Draw a pair of intersecting lines that forms a pair of complementary angles. Explain your reasoning.

The area of the shaded region in the first quadrant is: 0.75 units

The area under a curve between two points can be found by doing a definite integral between the two points.

Now,

Given:

To find: area bounded by the given lines and curve in the first quadrant.

Finding:

Now, according to the question, the lines x = 0 and y = 2 intersect at the point (0,2).

Point of Intersection of y = 2 and y = 3x - x²:

2 = 3x - x²

=> x² - 3x + 2 = 0

=> (x - 2)(x - 1) = 0

That is, the line and the curve intersect at two points: ( 1 , 2) and (2,2). But the point that is of our importance is only (1,2).

Thus, area shaded = [tex]\int\limits^1_0 {2 - 3x +x^{2}} \, dx[/tex] = 0.75 square units.

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(COMPLETE QUESTION:

What is the area in the first quadrant bounded by y=3x-x³ and the lines x=0, y=2?)

Answer:

8.38 × 10^7

Step-by-step explanation:

first digit of number X 10 raised to however many digits are after the first

The solution is Option D.

The length of the Zambezi river written in scientific notation is

L = 8.38 x 10⁷ feet

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

The length of the Zambezi river in feet L = 83,800,000 feet

Now , the scientific notation is given by in powers of 10

So ,

The value of L in scientific notation is given by

The value of L = 838 x 10⁵ feet

The value of L = 8.38 x 10² x 10⁵ feet

So , on simplifying the equation , we get

The value of L = 8.38 x 10⁷ feet

Therefore , the value of L is 8.38 x 10⁷ feet

Hence , The length of the Zambezi river written in scientific notation is

L = 8.38 x 10⁷ feet

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Answer:

The question isn't clear but i try to do for 7-(-1) solution only. 7-(-1) =8 mean that 7+1=8

Answer:

4

Step-by-step explanation:

16x4=64

Answer:

4 chapters

Step-by-step explanation:

If Raj can read 1 chapter in 16 minutes you need to figure out how many times 16 goes into 64. Divide 64 by 16 and you get 4. Which means Raj can read 4 chapters in 64 minutes.

The length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.

Generally, the equation for is  mathematically given as

Consider the following vector:

[tex]\begin{aligned}\mathbf{v} &=0 \mathbf{i}+4 \mathbf{j}+0 \mathbf{k} \\&=\langle 0,4,0\}\end{aligned}[/tex]

Let us assume that u is a vector that has a length of four, that begins at the origin, and rotates in the x-y plane.

This vector creates a circle with the origin serving as the circle's center and a radius of 4.

So, the coordinates of u can be taken as,

[tex]u=(x\pm \sqrt{4^2-x^2 ,0})[/tex]

Here, 0 [tex]\leq[/tex]x [tex]\leq[/tex] 4.

Now, the cross product of the two vectors u and v is,

[tex]\begin{array}{ccc}\mathbf{i} & \mathbf{j} & \mathbf{k} \\x & \pm \sqrt{4-x^2} & 0 \\0 & 4 & 0\end{array}[/tex]

[tex]&=\mathbf{i}(0-0)-\mathbf{j}(0-0)+\mathbf{k}(4 x-0) \\&=4 x \mathbf{k}\end{aligned}[/tex]

The length of the vector u* v is,

[tex]\begin{aligned}|\mathbf{u} \times \mathbf{v}| &=\sqrt{(4 x)^2} \\&=4 x\end{aligned}[/tex]

Here, 0 <=x <= 4.

If x=4, then u*v is,

[tex]\begin{aligned}\mathbf{u} \times \mathbf{v}| &=4 \times 4 \\&=16 \\|\mathbf{u} \times \mathbf{v}| &=4 \times 0 \\&=0\end{aligned}[/tex]

In conclusion, As a result, the length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.

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CQ

Let v = 4j and let u be a vector with length 4 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u

A certain vine grows at a rate of three inches per day. A researcher starts observing it

when it is 27 inches long.

I

1) What is the meaning of three inches in the problem?

2) What is 27 inches represent in the problem?

3) How long will be the vine after one day?

after two days?

4) Write an algebraic expression to represent the length of the vine after n days.

ans

Answer:

[tex]y\le -\frac{1}{3}x + 1[/tex]

Step-by-step explanation:

The equation of the line is y = mx + b

where

m is the slope = rise/run

b = y-intercept ie where the line crosses the y-axis at x = 0

The line crosses the y axis at y = 1 so the y-intercept is 1 and the point at which the line crosses is (0, 1)

We have the equation as

y = mx + 1

To find the slope, take any two points on the line. Find the corresponding difference in the y values and divide this difference by the corresponding difference in the x values

Two convenient points are (0, 1) and (3, 0)

Slope = [tex]\frac{0-1}{3-0} = -\frac{1}{3}[/tex]

Equation of the line :
[tex]y = -\frac{1}{3}x + 1[/tex]

To find out if the inequality in the shaded region is a ≥ or a ≤ inequality, take a point in the shaded region. Determine whether the chosen point x, y values satisfy which of the following equations

[tex]y\le -\frac{1}{3}x + 1[/tex]                 (1)

or

[tex]y\ge -\frac{1}{3}x + 1[/tex]                  (2)

The point (0,0) is inside the shaded region

Plug in these values into inequality (1)
[tex]0 = -\frac{1}{3}\cdot0 + 1[/tex] = 1

Is 0 ≤ 1 ?

Indeed it is so the inequality is
[tex]y\le -\frac{1}{3}x + 1[/tex]    (Answer)

The region on the opposite side of the line must be a ≥ inqeuality

The attached graph makes it clearer

Answer:

b = - 12

Step-by-step explanation:

substituting m = [tex]\frac{4}{5}[/tex] , x = 10, y = - 4 into y = mx + b , gives

- 4 = ([tex]\frac{4}{5}[/tex] × 10) + b

- 4 = (4 × 2) + b

- 4 = 8 + b ( subtract 8 from both sides )

- 12 = b

Answer: Nachelle is 1.35 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 24.15 meters. She stands 19.2 meters away from the tree, so … that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Step-by-step explanation:

Answer:

ones

Step-by-step explanation:

always start with the smallest number

Answer:

ones

then tens, tenths, hundreths

Step-by-step explanation:

hope this helps

Answer:

3.744

Step-by-step explanation:

2.34

* 1.6

-------

1404

+

234

---------

3.744

It is an isosceles triangle if a triangle has either two equal sides or two equal angles,

The converse of a statement is formed by switching the hypothesis and the conclusion.

Given the statement 'if a triangle has either two equal sides or two equal angles, then it is an isosceles triangle'

Hypothesis - if a triangle has either two equal sides or two equal angles, Conclusion - then it is an isosceles triangle

The converse will be created by switching the hypothesis with conclusion and vice versa to have ' It is an isosceles triangle if a triangle has either two equal sides or two equal angles,

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The slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.

If a table can be represented by a linear equation, then the slope/rate of change between every two pairs of values on the table must be the same. If it's not, then it is not a linear equation that represents y as a function of x.

Slope/rate of change between (1, 18) and (2, 15):

Slope = 18 - 15/1 - 2

Slope =-3

Slope/rate of change between (2, 15) and (8, 9):

Slope = 15 - 9 / 2 - 8

Slope = 6/-6 =

Slope = -1

Therefore, the slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.

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The value of 165 pounds is 74.8 kilograms

The given parameter is:

1 kilogram = 2.205 pounds

Multiply both sides by 165

So, we have

165 * 1 kilogram = 2.205 pounds * 165

Divide both sides by 2.205

So, we have

165/2.205 * 1 kilogram = 2.205 pounds * 165/2.205

Evaluate the products

So, we have

74.8 kilogram = 165 pounds

Rewrite as

165 pounds = 74.8 kilogram

Hence, the value of 165 pounds is 74.8 kilograms

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The percent of change is an increase in altitude of the weather balloon.

Change in altitude = New altitude - Original altitude

= 103 ft - 100 ft

= 3 ft

Percentage change = Change in altitude / Original altitude × 100

= 3 / 100 × 100

= 3%

Therefore, the percentage change in the altitude of the weather balloon is 3%.

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Answer:

12

Step-by-step explanation:

2 times 2 equals 4, 4 times 3 gets you 12.

the exponent 2 above the original 2 simply means to just times the original number by 2.

Note:

Love your handwriting!  

Answer:

2l + 2w

Step-by-step explanation:

using the distributive property

a(b + c) = ab + ac

2(l + w)

= 2l + 2w

The required weight after 43  hours is 72. 96mg

From the information given, we have that;

A Scientist begins with 180 milligrams of a radioactive substance

Let us take Po = 180 milligrams

Using the expression;

[tex]P(t) = Poe^k^t[/tex]

Substituting the values of t = 33, P = 90mg and Po = 180

90 = 180e^33t

[tex]e^3^3^t = \frac{1}{2}[/tex]

Take the log of both sides

[tex]33ln(e^k) = ln (\frac{1}{2} )[/tex]

[tex]k = -\frac{ln 2}{33}[/tex]

k = - 0. 0210

The equation becomes: P(t) = 150e^-0.0210

Substitute t as 43

[tex]P(43) = 180e^-^0^.^0^2^1^0 ^*^4^3[/tex]

P(43) = 72. 96 mg

Hence,  72. 96 mg will remain after 43 hours.

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The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .

Let the horizontal component of velocity be [tex]V_{x}[/tex] and the vertical component  of velocity be [tex]V_{y}[/tex].

The magnitude of the resultant velocity will be represented by V.

So, we can write

The horizontal component of velocity = [tex]V_{x}[/tex] = 22 m/s

The vertical component  of velocity = [tex]V_{y}[/tex] = 12 m/s

The relation between horizontal component, vertical component and resultant velocity is,

[tex]V^{2} = V_{x} ^{2} + V_{y} ^{2}[/tex]

On substituting value of horizontal component and vertical component, we get

[tex]V^{2}[/tex] = [tex](22)^{2} + (12)^{2}[/tex]

[tex]V^{2}[/tex] = 484 + 144

[tex]V^{2}[/tex] = 628

V = [tex]\sqrt{628}[/tex]

V = 25.06 m/s

The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .

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Answer:  x < -14.8

Step-by-step explanation:

    To solve for x, we will isolate the x-variable.

Given:

    [tex]\frac{-5x}{2}[/tex] > 37

Multiply both sides of the equation by 2:

    -5x > 74

Divide both sides of the equation by -5:

➜ Since we are dividing by a negative, we will flip the direction of the sign.

    x < -14.8

Step-by-step explanation:

15x²-14x+3

Product =45

Sum=-14

=(-9,-5)

15x²-9x-5x+3

3x(5x-3)-1(5x+3)

=(5x-3)(3x-1)

The probability that a randomly chosen participant in the survey will have visited both England and France is 0.5

Given data

number of clients = 70

travelled to England , France or both = 60

travelled to England = 45

travelled to France = 50

let:

E represent the client that visited England only,

F represent the number of client that visited France only,

EF represent the number of clients that visited both England and France only

we have

E + F + EF = 60

45 - EF + 50  - EF + EF = 60

45 + 50 - EF = 60

95 - EF = 60

95 - 60 = EF

EF = 35

E = 10

F = 15

probability

Pr = required outcome / possible outcome

= EF / clients surveyed

= 35 / 70

= 0.5

Explanation

EF represents the number of clients that visited England and France only, and it was solved to be 35. probability is the ratio of required outcome which 35 to the possible outcome which is the total number of clients 70. The ratio gives 0.5

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oopss wrong one my bad

Answer:

4 hr

Step-by-step explanation:

Step-by-step explanation:

there is no "x" in the whole scenario.

you and your teacher mean "h" ?

this we get by using Pythagoras, because h, half of the baseline and one of the 51 m sides create a new right-angled triangle :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.

so, for that new inner triangle we have then

51² = h² + (48/2)² = h² + 24²

2601 = h² + 576

h² = 2025

h = 45 m