries the workers picked increased by 5 units per unit of time.

The initial amount shows the number of baskets of berries the workers picked before the workers starts harvesting.

(c)The graph is shown below.

Since x represents the time in hours, therefore x is always greater that or equal to 0.

7 0

2 years ago

Read 2 more answers

Help please!! Solve the equation -5m = -20. m = 1/4 m = -1/4 m = -4 m = 4

koban [17]

Answer:

m=4

Step-by-step explanation:

-5m=-20

m= - 20/-5

m=4

4 0

3 years ago

I need the answers to number 2 and 3

lara31 [8.8K]

For 2 it is slope 3 and y intercept (0,5)
For 3 it is slope y=-4x-5

4 0

2 years ago

Read 2 more answers