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2 months ago

7

A Candlestick burns at a rate of 0.2 inches per hour. After 8 straight hours of burning , the candlestick is 13.4 inches tall. W

rite and solve a linear equation to find the original height of the candle.

1 answer:

lawyer [12.5K]2 months ago

8 0

The initial height of the candle is 14.8 inches.

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Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche

tester [12383]

Response:

The height of the water when it reaches 4 inches is $\frac{3}{8\times \pi} inch/s$ .

Detailed Explanation:

Flow rate of water from the cone = R= $\frac{3}{2} inch^3/s$

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

$\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}$

r = h/2

Volume of the cone = $V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2h$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}$

$\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}$

$\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

h = 4 inches

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2$

$\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s$

The height of the water when it is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

6 0

3 months ago

Find the maximum value of P=3x+2y subject to the following constraints:<br> Please help me!!!

Zina [12379]

The maximum value of P is determined to be 33.

Step-by-step explanation: Start by graphing the constraints represented by the lines

5x + y = 16, which has intercepts at (16, 0) and (0, 16), and

2x + 3y = 22, with intercepts at (11, 0) and (0, $\frac{22}{3}$ ). The solutions to both sets of constraints lie beneath the lines. Solve the equations 5x + y = 16 and 2x + 3y = 22 simultaneously to find their intersection point at (2, 6).

The vertices of the feasible region are determined to be (0, 0), (0, 16), (2, 6), and (11, 0). Evaluate the objective function at each vertex.

At (0, 0), P = 0. At (0, 16), P = 32. At (2, 6), P = 18. Finally, at (11, 0), P = 33. Thus, the maximum P value occurs when x = 11 and y = 0.

6 0

2 months ago

Write the converse of the following statement and determine its truth value:

AnnZ [12381]

Answer:
The converse is:
If the ratio of left-handers to right-handers is 1: 8, then for every 3 left-handed individuals, there are 24 right-handed individuals.
The truth value is: True
Step-by-step explanation:
This statement can be expressed as:
p -> If a class contains 3 left-handed individuals and 24 right-handed individuals,
q -> the ratio of left-handed to right-handed individuals is 1:8.
The converse of a conditional statement is:
if q then p.
Thus, we have the converse as:
if the ratio of lefties to righties is 1: 8, then for each 3 left-handed individuals, there are 24 right-handed individuals.
The truth value is as follows:
For p, we find the ratio = 3: 24,
which simplifies to.
Ratio = 1: 8.
For q, we have:
Ratio = 1: 8.
Since both conditions are accurate, the truth value is true.

4 0

1 month ago

The sum of the four angles in a rectangle is always 180 degrees true or false?

Zina [12379]

A rectangle consists of 4 sides
with each angle being a right angle
and by definition, a right angle measures 90 degrees
$90 + 90 + 90 + 90 = 360\\ or\\ 90 * 4 = 360$
False

7 0

1 month ago

Read 2 more answers

A set of speakers costs $22 and songs cost $1.25 each. The sales tax rate is 7.5%. The expression 0.075(22 + 1.25s) can be used

Leona [12618]

Answer:

1.65 + 0.09s

Step-by-step explanation:

Considering that:

Cost of speaker = $22

Cost per song = $1.25

Sales tax rate = 7.5%

To find the sales tax on the total purchase, use the expression: 0.075(22 + 1.25s)

Expanding this expression:

0.075(22 + 1.25s)

(0.075 * 22) + (0.075 * 1.25s)

1.65 + 0.09375s

Rounding to two decimal places:

The total sales tax on the purchase is:

1.65 + 0.09s

4 0

1 month ago