A motor boat can travel 45 km downstream in 2 h and 30 min; and 39 km upstream in 3 h and 15 min. What is the speed of the boat in still water? What is the speed of the current?
​

Answer:

6 cm²

Step-by-step explanation:

The formula to find the area of the parallelogram is :

Area = Base × Height

Given that,

Base ⇒ 3cm

Height ⇒ 2 cm

Let us find now.

Area = Base × Height

Area = 3cm × 2cm

Area = 6 cm²

The length of the curve will be given by the definite integral

[tex]\displaystyle \int_0^1 \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt[/tex]

From the given parametric equations, we get derivatives

[tex]x(t) = 3t^2 + 5 \implies \dfrac{dx}{dt} = 6t[/tex]

[tex]y(t) = 2t^3 + 5 \implies \dfrac{dy}{dt} = 6t^2[/tex]

Then the arc length integral becomes

[tex]\displaystyle \int_0^1 \sqrt{\left(6t\right)^2 + \left(6t^2\right)^2} \, dt = \int_0^1 \sqrt{36t^2 + 36t^4} \, dt \\\\ = \int_0^1 6|t| \sqrt{1 + t^2} \, dt[/tex]

Since 0 ≤ t ≤ 1, we have |t| = t, so

[tex]\displaystyle \int_0^1 6|t| \sqrt{1 + t^2} \, dt = 6 \int_0^1 t \sqrt{1 + t^2} \, dt[/tex]

For the remaining integral, substitute [tex]u = 1 + t^2[/tex] and [tex]du = 2t \, dt[/tex]. Then

[tex]\displaystyle 6 \int_0^1 t \sqrt{1 + t^2} \, dt = 3 \int_1^2 \sqrt{u} \, du \\\\ = 3\times \frac23 u^{3/2} \bigg|_{u=1}^2 \\\\ = 2 \left(2^{3/2} - 1^{3/2}\right) = 2^{5/2} - 2 = \boxed{4\sqrt2-2}[/tex]

Answer:

  1 plane

Step-by-step explanation:

In Euclidean geometry, three non-collinear points will define exactly one plane.

__

Two points will define a line. That line can exist in an infinity of different planes.

A third point not on the line can only lie in exactly one plane with that line.

Three non-collinear points in Euclidean geometry can lie on one unique plane.

In Euclidean geometry, any three non-collinear points (points not lying on the same line) uniquely determine a plane.

This means that there is only one plane that contains all three of those points.

So, given three non-collinear points, you can find exactly one plane that passes through all of them.

Hence, if the three points not on the same line can lie on one plane.

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[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 19 & 1\\ 600& x \end{array} \implies \cfrac{19}{600}~~=~~\cfrac{1}{x} \\\\\\ 19x=600\implies x=\cfrac{600}{19}\implies \stackrel{\textit{about half a minute}}{x\approx 31.58~seconds}[/tex]

Answer:

  10/19 min ≈ 0.5263 min

Step-by-step explanation:

The woman's sprinting speed is given in feet per second, and we are asked for it in minutes per 600 feet. To find the time, we can use the relation ...

  time = distance / speed

Using the given numbers will give a time in seconds, so we need to do a units conversion to find the answer in minutes.

__

  time = distance/speed

  time = (600 ft) / (19 ft/s) = (600/19) s

Converting the units gives ...

  time = (600/19) s × (1 min)/(60 s) = (600·1)/(19·60) min

The time it takes the woman to sprint 600 feet will be ...

  time = 600/(19·60) min = 10/19 min ≈ 0.5263 min

The perimeter of Rosalie's new rectangular mural is given by P = 21 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangular mural be represented as P

Now , the equation will be

Let the initial length of the rectangular mural be L = 3.5 feet

Let the initial width of the rectangular mural be W = 5.5 feet

Now , the new mural is having an extra length of 1.5 feet

So , the new length of the rectangular mural is L₁ = 3.5 + 1.5 = 5 feet

Now , Perimeter P of rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

Perimeter of rectangular mural = 2 ( 5 + 5.5 )

On simplifying the equation , we get

Perimeter of rectangular mural P = 2 x 10.5

Perimeter of rectangular mural P = 21 feet

Hence , the perimeter of rectangular mural is 21 feet

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Answer:

1400

Step-by-step explanation:

Answer:

( 3, -2 )

Step-by-step explanation:

3, -2 is on the line so it is a solution

the rest of the points aren't in the shaded area or on the line therefore they are not a solution

Have a great day! :)

The size of the unknown angle "x"

We'll have to check which one is appropriate from SOHCAHTOA.

In this question hypotenuse and adjacent is given so, we'll have to use cos.

[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]

Let's solve!

Let's substitute the values according to the formula.

[tex]cos \: x= \frac{8}{11}[/tex]

We'll have to use cos inverse.

[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]

[tex]x= 43.34175823[/tex]

Now we'll have to round off to 1 decimal place.

The value in hundredths place is less than 5 so we won't have to round up.

So, the final answer is:

[tex]\large\boxed{x= 43.3°}[/tex]

Therefore, the size of the unknown angle "x" is 43.3°

Answer:

z = 1/4

Step-by-step explanation:

See attached image

Answer:

z = 5

Step-by-step explanation:

simplify

5/(z-25) first

turning it into

((0 - 3/z) + 7/4z) - 5/(z - 25) = 0

then simplify 7/4z

((0 - 3/z) + 7/4z) - 5/(z-25) = 0

when the fractions denominator is 0 then the numerator must be 0

turning the equation into

-25  *  (z - 5)  = 0

solve

-25   =  0

something that is not zero cannot equal zero.

z - 5 = 0

5 - 5 = 0

z = 5

hope this helps:)

The total amount of water that Kiesha drinks in 12 days is 20 quarts

The average amount of water she drinks per day is 1 2/3 quarts

The number of days that Keshia drinks at least the average amount of water is 6 days

If she drinks 1 quart of day 13, the average reduces.

The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.

Average = total amount drank / number of days 1 2/3 quarts

New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts

The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.

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When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.

In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.

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Answer:

See below ~

Step-by-step explanation:

Classifying the triangles by sides and angles :

Triangle ABC

⇒ By Sides : Scalene (All sides are unequal)

⇒ By Angles : Right (There is a right angle = 90°)

============================================================

Triangle GHI

⇒ By Sides : Isosceles (2 sides are equal)

⇒ By Angles : Obtuse (One angle is greater than 90°)

============================================================

Triangle DEF

⇒ By Sides : Equilateral (All sides are equal)

⇒ By Angles : Acute (All angles are less than 90°)

An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,

4.75 = x + (-0.25)

4.75 + 0.25 = x

x = 5

Hence, the original height of the water in the pool in feet is 5.

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Answer:

Angle 1 = 90 degree

Angle 2 = 55 degree

Angle 3 = 35 degree

Step-by-step explanation:

A rhombus has four equal sides. Since the intersection angle of a rhombus is always 90 degree, angle 1 is 90 degree

Angle 3 = 180 degree - 90 degree - 55 degree = 35 degree

Angle 2 = 180 degree - 90 degree - 35 degree = 55 degree

Answer:

see the attachment photo!

The correct answer is 6 / 7 as it is closer to 1.

The fraction is defined as the division of the whole part into an equal number of parts.

The number near 1 will be calculated as:-

7/ 6 = 1.1666

6 / 7 = 0.8571

Difference of the first ratio from one.

1.1666 - 1  = 0.1666

Difference of the second ratio:-

1 - 0.8571 = 0.1429

So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.

Therefore the correct answer is 6 / 7 as it is closer to 1.

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We are given the equation for the height of the arrow. If you graph it, you see that it's a parabola and that the arrow kinda peaks and then falls back down. Another way of thinking about this problem is that you're looking for the time when the height is 0. You can see on the graph that there are two times that h=0. The first is obviously at t=0, when the arrow hasn't left the ground yet. The second is what we're looking for, when the arrow reaches the ground.

To solve this, let's set h=0. So 0=40t-5t^2. If you factor this, you get 5t(8-t) = 0. Continuing that leads to 5t=0 where t=0 which we already knew, and 8-t=0 where t=8. So that second time is when the arrow is back on the ground. Therefore your answer is 8 sec.

Answer:

2(x-5)

Step-by-step explanation:

Hope this helps

Answer:

2 · (x - 5)

Step-by-step explanation:

2 · (x - 5)

2 ·

"2 times"

when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)

(x - 5)

"difference of x and 5"

when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).

Answer:

See below ~

Step-by-step explanation:

⇒ Number of years since = 0 ⇒ t = 0

⇒ Apply in the formula

⇒ n(0) = 73e^(0.02 × 0)

⇒ n(0) = 73e⁰

⇒ n(0) = 73,000,000 rats

=============================================================

⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16

⇒ Applying in the formula

⇒ n(16) = 73e^(0.02 × 16)

⇒ n(16) = 73e^(0.32)

⇒ n(16) = 73 × 1.37712776 × 10⁶

⇒ n(16) = 100.530326 x 10⁶

⇒ n(16) = 100,530,326 rats

Answer:

Given function:  

[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]

where:

To calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:

[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]

To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:

[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]

Substituting the found value of t into the function to find the predicted number of rats in 2009:

[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]

Answer + Step-by-step explanation:

Question 4 :

Construct the angle 0MN :

1) Draw a segment MO

2) Put the protractor so that it is in line with the segment MO

At the same time ,line up the points M with the little circle of the protractor.

3) Spot 40° on the protractor ,then draw a point.

4) Use the ruler to connect point M through that point

Construct the angle MON :

1) Put the protractor so that it is in line with the segment MO

At the same time ,line up the points O with the little circle of the protractor

2) Spot 70° on the protractor ,then draw a point.

3) Use the ruler to connect point O through that point.

Construct the point N :

N is the point of intersection of the lines that go (respectively) through M and O.

Question 6 :

1) Draw a segment XZ such that XZ = 2.

2) construct the angle ZXY = 25°.   (follow the steps described in the Previous question).

NOTE : ∠Z = 180 - (∠X + ∠Y) = 180 - (25 + 45) = 110°

3) construct the angle XZY = 110° .  (follow the steps described in the Previous question)

4) Y is the point of intersection of the lines that go (respectively) through X and Z.

Answer:

360 degrees

..............

Answer:

Bonds

Step-by-step explanation:

A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).

The measures of BC will be 100°. Option D is correct.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

The angle at the center is twice as large as the angle at the perimeter.

BC = 2 ×∠CDB

BC=2×50°

BC= 100°

Hence option D is correct.

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Answer: (8, -4)

Step-by-step explanation:

-5x - 3y = -28
  x + 2y = 0

1. Multiply both sides of the bottom system by 5 to cancel the x out

   5(x+2y=0)

   5x + 10y = 0

2. rewrite

   -5x - 3y = -28

    5x + 10y = 0

3. add

   0x + 7y = -28

4. divide by 7

   7y = -28

5. y = -4

6. plug in -4 for y in one of the original equations

   x + 2(-4) = 0

7. simplify

   x = 8

9. solution is

   (8, -4)

Answer: 674 ft

Step-by-step explanation:

[tex]\tan 12^{\circ}=\frac{y}{1315} \\ \\ 1315\tan 12^{\circ}=y[/tex]

[tex]\tan 8^{\circ}=\frac{y}{x+1315} \\ \\ (x+1315)\tan 8^{\circ}=y \\ \\ (x+1315)\tan 8^{\circ}=1315 \tan12^{\circ} \\ \\ x \tan 8^{\circ}+1315 \tan 8^{\circ}=1315 \tan 12^{\circ} \\ \\ x \tan 8^{\circ}=1315 \tan 12^{\circ}-1315 \tan 8^{\circ} \\ \\ x=\frac{1315 \tan 12^{\circ}-1315 \tan 8^{\circ}}{\tan 8^{\circ}} \approx \boxed{674 \text{ ft}}[/tex]

Answer:

A and B are arithmetic sequences. they have a set and consistent increase/decrease in each term.

Step-by-step explanation:

Step-by-step explanation:

x = number of bottles Paula sold

y = number of bottles Pedro sold

x + y = 72

x = 72 - y

x/y = 3/5

(72 - y)/y = 3/5

5(72 - y) = 3y

360 - 5y = 3y

360 = 8y

y = 45

x + y = 72

x + 45 = 72

x = 27

so,

Paula sold 27 water bottles, and Pedro sold 45.

∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.

A right angle is defined as an angle that is formed when two straight line are perpendicular at an intersection creating a 90° angle when measured.

From the diagram, ∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.

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