Help please I beg you!

Look at the following number sequence. 3, 7, 11, 15, . . . Based on the pattern, what are the next two terms?

viva [34]

So, if we look at the number pattern, we can see the numbers go up by 4.

The rule is Add 4.

So, to find the next two terms, we would add 4 to the last number shown, which is 15.

15 + 4 = 19

19 + 4 = 23

So, the next two terms are →19← and →23←.

Glad I could help, and good luck!

AnonymousGiantsFan

5 0

3 years ago

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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

Need help plz plz thx

Vera_Pavlovna [14]

The answer is D. To solve 3/5 ÷ 4/7 you would change it to 3/5 × 7/4.

5 0

3 years ago

Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father bot

Lostsunrise [7]

Based on this information, William's blood type could be either B or O.

What is Segregation of alleles?

Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.
During meiosis, maternal and paternal alleles separate.

What is genotype vs phenotype ?

Genotype: An organism's genetic makeup.
Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.
Genotype - the set of alleles that make up an organism.

How does genotype influence phenotype ?

The alleles you have for a specific gene or collection of genes are referred to as your genotype.

The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.

Learn more about Genotype

brainly.com/question/16882362

#SPJ4

3 0

2 years ago

Which equations are equivalent to Y=2/3X-4 when written in slope-intercept form? Check all that apply. A =3X-2Y=4. B=2X-3Y=12. C

klemol [59]

Answer:

B and C

Step-by-step explanation:

Rearrange each equation into slope- intercept form

A

3x - 2y = 4 ( subtract 3x from both sides )

- 2y = - 3x + 4 ( divide all terms by - 2 )

y = $\frac{3}{2}$ x - 2 ← not equivalent

B

2x - 3y = 12 ( subtract 2x from both sides )

- 3y = - 2x + 12 ( divide all terms by - 2 )

y = $\frac{2}{3}$ x - 4 ← equivalent

C

- 4(2x - 3y ) = - 48 ( divide both sides by - 4 )

2x - 3y = 12 ← same as B ⇒ equivalent

D

2(x + 6) = 3y

3y = 2x + 12 ( divide all terms by 3 )

y = $\frac{2}{3}$ x + 4 ← not equivalent

E

2x - 3y = 4 ( subtract 2x from both sides )

- 3y = - 2x + 4 ( divide all terms by - 3 )

y = $\frac{2}{3}$ x - $\frac{4}{3}$ ← not equivalent

4 0

3 years ago

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