Find the area of the figure. (Sides meet at right angles.)
3 in
s in
5 in
9 in
8 in

(i) The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate is 1.2 units per second.

(i) By analytical geometry, we know that the slope of a line normal of a curve ([tex]m_{\perp}[/tex]) by the following expression:

[tex]m_{\perp} = - \frac{1}{\frac{dy}{dx} }[/tex] (1)

Where [tex]\frac{dy}{dx}[/tex] is the slope of the line tangent to the curve.

If we know that [tex]x = 1[/tex], then the slope of the normal to the curve is:

[tex]\frac{dy}{dx} = \frac{12}{2\cdot (1)+1}[/tex]

[tex]\frac{dy}{dx} = 4[/tex]

And the slope of a line normal of a curve is:

[tex]m_{\perp} = -\frac{1}{4}[/tex]

By definition of secant curve we calculate the remaining coordinate of the point Q:

[tex]m_{\perp} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (2)

Where:

If we know that [tex](x_{P}, y_{P}) = (1, 5)[/tex], [tex](x_{Q}, y_{Q}) = (x, 0)[/tex] and [tex]m_{\perp} = -\frac{1}{4}[/tex], then the remaining coordinate of point Q is:

[tex]-\frac{1}{4} = \frac{0-5}{x-1}[/tex]

[tex]-\frac{1}{4}\cdot (x-1) = -5[/tex]

[tex]-\frac{1}{4}\cdot x +\frac{1}{4} = -5[/tex]

[tex]\frac{1}{4}\cdot x = \frac{21}{4}[/tex]

[tex]x = 21[/tex]

The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is derived by separating the variables and integrating the resulting expression:

[tex]dy = \frac{12}{2\cdot x + 1}\,dx[/tex]

[tex]\int\, dy = 6\int {\frac{2\,dx}{2\cdot x + 1} }[/tex]

[tex]\int \, dy = 6\int {\frac{du}{u} }[/tex]

[tex]y = 6\cdot \ln u[/tex]

[tex]y = 6\cdot \ln (2\cdot x + 1)+C[/tex]

And the integration constant is found for [tex](x,y) = (1, 5)[/tex]:

[tex]5 = 6\cdot \ln(2\cdot 1 + 1) + C[/tex]

[tex]C = -1.592[/tex]

The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate by using the differential equation presented in statement and the definition of rate of change:

[tex]\frac{dy}{dt} = \left(\frac{12}{2\cdot x +1}\right)\cdot \frac{dx}{dt}[/tex] (3)

If we know that [tex]\frac{dx}{dt} = 0.3[/tex] and [tex]x = 1[/tex], then the rate of increase of the y-coordinate is:

[tex]\frac{dy}{dt} = \left[\frac{12}{2\cdot (1)+1} \right]\cdot (0.3)[/tex]

[tex]\frac{dy}{dt} = 1.2[/tex]

The rate of increase of the y-coordinate is 1.2 units per second.

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i). The coordinates of Q is equal to:

[tex](x,y) = (21, 0)[/tex]

ii). The equation of the curve is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate when x = 1:

[tex]1.2 units[/tex] per second

i). Using analytical geometry,

[tex]xp[/tex] and [tex]xq[/tex] are the P and Q's x-coordinates.

[tex]yp[/tex] and [tex]yq[/tex] are the P and Q's y-coordinates.

Since ([tex]xp[/tex], [tex]yp[/tex]) = (1,5) and ( [tex]xq[/tex], [tex]yq[/tex]) = [tex](x, 0)[/tex] and m⊥ = - 1/4, the left coordinate of Q's point:-

-1/4 = (0-5)/(x - 1)

∵[tex]x = 21[/tex]

Thus, the coordinates of y = (21, 0)

ii). Through isolating the variables and employing integration:-

[tex]dy = \frac{12}{(2.x + 1)} dx[/tex]

by integration and integration constant (1,5), the equation is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate:

[tex]dy/dt[/tex] = [tex]\frac{(12)}{(2.1 + 1)} .0.3[/tex]

∵ [tex]dy/dt[/tex] [tex]= 1.2[/tex]

Thus, the rate of increase for y-coordinate when x = 1 is 1.2 units per second.

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Answer:

I think x= 5

Step-by-step explanation:

because u put 2 where x is supposed to go so it would be -2(2)+9 and -2(2)=-4 and then add 9 and that =5

Answer:

C. There is one solution, because the coefficients of the variables on both sides of the equation are different.

Step-by-step explanation:

The solution is m = 1

~theLocoCoco

Answer:

Standard Form:

720.058

Expanded forms can be written like a sentence or stacked for readability as they are here.

Expanded Notation Form:

 720.058 =

 700  

+ 20  

+ 0  

+   0.0

+   0.05

+   0.008

Expanded Factors Form:

   720.058 =

 7 × 100  

+ 2 × 10  

+ 0 × 1  

+ 0 ×   0.1

+ 5 ×   0.01

+ 8 ×   0.001

Expanded Exponential Form:

 720.058 =

7 × 102

+ 2 × 101

+ 0 × 100

+ 0 × 10-1

+ 5 × 10-2

+ 8 × 10-3

Word Form:

720.058 =

seven hundred twenty and fifty-eight thousandths

Step-by-step explanation:

Answer:

700 + 20 + 0 + 0.050 + 0.008

Step-by-step explanation:

Answer:

An inequality is a mathematical expression that contains inequality signs. For example, y≤ 12x is an inequality. Inequalities are used to tell us that an expression is either larger or smaller than another expression. Equations and inequalities can contain both variables and constants.

Step-by-step explanation:

Answer: 81x + 31y

Step-by-step explanation:

Answer:

x = 57, x = 111

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180, that is

x + 67 + 56 = 180

x + 123 = 180 ( subtract 123 from both sides )

x = 57

---------------------------------------------------------------------

Similarly

x + 47 + 22 = 180

x + 69 = 180 ( subtract 69 from both sides )

x = 111

We can say that:

We must know that the sum of all the internal angles of a triangle is equal to 180°. So, just solve an equation to determine x in each triangle.

________________

Hope this helps! Good studies! ☺

Answer:

PQ=30

Step-by-step explanation:

Knowing that the segment has 3 parts that are 3:1:1 and sum up to 50, you could find how much 1 would equal by finding the total in relation to the ratio (doing 3+1+1) which gets you 5 parts. Then you can divide the total (50) by 5 to figure out how much one part would equal (10). Now, since you know that 1 part is equal to 10 and that PQ is 3 parts, you can find that PQ is equal to 3x10, or 30.

Answer:

x^4n^4

Step-by-step explanation:

Answer:

[tex]n^{4} x^{4}[/tex]  

I really hope this helps!

Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

Answer: $9.75.

Step-by-step explanation:

Given: Cost per stamp  = 39 cents

since 1 dollar = 100 cent , so 1 cent = 0.01 dollar

So,  Cost per stamp  = $0.39

Total stamps = 25

Cost of 25 stamps = (Cost per stamp)  x (Cost per stamp)

=$0.39 x 25

= $9.75

Hence, the price  for the sheet of stamps = $9.75.

Answer:

1. $539

2. $300

3. C

Step-by-step explanation:

May I have brainliest?

Answer:

a=4.8

Step-by-step explanation:

may be wrong tho

Answer: the variable is p=6 .

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

Answer:

p = 6

Step-by-step explanation:

Step 1: Simplify both sides.

3 + 2p − 4 = 11

3 + 2p + −4 = 11

(2p) + (3+−4) = 11 (Combine Like Terms)

2p + −1 = 11

2p − 1 = 11

Step 2: Add 1 to both sides.

2p − 1 + 1 = 11 + 1

2p = 12

Step 3: Divide both sides by 2.

2p/2 = 12/2

p=6

Answer:

its 10 with the remainder of 38

Step-by-step explanation:

The result of the division is remainder = 38 and quotient = 10

Division is the opposite of multiplying. When we know a multiplication fact, we can find a division fact: Example: 3 × 5 = 15, so 15 / 5 = 3. Also, 15 / 3 = 5.

Given that, 708 divided by 67

When dividing 708 by 67 will get 10 as quotient and 38 remainder

Hence, the result of the division is remainder = 38 and quotient = 10

Learn more about division, click;

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Answer:

It is ( D )

Step-by-step explanation:

Have a good day

Answer:

bruh 4 days duh

Step-by-step explanation:

Answer:

35.8

Step-by-step explanation:

                [tex]\frac{340.1}{9.5}[/tex]  = 358

 We know that our answer can never be greater than 358 since the dividend

is 340.1 and the divisor is 9.5;

  Also,

  Both values are to one decimal places and we can use this to solve the problem;

  9 can divide 340 in about 37 place with a remainder of 7,

    So, it is appropriate to make the solution 35.8

Answer: the answers are the second one and the last one

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

8/12 simplifies to 4/6. so x needs to be 4 for it to work

Answer:

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

                                                    DX = BX

                                                    m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The axes of symmetry are shown and labeled m and n. Reflection across either (or both) axis of symmetry will map the figure to itself. Apparently, you want to designate those reflections as ...

  Ra . . . where a = m

  Rb . . . where b = n

Answer:

hope this pic helps enjoy

Answer:

25t+95 or 5(5t + 19)

Step-by-step explanation:

The total of the sound fee = $25

The total of the rental fee = $95

Write is as an equation and you can get 25t + 95 or 5(5t + 19)

Answer:

3=k

Answer:

Step-by-step explanation:

4x^2-8x-5=0

The discriminant is the number under the √. In this case it's 144

Answer:

[tex]\Delta=144[/tex]

Step-by-step explanation:

For a quadratic in standard form, the discriminant is given by:

[tex]\Delta=b^2-4ac[/tex]

We have the equation:

[tex]4x^2-8x-5=0[/tex]

Hence, our a=4; b=-8; and c=-5.

Substituting into our formula, we acquire:

[tex]\Delta=(-8)^2-4(4)(-5)[/tex]

Evaluate:

[tex]\Delta=64+80[/tex]

Add:

[tex]\Delta=144[/tex]

Therefore, our discriminant is 144.

Notes:

Since our discriminant is a positive value, this tells us that our quadratic has two real roots.