When comparing the shapes of the two sets of data, what conclusion can someone draw?

Please show the working and answer. you can take a picture for the working.

baherus [9]

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, $\overline {RQ}$ ² = $\overline {SQ}$ ² + $\overline {SR}$ ² - 2 × $\overline {SQ}$ × $\overline {SR}$ × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

$\overline {RQ}$ ² = 5.4² + 9.7098² - 2 × 5.4×9.7098× cos(97.11024)

$\overline {RQ}$ ² ≈ 136.42

$\overline {RQ}$ = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 × $\overline {PQ}$ × $\overline {PR}$ × sin(∠SPQ)

By substituting the values, we have;

1/2 × $\overline {PQ}$ × $\overline {PR}$ × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

$\overline {RS}$ /(sin(∠SQR)) = $\overline {RQ}$ /(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

8 0

3 years ago

Jace went shopping for a new phone. The listed price of the phone was $50, but the price with tax came to $51.50. Find the perce

olchik [2.2K]

Answer:

1.50 I think

Step-by-step explanation:

51.50-50 equals 1.50

3 0

3 years ago

Was doing my work and need help

Arturiano [62]

3/4 divide by 5 is equal to 3/20

4 0

3 years ago

Read 2 more answers

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a

ASHA 777 [7]

Answer:

No, the cone will not hold all of the ice cream.

Step-by-step explanation:

Given:

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let it melt.

Now, to explain mathematically will the cone hold all of the ice cream.

Taking the value of π = 3.14.

So, to get the volume of waffle cone we put formula:

Height (h) = 6 inches.

Diameter = $2\frac{5}{8}=\frac{21}{8}\ inches.$

Thus radius (r) = Diameter ÷ 2 = $\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.$

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

$Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}$

$Volume=3.14\times 1.31\times 1.31\times 2$

$Volume=10.78\ inches^3.$

The volume of waffle cone = 10.78 inches³.

Now, to get the volume of scoop which is in the shape of sphere we put formula:

Diameter = $2\frac{7}{8} =\frac{23}{8} \ inches.$

Thus radius (r) = Diameter ÷ 2 $=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.$

$Volume = \frac{4}{3} \pi r^3$

$Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}$

$Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44$

$Volume=12.47\ inches^3.$

The volume of one scoop of ice cream = 12.47 inches³.

So, as the volume of scoop of ice cream is more than the volume of cone.

Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.

Therefore, no the cone will not hold all of the ice cream.

5 0

3 years ago

What is the value of 6 364 484 1.365 1.456

vlabodo [156]

Answer:

I think it is C

Step-by-step explanation:

If I'm wrong try B

4 0

3 years ago