Please help please im really confused

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

Use a calculator to find the approximate value of sin-1 (0.549)

tatyana61 [14]

This is the concept of algebra, we are required to approximate the arcsin of the value given using a calculator;
sin theta=[opposite]/[hypotenuse]
arcsin is the inverse of sin, thus;
arcsin(0.549)=33.2984
the answer is 33.3984°

6 0

3 years ago

Read 2 more answers

Which point is not on the graph of the equation y=10+x

RSB [31]

Answer:

C. (8, 2)

Step-by-step explanation:

To find which point is not on the graph, find which set of coordinates makes the equation incorrect.

When plugged into the equation, the point (8, 2) makes it incorrect:

y = 10 + x

2 = 10 + 8

2 = 18

2 $\neq$ 18

The equation is incorrect because 2 is not equal to 18.

So, the point that is not on the graph is C. (8, 2)

6 0

2 years ago

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing

tester [92]

The length of pendulum is 2.485 feet

<h3>Solution:</h3>

Given that,

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth

Therefore, the given formula is:

$T=2\pi \sqrt{\frac{L}{32} }$

We have to find the length of pendulum that makes one full swing in 1.75 seconds

So the modify the given equation to find "L"

$T=2\pi \sqrt{\frac{L}{32} }\\\\ \sqrt{\frac{L}{32} }=\frac{T}{2 \pi}\\\\\text{Taking square root on both sides }\\\\\frac{L}{32} = \frac{T^2}{4 \pi^2}\\\\L = \frac{T^2}{4 \pi^2} \times 32\\\\L = \frac{T^2}{\pi^2 } \times 8$

Substitute T = 1.75 seconds and $\pi = 3.14$

$L = \frac{1.75^2}{3.14 \times 3.14} \times 8\\\\L = \frac{3.0625}{9.8596} \times 8\\\\L = 2.485$

Thus length of pendulum is 2.485 feet approximately

7 0

3 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

2 years ago