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3 years ago

6

The length of one leg of a right triangle is 8 and the length of the hypotenuse is 24. Find the length of the missing leg to the

nearest hundredth.

1 answer:

joja [24]3 years ago

5 0

8^2 + b^2 = 24^2
64 + b^2 = 576
-64 -64
b^2 = 512
Take the square root from b^2 and 512 =
b = 22.627
Answer 22.63 (rounded up)

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If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?

Oduvanchick [21]

$\large\underline{\sf{Solution-}}$

<u>Given:</u>

$\rm \longmapsto x = a \sin \alpha \cos \beta$

$\rm \longmapsto y = b \sin \alpha \sin \beta$

$\rm \longmapsto z = c\cos \alpha$

Therefore:

$\rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta$

$\rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta$

$\rm \longmapsto \dfrac{z}{c} = \cos \alpha$

Now:

$\rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} }$

$\rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha$

$\rm = 1$

<u>Therefore:</u>

$\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1$

5 0

2 years ago

Parallelogram PARL is similar to parallelogram WXYZ. If AP = 25, PL = 29, and WZ = 145, find the value of c.

joja [24]

Answer:

The correct answer is 56

Step-by-step explanation:

Parallelogram PARL is similar to parallelogram WXYZ. If AP = 14, PL = 25, and WZ = 100, find the value of c.

100=25*4, so the other side must be also multiplicated by 4 ansd 14*4=56

4 0

2 years ago

A random sample of 77 fields of corn has a mean yield of 26.226.2 bushels per acre and standard deviation of 2.322.32 bushels pe

PSYCHO15rus [73]

Answer:

Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)

Step-by-step explanation:

n = 77

mean u = 26,226.2 bushels per acre

standard deviation s = 2,322.32

let E = true mean

let A = test statistic

Find 95% Confidence Interval

so

let A = (u - E) * ( $\sqrt{n}$ / s) be the test statistic

we want P( average_l < A < average_u ) = 95%

look for lower 2.5% and the upper 97.5% Because I think this is a 2-tail test

average_l = -1.96 which corresponds to the 2.5%

average_u = 1.96

P( -1.96 < A < 1.96) = 95%

P( -1.96 < (u - E) * ( $\sqrt{n}$ / s) < 1.96) = 95%

Solve for the true mean E ok

E < u + 1.96* (s / $\sqrt{n}$ )

from -1.96 < (u - E) * ( $\sqrt{n}$ / s)

E < 26,226.2 + 1.96*( 2,322.32 / $\sqrt{77}$ )

E < 26,226.2 + 1.96*( 2,322.32 / $\sqrt{77}$ )

E < 26,226.2 + 518.7197348105429466

upper bound is 26,744.9197

or

u - 1.96* (s / $\sqrt{n}$ ) < E

26,226.2 - 518.7197348105429466 < E

25,707.48026519 < E

lower bound is 25,707.48026519

Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)

7 0

2 years ago

PLS HELP!!!! A rectangle shown has a length of 11cm and a width of 4.2cm. A circle is drawn inside that touches the rectangle at

oee [108]

Answer:

C

Step-by-step explanation:

3 0

2 years ago

I hope you guys can see the question, if not just let me know

QveST [7]

Answer:

The correct answer is 6.

Step-by-step explanation:

When translating and reflecting figures, the shape remains the same. So, the side of 2x-4 is corresponding to the side of 8 and they are equal to each other.

To solve, set up an equation like this to find x:

2x-4=8

Then, add 4 to both sides of the equation:

2x=12

The goal is to get x by itself and in order to do that, divide both sides by 2:

x=6

The value of x is 6. I hope this helps! ☺

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3 years ago