A mass of water at 100°c is added to another mass Q of water at a temperature T and the resulting temperature is theta. Describe an expression for theta in terms of the quantities (specific heat capacity of water is 4.2JKg-¹K-¹).​

I'm going to assume the limit is

[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3}[/tex]

since problems like this usually involve indeterminate forms, and

√(x + 1) - 2 = x - 3 = 0

when x = 3.

To get around the discontinuity in the limand at x = 3, rationalize the numerator:

[tex]\dfrac{\sqrt{x+1} - 2}{x - 3} \times \dfrac{\sqrt{x + 1} + 2}{\sqrt{x + 1} + 2} = \dfrac{\left(\sqrt{x+1}\right)^2 - 2^2}{(x-3) \left(\sqrt{x+1}+2\right)} = \dfrac{x-3}{(x-3)\left(\sqrt{x+1}+2\right)}[/tex]

Now as x approaches 3, the factors of x - 3 cancel, the resulting limand is continuous at x = 3, and we have

[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \boxed{\frac14}[/tex]

The point that lies on the perpendicular bisector of AB is point N

The circle is given as:

Circle N

The chord is given as:

Chord AB

The perpendicular bisector of the chord is any line drawn from the center of the circle that divides the chord in equal halves.

This means that the point starts from point N

Hence, the point that lies on the perpendicular bisector of AB is point N

Read more about perpendicular bisectors at:

https://brainly.com/question/929137

#SPJ1

Answer:

34086 mm

Step-by-step explanation:

34m = 34000 mm

8cm = 80 mm

6mm = 6mm

34000+80+6 = 34086 mm

Answer:

34086 mm

34m = 34000m

8cm  = 80mm

Answer:

96 inches

Step-by-step explanation:

1:24

4:x

cross multiply:

x=4*24

x=96

Answer: D.

Step-by-step explanation:

5/9 + 2/4

find common denominator

common denominator=36

5 x 4=20    2 x 9=18

9 x 4=36    4 x 9=36

20/36 + 18/36

20 + 18=38

38/36 simplify

1 2/36 (if not in simpliest form)

Answer:

243 students' favorite color is red

Step-by-step explanation:

if 55% of the students said their favorite color was blue, then 45% chose that red was their favorite color

we can get 45% of 540 using a cross-multiplication equation

45% is 45/100

45/100 is to ?/540

the (?) represents the value of students who chose red as their favorite color (we do not know this but we can figure it out using cross-multiplication)

45 times 540 is 24300

24300/100 = 243.

Give brainliest, please!

hope this helps :)

Answer:

25/8 in decimal form is 3.125.

Step-by-step explanation:

I hope this helps! :)

Answer:

-1

Step-by-step explanation:

Find the difference of each sequence

19 - 15 = 4

15 - 11 = 4

11 - 7 = 4

7- 3 = 4

3 - ? = 4

Subtract 4 from the 3

3 - 4 = -1

Therefore, the next term is -1

Answer:

It b(4) because if you time 3 times 4 it equals 15.

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

La suma de dos números enteros negativos siempre será negativa. El signo de la suma de dos números enteros con signos diferentes dependera de cual tiene mayor valor absoluto.

La suma de dos números A y B se escribe como:

A + B.

Sí ambos números son negativos, los podemos escribir como:

A = -a

B = -b

Donde a y b son positivos.

Entonces la suma de esos dos nos dará:

(-a) + (-b) = -(a + b).

Es decir, el resultado de la suma es un número negativo.

Un ejemplo es sí tomamos:

A = -1

B = -4

(-1) + (-4) = -(1 + 4) = -5.

En este caso dependerá de que número tenga mayor valor absoluto.

Por ejemplo, sí usamos:

A = 2

B = -4

2 + (-4) = -2

El resultado es negativo, pues el número negativo tiene mayor valor absoluto.

Por otro lado, sí tenemos:

A = -2

B = 4

(-2) + 4 = 2

El resultado es positivo, pues el número positivo tiene mayor valor absoluto.

Sí quieres aprender más sobre sumas:

https://brainly.com/question/11562149

#SPJ1

The measure of the three missing angles in the given rhombus are:

x = 122°

z = 58°

y = 122°

A rhombus is a quadrilateral with four interior angles. In a rhombus, the opposite angles are congruent while the adjacent angles are supplementary to each other.

x and 58° are adjacent angles and are therefore supplementary.

x = 180 - 58 = 122°

z = 58° (opposite angles)

y = x = 122° (opposite angles)

Learn more about a rhombus on:

https://brainly.com/question/20627264

#SPJ1

Answer:

72cm²

Step-by-step explanation:

Hello!

The formula for area of a trapezoid: [tex]A = \frac12(b_1 + b_2)h[/tex]

We find the average of the bases, and multiply it by the height.

The area of the trapezoid is 72cm²

Answer:

A: X < 7

Step-by-step explanation:

Step-by-step explanation:

cos x = 2/6.5 = 0.3

arccos 0.3 = 72.54 degree

Answer:

Division

Step-by-step explanation:

You can use division to divide fractions.

Say you have a problem

3/4 divided by 2/5

Turn 2/5 into its reciprocal

That would be 5/2

then multiply 3/4 and 5/2

Which would be 15/8

Which is your answer

(not sure if this is what you are really asking)

The lateral area is 117 square centimeters and the surface area is 292.72 square centimeters

The given parameters are:

The lateral area is calculated using:

Lateral = 0.5 * (Perimeter of base) * Slant height

This gives

Lateral = 0.5 * (3 * 6) * 13

Evaluate

Lateral = 117

Hence, the lateral area is 117 square centimeters

The surface area is calculated using:

Surface = l²√3

This gives

Surface = 13² * √3

Evaluate

Surface = 292.72

Hence, the surface area is 292.72 square centimeters

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Answer:

L = 117 cm2 ; S = 132.6 cm2

Step-by-step explanation:

Substitute the known value of the base edge length s=6 cm into the formula for the perimeter of the regular triangle, P=3s.

P=3(6)=18

Therefore, the perimeter of the regular triangle is 18 cm.

Substitute the known values of the perimeter P=18 cm and the slant height l=13 cm into the formula for the lateral area of a regular pyramid, L=1/2Pl.

L=1/2(18)(13)=117

Therefore, the lateral area of the pyramid is 117 cm2.

The surface area of a regular pyramid with lateral area L and base area B is S=L+B, or S=1/2Pl+B.

The base of the regular triangular pyramid is the equilateral triangle. The area of the triangle with the base b and the height h is B=1/2bh.

Answer:

a) 56

Step-by-step explanation:

(2x2x6)+(4x4x2)

24+32

The correct value of this algebraic expression is -1/16

Given the expression, [tex]\large \sf \dfrac{-b}{2a}[/tex], let's just: change the letters to the numbers and then perform the given operations.

*Equal signs will be positive ⇒ (-) (-)= + & (+) (+) = +

*Different signs will be negative ⇒ (-) (+) = - & (+) (-) = -

[tex]\\\large \sf \dfrac{-b}{2a} , \ a=-8 \ , \ b=-1[/tex]

[tex]\large \sf \dfrac{-(-1)}{2 \cdot (-8)}[/tex]

[tex]\large \sf \dfrac{1}{2 \cdot (-8)}[/tex]

[tex]\large \sf \dfrac{1}{-16}[/tex]

[tex]\blue{\boxed{\large \sf -\dfrac{1}{16} }}\\[/tex]

Therefore, the final answer to this simplification will be -1/16

Answer:

[tex]x = -\dfrac 23\\\\x = -2[/tex]

Step by step explanation:

[tex]3x^2 +8x +4 =0\\\\\text{The quadratic formula,}~ x = \dfrac{-b\pm\sqrt{b^2 -4ac}}{2a}.\\\\\text{By comparing}~ 3x^2 +8x +4~ \text{with the standard form}~ ax^2 +bx +c,\\\\a = 3, ~b = 8 ,~ c = 4\\\\\text{Now,}~\\\\x = \dfrac{-8\pm\sqrt{8^2 -4 \times 3 \times 4}}{2(3)}\\\\\\~~~=\dfrac{-8\pm\sqrt{64-48}}{6}\\\\\\~~~=\dfrac{-8\pm\sqrt{16}}{6}\\\\\\~~~=\dfrac{-8\pm 4 }{6}\\[/tex]

[tex]x = \dfrac{-8+4}{6}=-\dfrac{4}{6}= -\dfrac 23\\\\x= \dfrac{-8-4}{6}= -\dfrac{12}{6}=-2[/tex]

The finance charge will be $ 0.76. Then the new balance will be $ 55.54.

Finance costs are paid to the provider in exchange for supplying cash or granting the loan.

The account balance on April 1st is $50.51.

On April 15th payment of $15.00 is made.

On April 25th a purchase of $19.27 is made.

The annual rate is 18%.

Then the finance charge will be

⇒ $ 50.51 x 0.18 / 12

⇒ $ 0.76

Then the new balance will be

New balance = $ 50.51 - $ 15 + $ 19.27 + $ 0.76

New balance = $ 55.54

More about the finance charge link is given below.

https://brainly.com/question/2588555

#SPJ1

Answer:

26

Step-by-step explanation:

18,23,24,28,29,30

(6 in total + 1)/2=3.5.

- the number which is 3.5 is between 24 and 28.

- middle number between these two is 26.

Answer:

5

Step-by-step explanation:

10c+15=5(2c+3)

use distributive property

10c+15=10c+15

Hope this helps!

If not, I am sorry.

Answer:

You would have to insert 5 for there to be infinite solutions.

Using the circle theorems, the value of z is 45

From the question, we are to determine the value of z

From the given information,

KM is a diameter

∴ ∠KLM = 90° (Angle in a semicircle)

Also, ΔKLM is isosceles

∴ ∠KML = ∠MKL (Base angles of an isosceles triangle)

Then,

∠KML + ∠MKL + ∠KLM = 180° (Sum of angles in a triangle)

2× ∠KML + 90° = 180°

2× ∠KML = 180° - 90°

2× ∠KML = 90°

∠KML = 90°/2

∠KML = 45°

Now, we can observe that

z° = ∠KML (Angles in alternate segment)

But,

∠KML = 45°

∴ z = 45

Hence, the value of z is 45

Learn more on Circle Geometry here: https://brainly.com/question/17074363

#SPJ1

Answer:

(a) 6ab² - 8a²b + 3ab

Step-by-step explanation:

Given: 5ab² - 12a²b + 3ab + ab² + 4a²b

In this question, we will be combining like terms.

What are like terms?

Like terms are terms with the same variables and power. For example, 2x and 4x, as well as 2a² and 4a².

Combine like terms:

5ab² - 12a²b + 3ab + ab² + 4a²b

(5ab² + ab²) + (-12a²b + 4a²b) + 3ab

6ab² - 8a²b + 3ab

d

Step-by-step explanation:

Answer with step by step explanation

To find the equation of the line from the given equation, you have to make y as the subject in the equation.

Let us find now.

x + 3y = -4

3y = -4 - x

3y = -x - 4

Divide the whole equation by 3.

y = -x/3 - 4/3

Therefore, the equation of the line is:

y = -x/3 - 4/3

And now we have to find the slope and the y - intercept of the line.

That is, we have to find the m & c of y = m x + c.

Here,

m ⇒ slope

c ⇒ y - intercept

So, to find it we have to find the values which were replaced with m & c.

Let us find now.

y = m x + c

y = -x/3 - 4/3

Now it is clear that, -1/3 & -4/3 are replaced with m & c respectively.

Therefore,

slope ⇒ -1/3

y - intercept ⇒ -4/3

To solve this, we need to use our trigonometric equations

  ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

  [tex]tan(58)=\frac{22}{x} \\22=x*tan(58)\\x=\frac{22}{tan(58)} \\x=13.75[/tex]

Answer: 13.8 (rounded to nearest tenth)

Hope that helps!