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2 years ago

Find the equation of the surface. the bottom hemisphere of a sphere centered at (8, -7, 0) with radius 10.

1 answer:

7 0

The equation of the sphere is
.. (x -8)^2 +(y +7)^2 +z^2 = 10^2

Then the bottom hemisphere has the equation
.. z = -√(100 -(x -8)^2 -(y +7)^2)

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Alex the electrician needs 34 yards of electrical wire to complete his job. He has a coil of wiring in his workshop. The coiled

bogdanovich [222]

Answer: This coil will not be enough to complete the job.

Step-by-step explanation:

The circumference of the coil of wiring can be calculated with:

$C=2\pi r$

Where r is the radius and $\pi=3.14$

The radius can be calculated by dividing the diameter by 2. Then:

$r=\frac{18in}{2}\\\\r=9in$

Convert 9 inches to yards (1 yard=36 inches):

$(9in)(\frac{1yd}{36in})=0.25yd$

Substitute this radius into the formula:

$C=2(3.14)(0.25yd)\\C=1.57yd$

Since there are 21 circles of wire, you need to multiply $C=1.57yd$ by 21:

$C_T=(1.57yd)(21)=32.97yd$

The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.

8 0

2 years ago

Jillian walked 0.5 miles before she started jogging at an average pace of 5 miles per hour. The equation d = 0.5 + 5t can be use

Mekhanik [1.2K]

Answer: independent variable: time (t). Dependent variable: distance (d).

Step-by-step explanation: an independent variable is a variable whose variation does not depend on that of another. In the given problem, the independent variable is time, because time will pass by no matter what (without depending in any other variable). The dependent variable in this case is the distance, because how far Jillian goes, depends on how much time she expends walking and jogging.

8 0

2 years ago

Read 2 more answers

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18pi meters. Wh

ella [17]

Answer

Circumference(C) of a circle is given by:

$C = 2\pi r$

where r is the radius and value of $\pi = 3.14$

As per the given statement:

A building engineer analyzes a concrete column with a circular cross section.

The circumference of the column is $18 \pi$ meters.

then;

$18 \pi= 2\pi r$

Divide both sides by $2 \pi$ we have;

9 = r

r = 9 meters

We have to find the area of the cross section of the column

Area of a circle is given by:

$A = \pi r^2$

then;

$A = \pi \cdot 9^2 = 81 \pi$ meter square.

therefore, the area A of the cross section of the column is $81 \pi$ meter square.

3 0

2 years ago

Read 2 more answers

A 16-inch candle is lit and burns at a constant rate of 0.8 inches per hour. Let t represent the number of hours since the candl

Tamiku [17]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

The initial length of the candle is 16 inch. It also given that, it burns with a constant rate of 0.8 inch per hour.

After one hour since the candle was lit, the length of the candle will be (16 - 0.8) = 15.2 inch.

After two hour since the candle was lit, the length of the candle will be (15.2 - 0.8) = 14.4 inch. The length of the candle after two hours can also be represented by {16 - 2(0.8)}.

Hence, the length of the candle after t hours when it was lit can be represented by the function, $f(t) = 16 - 0.8t$ . $f(t) = 0$ at t = 20.