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2 years ago

11

The cost of 5 gallons of gasoline is $20. Write an equation to show the relationship between the cost, c, and the gallons of gas

oline, g.

1 answer:

EastWind [94]2 years ago

3 0

Answer:

the gas 4$

Step-by-step explanation:

5x=20

divide 5/5 to cancel the 5 then 20/5 and there you have it 4

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If a=i+7j+k and b=i+11j+k, find a unit vector with positive first coordinate orthogonal to both a and

Scilla [17]

Take the cross product, then normalize the result.

$\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&7&1\\1&11&1\end{vmatrix}=-4\,\mathbf i+4\,\mathbf k$

This has norm

$\|\mathbf a\times\mathbf b\|=\sqrt{(-4)^2+4^2}=4\sqrt2$

and so a unit vector orthogonal to both given vectors is

$\dfrac{\mathbf a\times\mathbf b}{\|\mathbf a\times\mathbf b\|}=-\dfrac1{\sqrt2}\,\mathbf i+\dfrac1{\sqrt2}\,\mathbf k$

An equally correct answer would be the negative of this vector, since $\mathbf b\times\mathbf a=-\mathbf a\times\mathbf b$ .

5 0

3 years ago

Joaquin writes the following list of numbers.

swat32

From the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Any number that can be written in the form of p/q, where p and q are integers, and q ≠ 0, are called rational numbers.

All terminating and non-terminating recurring decimals are rational numbers.

All the numbers that cannot be represented in the rational form of p/q are irrational numbers.

All non-terminating non-recurring decimals are irrational.

All square roots of imperfect square numbers, that is, surds, are irrational numbers.

In the question, we are asked to classify the given list of numbers into rational and irrational numbers.

5.737737773...: It is an irrational number, since its a non-terminating non-recurring decimal.
26: It is rational as it can be represented in the p/q form (26/1).
√45: It is irrational as it is a square root of an imperfect square number, that is, it is a surd.
-3/2: It is rational as it is in the form p/q.
0: It is rational as it can be represented in the p/q form (0/1).
9: It is rational as it can be represented in the p/q form (9/1).

Thus, from the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Learn more about rational and irrational numbers at

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The provided question is incorrect. The correct question is:

Joaquin writes the following list of numbers.

5.737737773..., 26, √45, -3/2, 0, 9.

Which numbers are rational?

Which numbers are irrational?

6 0

1 year ago

(7 + 7i)(2 − 2i)

Ostrovityanka [42]

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

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3 0

2 years ago

In the equation -y = 10x, what is the unit rate?

Umnica [9.8K]

You have to multiply by a -1 both sides,
it would be 10 1/2

7 0

2 years ago

Help ASAP! I’m confused. Thanks!!

KATRIN_1 [288]

Answer:

B

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers