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4 years ago

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An object was measured to have a mass of 22.50 g and a volume of 9.45 mL. Divide the mass by the volume to determine its density

. Report the answer with the appropriate number of significant digits

1 answer:

AleksandrR [38]4 years ago

8 0

The density of the object is defined as the ratio between its mass and its volume:
$d= \frac{m}{V}$
In this problem, the mass is m=22.50 g and the volume is V=9.45 mL, so the density is
$d= \frac{22.50 g}{9.45 mL}=2.38 g/mL$

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A small radio transmitter broadcasts in a 30 mile radius. If you drive along a straight line from a city 33 miles north of the t

Paha777 [63]

Answer:

34.26miles from 49.58miles of the drive (69.11% of the drive).

Step-by-step explanation:

A problem of Analytic Geometry. This question can be solved using the resulting values from equaling the equations of the line (for the drive) and circle (with radius equals 30miles for radio transmitter broadcasting), and calculating the total distances from coincident points between circle and line, and total drive.

A graph is attached showing part of the circle and line with coincident points.

<h3>Line's Equation</h3>

Assuming transmitter is located (0, 0). From a city 33 miles north of the transmitter (0, 33) to a second city 37 miles east of the transmitter (37, 0).

Then, the equation for the line is (taking the two points from the start to the end):

$\\ y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}*(x-x_{1})$

$\\ y-33=\frac{0-33}{37-0}*(x-0)}$

$\\ y-33=\frac{-33}{37}*x}$

$\\ y=\frac{-33}{37}*x} + 33$ [1]

<h3>Circle's Equation</h3>

The equation for the circle whose center (0, 0) is:

$\\ (x-0)^2 + (y-0)^2 = 30^2$

$\\ x^2 + y^2 = 30^2$

$\\ y^2 = 30^2 - x^2$

$\\ y = \frac{+}{-}\sqrt{30^2- x^2}$ [2]

Equaling [1] and [2], to determine the points where starting to receive the radio transmitter signals to the point where finishing those signals:

$\\ \frac{-33}{37}*x + 33 = \sqrt{30^2- x^2}$

Solving this equation for <em>x</em>, we have two solutions for it (from <em>WolframAlpha</em>):

$\\ x_{1} = 40293/2458 - (111 \sqrt(80151))/2458 \approx 3.60775$

$\\ x_{2} = 40293/2458 + (111 \sqrt(80151))/2458 \approx 29.1774$

Then, using [1], the corresponding values for <em>y</em> are:

$\\ y_{1}=\frac{-33}{37}*(3.60775) \approx 29.78$

$\\ y_{2}=\frac{-33}{37}*(29.1774) \approx 6.97$

So,

$\\ (x_{1}=3.61, y_{1}=29.78)$

$\\ (x_{2}=29.18, y_{2}=6.97)$

Well, the distance of the drive is:

$\\ d = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$

$\\ d = \sqrt{(29.18-3.61)^2 + (6.97-29.78)^2}$

$\\ d \approx 34.2654$ miles.

The total distance traveled is:

$\\ d = \sqrt{(37-0)^2 + (0-33)^2}$

$\\ d \approx 49.5782$ miles

Thus, during the drive, the signal of the radio transmitter was picked up for 34.26miles from the total of the 49.58 traveled, that is, a fraction equivalent to $\\ \frac{34.2654}{49.5782} \approx 0.6911$ or 69.11% of the drive.

4 0

3 years ago

Match each statement to the reasons given for the geometric proof.

Savatey [412]

Answer: 5, 3, 1, 2, 6, 4

<u>Step-by-step explanation:</u>

The proof should be written as follows (which is a different order than provided):

<u>Statement </u> <u>Reason </u>

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

6. AE = CE and BE = DE 6. CPCTC

This is the order provided in your question:

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

6. AE = CE and BE = DE 6. CPCTC

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem

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3 years ago

PLZZZ HELP WHAT IS THIS:) <3

7nadin3 [17]

A^2 + b^2 = c^2 in right triangles.
4^2 + b^2 = 8.5^2
16 + b^2 = 72.25
b^2 = 56.25
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3 years ago

Read 2 more answers

Arrange0.2,¼,30%,10%in ascending and descending order

BARSIC [14]

Answer:

Ascending- 10%, 0.2, 1/4, 30%

Descending- 30%, 1/4, 0.2, 10%

Step-by-step explanation:

0.2 = 2/10 = 4/20

1/4 = 5/20

30% = 30/100 = 6/20

10% = 10/100 = 2/20

Ascending

-2/20, 4/20, 5/20, 6/20

- 10%, 0.2, 1/4, 30%

Descending

- 6/20, 5/20, 4/20, 2/20

- 30%, 1/4, 0.2, 10%

7 0

3 years ago

PLEASE HELP!! Find the sixth term of the sequence 14,9,4,..

jeka94

Answer:

39

Step-by-step explanation:

We notice this is an arithmetic sequence.

14, 9, 4.

common difference = d = 14 - 9 = 5

first term a_1 = 14

Find 6th term a_6

a_n = (n -1)*d + a_1

a_6 = (6 -1)*5 + 14

a_6 = 5*5 + 14 = 25 + 14 = 39

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3 years ago