Which of the given points would be in a table generated by the equation below?

A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)

guapka [62]

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

4 0

3 years ago

Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1,

Dahasolnce [82]

Answer:

The direction cosines are:

$\frac{5}{\sqrt{42} }$ , $\frac{1}{\sqrt{42} }$ and $\frac{4}{\sqrt{42} }$ with respect to the x, y and z axes respectively.

The direction angles are:

40°, 81° and 52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = $\frac{a . i}{|a| . |i|}$ ---------------------(i)

cos β = $\frac{a.j}{|a||j|}$ ---------------------(ii)

cos γ = $\frac{a.k}{|a|.|k|}$ ----------------------(iii)

And from these we can get the direction angles as follows;

α = cos⁻¹ ( $\frac{a . i}{|a| . |i|}$ )

β = cos⁻¹ ( $\frac{a.j}{|a||j|}$ )

γ = cos⁻¹ ( $\frac{a.k}{|a|.|k|}$ )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i = (5i + j + 4k) . (i)

a . i = 5 [a.i is just the x component of the vector]

a . j = 1 [the y component of the vector]

a . k = 4 [the z component of the vector]

Also

|a|. |i| = |a|. |j| = |a|. |k| = |a| [since |i| = |j| = |k| = 1]

|a| = $\sqrt{5^2 + 1^2 + 4^2}$

|a| = $\sqrt{25 + 1 + 16}$

|a| = $\sqrt{42}$

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = $\frac{5}{\sqrt{42} }$

cos β = $\frac{1}{\sqrt{42} }$

cos γ = $\frac{4}{\sqrt{42} }$

From the value, now find the direction angles as follows;

α = cos⁻¹ ( $\frac{a . i}{|a| . |i|}$ )

α = cos⁻¹ ( $\frac{5}{\sqrt{42} }$ )

α = cos⁻¹ ( $\frac{5}{6.481}$ )

α = cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( $\frac{a.j}{|a||j|}$ )

β = cos⁻¹ ( $\frac{1}{\sqrt{42} }$ )

β = cos⁻¹ ( $\frac{1}{6.481 }$ )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( $\frac{a.k}{|a|.|k|}$ )

γ = cos⁻¹ ( $\frac{4}{\sqrt{42} }$ )

γ = cos⁻¹ ( $\frac{4}{6.481}$ )

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

Conclusion:

The direction cosines are:

$\frac{5}{\sqrt{42} }$ , $\frac{1}{\sqrt{42} }$ and $\frac{4}{\sqrt{42} }$ with respect to the x, y and z axes respectively.

The direction angles are:

40°, 81° and 52° with respect to the x, y and z axes respectively.

3 0

3 years ago

Solve for n -8 = 6+n

bezimeni [28]

Answer:

no solution

Step-by-step explanation:

n -8 = 6+n

Subtract n from each side

n-n -8 = 6+n-n

-8 = 6

This is never true so there is no solution

8 0

3 years ago

Read 2 more answers

A local animal shelter has 27 dogs and 23 cats. What percent of the animals are dogs?

SVEN [57.7K]

Answer:

54%

Step-by-step explanation:

total animals=27+23=50

$dogs=\frac{27}{50} \times100=54$

6 0

3 years ago

. A recent report in a women magazine stated that the average age for women to marry in the United States is now 25 years of age

Setler [38]

Answer: 0.0136

Step-by-step explanation:

Given : Mean : $\mu=25$

Standard deviation : $\sigma=3.2$

Sample size : $n=50$

The formula to calculate the z-score :-

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x = 24

$z=\dfrac{24-25}{\dfrac{3.2}{\sqrt{50}}}=-2.21$

The p-value = $P(z\leq-2.21)= 0.0135526\approx0.0136$

Hence, the probability that the sample mean age for 50 randomly selected women to marry is at most 24 years = 0.0136

3 0

3 years ago