Please help ..........

Answer:

The unit vector u is (-5/√29) i - (2/√29) j

Step-by-step explanation:

* Lets revise the meaning of unit vector

- The unit vector is the vector ÷ the magnitude of the vector

- If the vector w = xi + yj

- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w

- The unit vector u in the direction of w is u = w/IwI

- The unit vector u = (xi + yj)/√(x² + y²)

- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j

* Now lets solve the problem

∵ v = -5i - 2j

∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29

- The unit vector u = v/IvI

∴ u = (-5i - 2j)/√29 ⇒ spilt the terms

∴ u = (-5/√29) i - (2/√29) j

* The unit vector u is (-5/√29) i - (2/√29) j

if the cone has a diameter of 12, thus its radius is half that, namely 6.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=20 \end{cases}\implies V=\cfrac{\pi (6)^2(20)}{3}\implies V=240\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill V\approx 753.98~\hfill[/tex]

The volume of cone is 240π m³.

The mathematical term "volume" indicates the amount of three-dimensional space that an object or closed surface occupies. The volume is measured in cubic units like m³, cm³, in³, and so on.

Volume is also sometimes referred to as capacity.

Given diameter of cone = 12m

radius = diameter/2 = 12/2 = 6m

height of cone = 20m

volume of cone is given by 1/3πr²h

where r = radius and h = height

volume = 1/3 x π x (6)² x 20

volume = 240π m³

Hence the volume is 240π m³.

Learn more about volume;

https://brainly.com/question/13338592

#SPJ5

Question 1.

They usually charge $7 per day to swim at the pool. The offer consist of: Paying an enrollment fee is $30 and then $4 per day.

It means that by enrolling you save 3$ per day. If you save $3 per day, in 10 days you would be saving $30 dollars which is the enrollment fee. This can be calculated by applying the rule of three:

If I save $3 -------------> 1 day?

             $30 ----------> How many days?

Days = ($30 * 1day)/$3 = 10 days.

Then, after 10 days, the offer becomes a better deal.

Question 2.

I only have $60 to spend the rest of the summer. Which offer would be the best value?

NOT paying the enrollment fee would be the best value. The reason is the following:

If I pay the enrollment fee, I spend $30. So I just have $30 remaining. Then, paying $4 a day, it means that I could just pay 7 daily passes, it means that I could go to the pool just seven days.

If I don't pay the enrollment fee, I would have the entire $60 dollars to buy daily passes. The price of each pass would be $7, so $60/7 = 8.5. It means that I could go just 8 days to the pool. One day more than the other option.

So if I only have $60, the best option is NOT to pay the enrollment fee.

Question 3.

If the swim center decides to change the the enrollment fee to $23 and then paying just $4 per daily pass. Then:

If I have only $60 dollars, after paying the enrollment fee I will only have $37.

If each daily pass costs $4, then I will be able to buy $37/$4 = 9.25 = 9 daily passes.

So, if the swim center decides to change the enrollment fee to $23, the the best option is paying the enrollment fee.

Without further context or diagrams, it's challenging to determine the radii of the stated circles. In general, properties of the equilateral triangle and the relationship between the radius of the circle and the side of the triangle are used in these geometrical problems. More details would permit applying these principles to reach a solution.

Based on the information provided, it appears that there might be some missing context or diagrams for this question. Without further elucidation on Amanda's particular design, it would be difficult to accurately determine the radius of the 'large circle' and the 'smaller circles'.

Generally, in such geometric problems which have circles inside an equilateral triangle, one often uses properties of the equilateral triangle and relations between the radius of the circle and side of the triangle. For instance, in an equilateral triangle, where a circle fits exactly inside the triangle (incircle), the radius could be found by the formula (side of equilateral triangle) / (2*sqrt(3)). Similarly, when a circle is drawn outside the triangle (circumcircle), encompassing it, the radius is calculated as (side of equilateral triangle) / sqrt(3).

However, without additional context or a clear diagram, it's impossible to apply these principles to solve Amanda's challenge.

https://brainly.com/question/32028193

#SPJ12

it should be 32 inches

For this case we have that by definition, the slope point equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

By definition, if two lines are perpendicular, the product of their slopes is -1. That is to say:

[tex]m_ {1} * m_ {2} = - 1\\If\ it\ tells\ us: m_ {1} = - \frac {3} {2}:\\- \frac {3} {2} * m_ {2} = - 1\\m_ {2} = \frac {2} {3}[/tex]

Substituting:

[tex]y = \frac {2} {3} x + b[/tex]

We substitute the point to find "b":

[tex]3 = \frac {2} {3} 6 + b\\3 = 4 + b\\b = 3-4\\b = -1[/tex]

Finally:

[tex]y = \frac {2} {3} x-1[/tex]

Answer:

[tex]y = \frac {2} {3} x-1[/tex]

Answer:

3/10

Step-by-step explanation:

Answer:

the answer to that is 1/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rewrite this equation in standard form:

x² - 2x + 1 - 1 + y² + 6y + 9 = 0, or

  (x - 1)² + (y + 3)² = 1

Compare this to:

   (x + h)² + (y + 3)² = r²

We see here that (h, k), the center of the circle, is (1, -3), and the radius of the circle is 1.

Answer:

the center is at (1, -3)

Step-by-step explanation:

The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r".

So we need to write the ecuation x^2 + y^2 - 2x + 6y + 9 = 0 in the format above.

So we have:

x^2 + y^2 - 2x + 6y + 9 = (x^2 -2x + 1) + (y^2 + 6y + 9) - 1

(x^2 -2x + 1) + (y^2 + 6y + 9) - 1 = (x-1)^2 + (y+3)^2 - 1

So now, looking at the equation:  (x-1)^2 + (y+3)^2 = 1

We know that h=1 and k=-3. So the center is at (1, -3)

Answer:

irts 400 inch

Step-by-step explanation:

Answer: V ≈ 1333.3π [tex]cm^{3}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

No, just because the amount of recylcing has gone up this year does not mean that we can conclude it's more this year than ever before. We are only given information for this year and last year, we can't come to that conclusion unless we are given information about the amount of recyling done in all the years.

I reject this conclusion because it says that the people have recycled more this year than ever before.

Generally ever before mean since a long time ago and from the data given we only have recording of last year, not any year before that. If the conclusion had said that the people in mesopotamiaville are recycling more this year than last year. It would have been correct but instead it has given us an invalid conclusion because from the data we have been given we can not possibly gather any other information that can help us accept or reject the conclusion. So therefore the conclusion given is invalid. Hence the reason I reject this conclusion.

hope this helps

Final answer:

Ryan invested £300 in a simple interest account with a 4% annual rate to achieve a £24 increase over 2 years.

Explanation:

Understanding Simple Interest Calculations

Ryan's investment scenario involves calculating simple interest, which is straightforward and doesn't compound over time. To find the principal amount Ryan invested, we can use the simple interest formula:

I = PRT

Where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years. Given that the interest (£24) accrued over 2 years at a rate of 4%, we can set up the equation:

£24 = P * 0.04 * 2

Rearranging the equation to solve for P gives us:

P = £24 / (0.04 * 2)

So, the principal amount Ryan invested would be £300. This is the amount that, when increased by a 4% simple interest rate over 2 years, resulted in a £24 increase in value.

Answer:

8%

Step-by-step explanation:

I = PRT (Interest = Principal x Rate x Time)

Note that:

Interest = $320

Principal = $2000

Time = 2 years

Plug in the corresponding number to the corresponding variables.

320 = (2000)(r)(2)

Simplify. Combine like terms.

320 = (4000)r

Isolate the variable, r. Divide 4000 from both sides.

(320)/4000 = (4000r)/4000

r = 320/4000

r = 0.08

Change the decimal into a percentage.

r = 0.08 = 8/100 = 8%

8% is your interest rate.

~

Answer: 8%

Step-by-step explanation:

Answer:

The answer is 20 inches

Step-by-step explanation:

Answer:

The height of the triangular prism is [tex]26\ mm[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the triangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the triangular base

h is the height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(7)(18)=63\ mm^{2}[/tex]

we have

[tex]V=1,638\ mm^{3}[/tex]

[tex]h=x\ mm[/tex]

substitute and solve for x

[tex]1,638=(63)x[/tex]

[tex]x=1,638/(63)=26\ mm[/tex]

Answer:

C. 26mm

Step-by-step explanation: Just did the assignment

Answer:

Step-by-step explanation:

Both of the following are characteristics of this graph

It will use a closed circle.

The ray will move to the left.

Answer:

(-5,2)

Step-by-step explanation:

Answer:

A. 7

Step-by-step explanation:

you bring down the 1 and multiply it by -2 then -2 goes to add with 2, which makes it 0. Then 0 x -2 is 0. 0 then goes to add with -3, then -3 comes down. -2 x -3 is 6. 6+1 is 7.

The remainder in the synthetic division problem is 7.

To find the remainder using synthetic division, follow these steps:

Step 1: Write the coefficients of the polynomial in descending order, including placeholders for missing terms. In this case, the polynomial is given as:

[tex]1x^3 + 2x^2 - 3x + 1[/tex]

Step 2: Since we are dividing by (x + 2), change the sign of the divisor and set it equal to zero to find the value we'll use in the synthetic division.

x + 2 = 0

x = -2

Step 3: Set up the synthetic division table:

       -2  |   1   2   -3   1

Step 4: Perform the synthetic division:

Bring down the first coefficient:         1

Multiply -2 by 1:                             -2

Add the result to the next coefficient:   2 - 2 = 0

Multiply -2 by 0:                              0

Add the result to the next coefficient:   -3 + 0 = -3

Multiply -2 by -3:                            6

Add the result to the next coefficient:   1 + 6 = 7

Step 5: The last entry in the synthetic division row (7 in this case) is the remainder.

The remainder in the synthetic division problem is 7.

To know more about synthetic division, refer here:

https://brainly.com/question/29146605

#SPJ2

The answer is C.50. That is the answer.

ANSWER

B' has coordinates (16,14).

EXPLANATION

The given coordinates of square ABCD are :

A (2,7) , C (8,1),D (2,1)

In order to form a square, the coordinates of B should be: (8,7)

The mapping for dilation with a scale factor 2, about the origin is

[tex](x,y)\to (2x,2y)[/tex]

This implies that:

[tex]B(8,7)\to B'(2 \times 8,2 \times 7)[/tex]

When we simplify we get:

[tex]B(8,7)\to B'(16,14)[/tex]

Hence B' has coordinates (16,14).

Pythagoras & his colleagues

Answer:

It was named after Pythagoras, a Greek mathematician and philosopher. The theorem bears his name although we have evidence that the Babylonians knew this relationship some 1000 years earlier.

Step-by-step explanation:

We are gonna use the formula y=mx+b

Then, B= 10 T=25

So, the final equation is: 10b+25t(greater than or equal to) 175

An inequality that models how much Liz earns from babysitting and tutoring is 10b+25t≥175.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let b represent the number of hours Liz babysits. Let t represent the number of hours she spends tutoring.

Given Liz babysits for $10 per hour and tutors for $25 per hour. She wants to make at least $175 each week. Therefore, the inequality can be written as,

($10 × b) + ($25 × t) ≥ $175

10b + 25t ≥ 175

Hence, an inequality that models how much Liz earns from babysitting and tutoring is 10b+25t≥175.

Learn more about Inequality:

https://brainly.com/question/19491153

#SPJ2

Answer:

  $362.57

Step-by-step explanation:

A suitable calculator or finance app can find the monthly payment for you. This result comes from a TI-84 calculator.

___

The second attachment shows the parameters of the payment function. With 20% down, Anthony is only financing 80% of the price of his car. Of course, there are 12 months in a year, so 4 years worth of payments will be 48 payments. The calculator uses negative values for amounts you pay.

___

No doubt your reference material shows you a formula for computing loan payments. One such is ...

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate, 0.068/12, and n is the number of payments, 48. The principal amount of the loan, P, will be 19,000×0.80. This formula gives the same result as that shown above and below.

Answer:

Total price paid is 20,033.60

Step-by-step explanation:

20% of 19,000 is 3,800

19,000 - 3,800 = 15,200

6.8% of 15,200 is 1,033.60

3,800 + 15,200 + 1,033.60 = 20,033.60

Answer:

  96 or better

Step-by-step explanation:

Brenda has scored relative to her desired average +2, -1, and -4 points, or a total of -3 points. To ensure her average is 93, she must score at least 3 points above her desired average: 96 or better.

Answer:

4.5 centimeters

Step-by-step explanation:

A = L * W

45 = 10 * W

W = 45/10

W = 4.5cm

Answer:

y = -5x + 1

Step-by-step explanation:

y = -5x + 1 is correct.  

Note that at x = 0, y = 0 + 1 = 1 → (0, 1), and

                at x = 1, y = -5 + 1 = -4 → (1, -4), and

                 at x = -1, y = 5 + 1 = 6  → (-1, 6)

The linear function that maps the diagram is:

[tex]y = -5x + 1[/tex]

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

In the diagram, when [tex]x = 0, y = 1[/tex], thus, the y-intercept is [tex]n = 1[/tex], and:

[tex]y = mx + 1[/tex]

Point (1,-4) is on the diagram, which means that when [tex]x = 1, y = -4[/tex], and this is used to find m.

[tex]y = mx + 1[/tex]

[tex]-4 = m + 1[/tex]

[tex]m = -5[/tex]

Then, the equation is:

[tex]y = -5x + 1[/tex]

A similar problem is given at https://brainly.com/question/16302622

Answer:

Step-by-step explanation:

Left Frame

f(x) is a horizontal line from x = 1 to x = 3. So the y values are the same in that interval.

when y = 1, x = 3

so f(3) = 1

The answer is III

Question Second from the right

The trick is to get the denominator so it is not a complex number. You do that by multiplying by the conjugate which is 8 - 2i. If you do that to the denominator, you must do it to the numerator.

Denominator: (8 + 2i)(8 - 2i) = 64 - 16i + 16i - 4i^2

Denominator: 64 + 4

Denominator: 68

Numerator: (3 - 5i)(8 - 2i)

Numerator: 24 - 6i - 40i + 10*i^2

Numerator: 24 - 46i - 10

Numerator: 14 - 46i

So in some form or other the answer is

[tex]\dfrac{14 - 46i}{68} = \dfrac{7}{34} - \dfrac{23i}{34}[/tex]

Right Frame

Here, the slopes must be the same. So calculate the slope of the left line and make that equal to the slope of the right line's expression

Left Line

Left = (y2 - y1)/( x2 - x1) = (2 - 0)/(0 - - 5) = 2/5

Right line

Right  = (y2 - y1) / (x2 - x1) = (0 - - 4) / (p - 0) = 4/p

Now Equate them (they are parallel and have the same slope)

2/5 = 4/p           Cross multiply

2p = 5*4            Combine the right

2p = 20              Divide by 2

2p/2 = 20/2       Do the division

p = 10

The answer is -- 36

Answer:

the answer is 36

Step-by-step explanation:

Answer:

B. Right by 4 units

Step-by-step explanation:

Let's start by expressing g(x) formula in a simpler form.  x² - 8x + 16 is quite easy to factor into (x - 4)²

so, we have g(x) = (x - 4)² and f(x) = x²

For which value of x will g(x) and f(x) = 0?

g(x) will equal 0 if x = 4

f(x) will equal 0 if x = 0

So, the difference is 4 units.  

Since f(x) would have to move from 0 to 4 to join g(x), the movement will be to the right.

ANSWER

[tex]x \leqslant - 3,x \geqslant 4[/tex]

EXPLANATION

The given inequality is

[tex](x - 4)(x + 3) \geqslant 0[/tex]

To solve this inequality, we need to solve the corresponding equation:

[tex](x - 4)(x + 3) = 0[/tex]

This implies that

[tex]x = - 3 \: or \: x = 4[/tex]

We now plot the solutions of the equation and use it to solve the corresponding inequality as shown in the attachment.

These values divide the number line into 3 regions.

The region(s) that satisfies the inequality is the solution set

From the graph the solution is

[tex]x \leqslant - 3,x \geqslant 4[/tex]

ANSWER

P(X=4 or X=1)=0.2

EXPLANATION

From the table, the probability that X=4 is P(X=4)=0.15

and the table, the probability that X=1 is P(X=1)=0.05

We want to find P(X=4 or X=1)

Recall that

P(X=4 or X=1)=P(X=4)+P(X=1)

We substitute the given probability values to obtain:

P(X=4 or X=1)=0.15+0.05

P(X=4 or X=1)=0.2

Answer: 0.2 is the answer

Step-by-step explanation:

hope this helps :]