Find the average rate of change for the given function from x = 1 to x = 2

Answer:

The components of [tex]\vec{b}[/tex] parallel and perpendicular to [tex]\vec {a}[/tex] are [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex] and [tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex], respectively.

Step-by-step explanation:

Let be [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec a = 3\,i-j[/tex], the component of [tex]\vec b[/tex] parallel to [tex]\vec a[/tex] is calculated by the following expression:

[tex]\vec b_{\parallel} = (\vec b \bullet \hat{a}) \cdot \hat{a}[/tex]

Where [tex]\hat{a}[/tex] is the unit vector of [tex]\vec a[/tex], dimensionless and [tex]\bullet[/tex] is the operator of scalar product.

The unit vector of [tex]\vec a[/tex] is:

[tex]\hat{a} = \frac{\vec {a}}{\|\vec a\|}[/tex]

Where [tex]\|\vec {a}\|[/tex] is the norm of [tex]\vec a[/tex], whose value is determined by Pythagorean Theorem.

The component of [tex]\vec{b}[/tex] parallel to [tex]\vec {a}[/tex] is:

[tex]\|\vec {a}\| = \sqrt{3^{2}+(-1)^{2}+0^{2}}[/tex]

[tex]\|\vec {a}\| = \sqrt{10}[/tex]

[tex]\hat{a} = \frac{1}{\sqrt{10}} \cdot (3\,i-j)[/tex]

[tex]\hat{a} = \frac{3}{\sqrt{10}}\,i -\frac{1}{\sqrt{10}} \,j[/tex]

[tex]\vec{b}\bullet \hat{a} = (2)\cdot \left(\frac{3}{\sqrt{10}} \right)+(1)\cdot \left(-\frac{1}{\sqrt{10}} \right)+(-3)\cdot \left(0\right)[/tex]

[tex]\vec b \bullet \hat{a} = \frac{5}{\sqrt{10}}[/tex]

[tex]\vec b_{\parallel} = \frac{5}{\sqrt{10}}\cdot \left(\frac{3}{\sqrt{10}}\,i-\frac{1}{\sqrt{10}}\,j \right)[/tex]

[tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex]

Now, the component of [tex]\vec {b}[/tex] perpendicular to [tex]\vec{a}[/tex] is found by vector subtraction:

[tex]\vec{b}_{\perp} = \vec {b}-\vec {b}_{\parallel}[/tex]

If [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex], then:

[tex]\vec{b}_{\perp} = (2\,i+j-3\,k)-\left(\frac{3}{2}\,i-\frac{1}{2}\,j \right)[/tex]

[tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex]

Answer:It will be -14 degrees, because in the negative side, droping or subtracting, would instead be adding. -9 - 5 = -14.

                                                                    9 + 5 = 14

Step-by-step explanation:

C D E

Step-by-step explanation:

All the numbers above (C D E) are negative, making them less than 0.

Answer:

C, D, and E. They are all negative, which means they are less than zero.

1.2 and 7/2 are more than one. 7/2 simplifies to 3 1/2.

Answer:

Step-by-step explanation

In this problem. we are required to re-write the given number from  scientific notation to standard notation and from standard notation to scientific notation

Exercise a

5.32 x 10-6 meters.

Since we have  10-6, this tells us that we are meant to shift 6 decimal points to the left that is we have

0.00000532 meters

Exercise b

In this example, we are expected to shift 5 decimals away from the decimal point to the right to arrive at the answer therefore we have to multiply by 10^5

hence the equivalent figure in scientific notation is   1.21*10^5 hence

121,000 meters.

1.21*10^5 meters

Answer:

the answer is 988 .........

Answer:

Use the distance formula to determine the distance between two points.

5 √ 5

Answer:

$305

Step-by-step explanation:

You have to use the following formula to calculate the accrued amount:

A=P(1 + rt), where:

A= accrued amount

P= principal amount= $250

r= rate of interest= 11%

t= time period= 2 years

Now, you have to replace the values in the formula:

A=250*(1+0.11*2)

A=250*(1+0.22)

A=250*1.22

A=305

According to this, at the end of 2 years, Jess owes the bank $305.

Answer:

It's D.

Step-by-step explanation:

If you want me to explain it, I will.  But it seems like you need the answer fast.  So if you still don't understand it later, then I will try to explain it...but it'll take some time.  :)

All you have to do is move all the points to the right 6 numbers because it says x+6.  For example, A is (-5,-1).  Move to the right 6 times, so (-5+6,-1) which is (1, -1).  So the new point of A is (1, -1).  Do the same with the others.  Now that we got the new rectangle in the fourth quadrant, you want to move it counterclockwise around the origin, which is 0.  Clockwise is like a clock, it goes around the middle going to the right.  Counterclowise is the same, except it goes to the left around the middle of the clock.  You can sort of apply that to this.  Go counterclockwise around the middle, in this case being the origin, 0. Move the rectangle up to the first quadrant because counterclockwise is going around to the left.  So, if the rectangle goes around to the left, then that means that it is now vertical...because it turns to the left making it straight if you go counterclockwise.  Now the point A is on the bottom left because the rectangle got turned.  If you turned it properly, then A should be at (1,1).  Apply the same thing to the other points.  D is the only one with point A being at the point (1,1), so that is correct.  Check the other points anyway.

Answer:

Step-by-step explanation:

Answer:

jgvi hhvh ihvyv

Step-by-step explanation:

tan(20) can be written in fractions if you want to, but it is easier to write it in a decimal number when it is punched into a calculator.

You can find the exact value of sin, cos, and tan for some values.

tan() is a trigonometric function that is used when calculating angles or side lengths in a triangle.

Answer:

p=0

Step-by-step explanation:

When you isolate both variables, one side becomes 0.

Answer:

p = 0

Step-by-step explanation:

16p=208p

Subtract 208p from both sides.

16p−208p=0

Combine 16p and −208p to get −192p.

−192p=0

Product of two numbers is equal to 0 if at least one of them is 0. Since −192 is not equal to 0, p must be equal to 0.

p=0

2(4z−2) = 44

Simplify both sides of the equation.

Distribute:

(2)(4z)+(2)(−2) = 44

8z + −4 = 44

8z − 4 = 44

Add 4 to both sides.

8z − 4 + 4 = 44 + 4

8z = 48

Divide both sides by 8

8z/8    48/8

z = 6

Answer:

z=6

Step-by-step explanation:

Answer:

slope = 3

Step-by-step explanation:

The slope of a line parallel to the given equation share the same slope. Note the slope intercept formula:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

First, isolate the variable, y. Subtract 3x from both sides:

3x (-3x) - y = 1 (-3x)

-y = -3x + 1

Next, divide -1 from both sides:

(-y)/-1 = (-3x + 1)/-1

y = 3x - 1

You are solving for the slope of a line parallel to the given equation. Since you are solving for parallel, the slope would be shared.

3 would be the slope of the line.

~

Answer:

  152°

Step-by-step explanation:

Angles B and A of the isosceles triangle have the same measures, so we have ...

  ∠B = ∠A

  (x -14)° = (x/2)°

  2x -28 = x . . . . . . divide by °, multiply by 2

  x = 28 . . . . . . . . . .add 28-x to both sides

Then the base angles, A and B, both have measure (x/2)° = 14°.

The third angle, C, will bring the total to 180°.

  ∠A + ∠B + ∠C = 180°

  ∠C = 180° - 2(14°)

  ∠C = 152°

Answer:

[tex]=2w\left(w+4\right)\left(w-4\right)[/tex]

Step-by-step explanation:

[tex]2w^3 - 3\\\\\mathrm{Factor\:out\:common\:term\:}2w:\quad 2w\left(w^2-16\right)\\=2w\left(w^2-16\right)\\\\\mathrm{Factor}\:w^2-16:\quad \left(w+4\right)\left(w-4\right)\\=2w\left(w+4\right)\left(w-4\right)[/tex]

Answer:

[tex]=2w\left(w+4\right)\left(w-4\right)[/tex]

Step-by-step explanation:

[tex]2w^3 - 32w\\[/tex]

Factor out 2w from the expression

[tex]2w(w^2+16)[/tex]

Factor (w^2+16) according to difference of two squares principle

[tex](w^2 +16) = (w+4)(w-4)\\2w((w+4)(w-4)))[/tex]

Answer: y = -9x − 10

Step-by-step explanation: y represents the elevation of the bottlenose dolphin. The dolphin begins at 10 feet below sea level or -10. It then becomes to dive, go deeper under the water at a rate of 9 feet per second, or -9.

The equation y = -9x - 10 will equal the amount of feet below sea level that the dolphin is at. Below sea level will always be indicated with a negative number.

Answer:

Amount to deposit= $26799.0

Step-by-step explanation:

Amount A = $60,000

Years t = 8 years,

Rate R = 9% .

A= p(1+r/n)^(nt)

60000= p(1+0.09/9)^(9*9)

60000= p(1+0.01)^(81)

60000= p(1.01)^81

60000= p(2.23888)

60000/2.23888= p

26799.1138= p

P= $26799.0

Amount to deposit= $26799.0

To be able to have $60,000 after 8 years at a rate of 9% per annum, the amount to deposit today is $30,111.98

You can solve this using the Future Value formula which is:

Future value = Present value x ( 1 + rate)^ number of years

You have everything except the present value so solve for it:

60,000 = PV x ( 1 + 9%)⁸

60,000 = PV x 1.9925626416901921

PV = 60,000 / 1.9925626416901921

PV = $30,111.98

In conclusion, you should deposit $30,111.98 today.

Find out more about this at https://brainly.com/question/14715827.

Answer:

Temperature dropped by 28°C in two hours

Step-by-step explanation:

Initial measurement:

Measurement 2 hours later:

The difference:

Temperature dropped by 28°C in two hours

Answer:

He will pay $922 Eve month where

$238.6667 is the interest in the payment

Step-by-step explanation:

Eric Shotwell borrows $24,600 from a certain bank. The interest charge amounts to $8,592 to be paid back in 36 months monthly.

Total money to be paid back

= 24600+8592

Total money to be paid back

= $33192

Now for each month in 36 months, a certain amount must be paid

That amount= 33192/36

= $922

But if the interest wasn't added

He'll pay= 24600/36

=$683.333

So the interest amount in the payment every month= 922-683.333.

= $238.6667

He will pay $922 Eve month where

$238.6667 is the interest in the payment

Total money to be paid back

= 24600+8592

= $33192

Now for each month in 36 months, a certain amount must be paid

That amount= [tex]33192\div36[/tex]

= $922

Now in the case when the interest wasn't added

He'll pay= [tex]24600\div 36[/tex]

=$683.333

So the interest amount in the payment every month is

= 922-683.333.

= $238.6667

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Answer:

1. Gender - qualitative

2. Age - Quantitative (Discrete)

3. Grade point Average - quantitative (Continuous )

4. Number of courses currently enrolled - quantitative (discreet)

5. Enrollment Status - qualitative

Step-by-step explanation:

Qualitative variables are those which are non-numeric, usually made up of strings or words. The quantitative variables are numeric, usually composed of digits and numbers.

Discreet variables have a finite or limited number of values which are countable as opposed to continuous variables with a non-finite range and hence, uncountable.

Gender is a qualitative variable as it is composed of non-nemeric labels which could be either Male or Female.

Age - is numeric and hence quantitative, since age is usually expressed in years, hence it is discreet.

Grade point Average is a quantitative and continuous variable due to its numeric nature and the fact that it can take up an infinite number of possible values including decimal values.

Number of courses enrolled is numeric can take a finite number of values, hence, it is discreet.

Enrollment status is qualitative as it is split into :

Part time or full time.

Complementary and adjacent.

The two angles are complementary because they add up to 90°. It's given that line JL is perpendicular to line MN, and perpendicular means they form a 90° angle where they intersect.

The two angles are adjacent because they are next to each other.

Answer:

Set of rational numbers

Step-by-step explanation:

Answer:

the set of rational numbers

Step-by-step explanation:

Edge 2021

Answer:

2(x-7) > 1/10

Step-by-step explanation:

The statement says, twice the difference of x and 7.  This implies that it wants the difference of x and 7, x - 7, and it wants twice that difference so:

2 ( x - 7 )

The statement continues that this twice the difference of x and 7 is greater than the reciprocal of 10.  The reciprocal of 10 is 0.1 or 1/10.

Hence, the statement should be written as such:

2 ( x - 7 ) > 1/10   OR    2 ( x - 7 ) > 0.1

Cheers.

Answer: 3600

Step-by-step explanation: N= 3,600

3,600/12= 300

Answer:

n=0, or n=3600

Step-by-step explanation:

If your question is n/12 = 300n, n=0

Otherwise n/12=300, n=3600

Multiply both sides by 12 to isolate variable

Answer:

Step-by-step explanation:

5X * 4-->20X

8(2X+3)--> 16X+24

20X=16X+24

4X=24

x=6

Answer:

x = 6

Step-by-step explanation:

(5x) ×4=8× (2x+3)

20x = 16x + 24

20x- 16x = 24

4x = 24

divide both sides by 4 to get the value of x

4x/4 = 24/ 4

x = 6

Answer: Associative property

Step-by-step explanation:

From the question, we are informed that Jada is evaluating 8 × 3 × 4 and that she doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first.

The property that Jada is using is the Associative property. This has to do with regrouping of the numbers and then multiplying the numbers in different groups.

Answer:

Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.

Step-by-step explanation:

The dimensions of a dollar bill are 15.5956 cm by 6.6294 cm by 0.010922 cm. The U.S. federal government spent $3.8 trillion in fiscal year 2011.

An Olympic swimming pool is 50 m long, 25 m wide, and 1.5 m deep. How many Olympic pools would be filled by the dollar bills spent by the U.S. federal government in 2011

From above,

The volume for the dimension of the dollar bill = 15.5956 cm × 6.6294 cm × 0.010922 cm

The volume for the dimension of the dollar bill = 1.12922 cm³

The volume for the dimension of the dollar bill = 1.12922 × 10⁻⁶ m³

The volume of the pool = 50 m  ×  25 m  ×  1.5 m

The volume of the pool = 1875 m³

Number of dollars bills that can be fitted in pool = volume of the pool/volume of the dimension of dollar bills

Number of dollars bills that can be fitted in Olympic pool =1875 m³ / 1.12922 × 10⁻⁶ m³

Number of dollars bills that can be fitted in Olympic pool = 1,660,438,180

Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.