⭐ Question 4(challenging)
What is...
Square root of 61 plus [tex]\pi[/tex] times six to the power of ten

Answer:

Question 3

Find the range of the function for the domain 2 < x < 3

[tex]f(2)=(2)^2-1=3[/tex]

[tex]f(3)=(3)^2-1=8[/tex]

Therefore, the range of [tex]f(x)=x^2-1[/tex] is [tex]3 < f(x) < 8[/tex] with domain 2 < x < 3

This means that for the function to be continuous, when the domain is x=3, f(x) = 8

[tex]f(3)=2a(3)=6a[/tex]

[tex]\implies 6a=8\implies a=\dfrac43[/tex]

Similarly, when the domain is x > 3, f(x) > 8

[tex]f(3)=b(3)-4=3b-4[/tex]

[tex]\implies 3b-4 > 8 \implies b = 4[/tex]

Therefore, [tex]a=\dfrac43[/tex] and b = 4

Question 5

[tex]\textsf{let}\:u=\ln (x)[/tex]

[tex]\implies \dfrac{du}{dx}=\dfrac{1}{x}\implies dx=x\:du[/tex]

[tex]x=1\implies u=0[/tex]

[tex]x=3 \implies u=\ln 3[/tex]

[tex]\implies \displaystyle \int\limits_{1}^{3} \dfrac{\ln x \sin (\ln x)}{x} \,\:dx=\displaystyle \int\limits_{0}^{\ln 3} \dfrac{u \sin u}{x} \, \cdot x\:du=\displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du[/tex]

Use integration by parts:

[tex]\displaystyle \int u\dfrac{dv}{dx} \, dx=uv- \displaystyle \int v \dfrac{du}{dx} \, dx[/tex]

[tex]\textsf{where}\:u=u\:\textsf{and}\:\dfrac{dv}{dx}=\sin u[/tex]

[tex]\implies \dfrac{du}{dx}=1\:\textsf{and}\:v=\int \sin u=-\cos u[/tex]

[tex]\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du=-u \cos u- \int\limits_{0}^{\ln 3}-\cos u \,\:du[/tex]

[tex]\begin{aligned}\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du & =\left[-u \cos u+ \sin u\right]_{0}^{\ln 3}\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-[-0 \cos (0)+ \sin (0)]\\\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-0\\\\ & = 0.3908925527...\end{aligned}[/tex]

5.25 g

Step-by-step explanation:

The half-life of a radioactive substance is the amount of time it takes for half the mass of the substance to decay.

In this question no calculations are required to get half-life. This is because it is given that it took 3 years for the 14g to halve to 7g.

To find amount of the substance after a further 4 years, we’ll use the formula;

Final amount = initial amount / 2ⁿ

Where n = elapse time / half-life

We begin by finding n;

n = 4 years / 3 years

= 4/3

Final amount;

=  initial amount / 2ⁿ

= 7  / 2 ^ (4/3)

= 5.25 g

Learn More:

For more on half-lives calculations check out;

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https://brainly.com/question/1831303

https://brainly.com/question/2674699

The probability that a flight departed on time given that it arrives is 0.92

The conditional probability of event B occurring giving that event A has occurred is expressed as

P(B|A) = P(A and B)/P(A)

Given the following parameters

P(A and B) = The probability that a flight departs and arrives on time = 0.84

P(A) = The probability that an airplane flight departs on time = 0.91

P(B | A) = 0.84/0.91
P(B | A) = 0.92

Hence the probability that a flight departed on time given that it arrives is 0.92

Learn more on conditional probability here: https://brainly.com/question/25870256

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Answer:

x = -1/7

Step-by-step explanation:

3/5x + 5 = 4/5

3/5x + 5/1 = 4/5

3 + 25x/5x = 4/5

4(5x) = 5(3 + 25x)

20x = 15 + 125x

-15 = 125x - 20x

-15 = 105x

-15/105 = x

-1/7 = x

Answer:

5 faces

Step-by-step explanation:

A traingular prism has 5 faces. The square on the bottom and the four traingles that make up the sides.

hope this helps :)

Answer:

5

8

5

step by step

Love your pfp

Answer:

Area of a triangle is 1/2 x base x height.

area of triangle = 1/2 x 20 x 17 = 170 square feet.

the image shows 4 triangles, total area = 170 x 4 = 680 square feet.

the answer is A. 680 sq. ft.

Hope this helps you!!

Please Mark me as Brainleast!!!!!!!!!!!!!

Answer: the answer is a which is 680 ft²

Step-by-step explanation: we will make 17 Times 220 divided by 2 equals 170 times by 4 equals 680 . Hope it helps you buddy .

Answer:

tbh I'm in 6 grade-_- and it's maybe higher than 10$

Answer:

Examples of 2D shapes

2D Shape Properties

Pentagon A shape with five sides and five equal angles.

Kite A quadrilateral with two pairs of sides of the same length.

Rhombus A quadrilateral with both pairs of opposite sides parallel and all sides of the same length. Unlike a square, however, its angles are not all 90˚.

Step-by-step explanation:

Answer:

6

out of the total donuts (90), Ryan ate 12 cream filled donuts. 45 is half of that, therefore he should eat half the cream filled donuts

Check the picture below.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(160)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(90)(120)}}\implies 3200~~ + ~~5400\implies 8600[/tex]

Answer:

2 reflection across the y axis

The calculation that represents the cost of 2 dozen iris bulbs is ($5 * 6) + ($4 * 6) + ($3 * 12)

An equation is an expression that shows the relationship between two or more variables and numbers.

The cost of 2 dozens of iris bulbs is given by the equation:

Cost = ($5 * 6) + ($4 * 6) + ($3 * 12)

The calculation that represents the cost of 2 dozen iris bulbs is ($5 * 6) + ($4 * 6) + ($3 * 12)

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Answer:

True! We can tell that it is still there through weight becuase weight is a method of evidence/measurement. Hope this helps!

Answer:

Price before Taxes: $ 25.00

Sales Tax (8.5%): $ 2.13

Total Price with Tax: $ 27.1

Step-by-step explanation:

Answer:

Answer is 48

Step-by-step explanation:

6x8 = 48

Hope it helps!

Answer:

area=b•h

6 units • 8 units = 48 units²

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

An equation is an expression that shows the relationship between two or more numbers and variables.

The zeros of the function is at:

g(x) = 0, hence:

x³ - x² - 4x + 4 = 0

(x - 1)(x² - 4) = 0

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

x = 1, x = -2 and x = 2

The y intercept is at x = 0, hence:

g(0) = 0³ - 0² - 4(0) + 4 = 4

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

Find out more on equation at: https://brainly.com/question/2972832

Answer:

c:) 150 in²

Step-by-step explanation:

It's basically and SAS triangle

SAS is Side, Angle, Side

side 15 in angle 90° and 20 in

a = 20 in

b = 25 in

c = 15 in

Angles:

A = 53.1301 °

B = 90 °

C = 36.8699 °

Other:

P = 60 in

s = 30 in

K = 150 in2

r = 5 in

R = 12.5 in

Agenda:

A = angle A

B = angle B

C = angle C

a = side a

b = side b

c = side c

P = perimeter

s = semi-perimeter

K = area

r = radius of inscribed circle

R = radius of circumscribed circle

[tex]tan (M) = \frac{side-opposite-angle-M}{side-adjacent-angle-M} =\frac{8\sqrt{2} }{4} =2\sqrt{2}[/tex]

Hope that helps!

ps. I attached a sheet of trigonometry identities

Step-by-step explanation:

if width = 3 length = 5 hight = 10

Volume of rectangular prism = 3×5×10

= 150

[tex] \frac{ab}{de} = \frac{bc}{ef} = \frac{ac}{df} [/tex]=k

[tex] \frac{6}{18} = \frac{12}{ef} [/tex]

[tex]ef = 36[/tex]

[tex] \frac{12}{36} = \frac{ac}{15} [/tex]

[tex]ac = 5[/tex]

[tex] \frac{6}{18} = \frac{12}{36} = \frac{5}{15} = \frac{1}{3} [/tex]

I hope it helps

Answer:f θ =2sin θ + square root of 3.

Step-by-step explanation: I think this is right

The area of the property is the product of its dimensions, and the expression for the area is (x + 10)²

The area of the land is the product of its dimensions.

Let the length and the width of the land be x.

So, the area measured by the appraisal is:

Area = x²

One side of the land is 10 more than the measured length.

So, we have:

Area = (x + 10)²

Substitute 12 for x

Area = (12 + 10)²

Evaluate

Area = 484

Hence, the area of the property is 484

Read more about area at:

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Answer:

A

Step-by-step explanation:

If 50 is the diameter that thr radius is 25 and the equation to find the area of a circle is pi(r^2). So you would do pi(25^2) and that is 1963

Answer:

6/7

Step-by-step explanation:

you juts switch the top and bottom

Brainleist please

Answer:

[tex] \hookrightarrow \sf \bold{ - \frac{1}{2} }[/tex]

Step-by-step explanation:

⇢ [tex] \bold{5x+5=3x+4} [/tex]

⇢ - 3x + 5x = 4 - 5

⇢ 2x = -1

⇢ 2x/2.= -1/2

⇢ x = -1/2

5x+5=3x+4

5x-3x=4-5

2x=-1

2x/2=-1/2

x=-1/2

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=12\\ \theta = 70 \end{cases}\implies \begin{array}{llll} A=\cfrac{(70)\pi (12)^2}{360}\implies A=28\pi \\\\\\ A\approx 87.96~cm^2 \end{array}[/tex]

Answer:

Step-by-step explanation:

There's a saying to this kind of equation: Rate + Time = Distance and B best fits the saying, so B must be right (Don't quote me on that, it may be wrong)

the linear equation that can be used to find the distance that Eric travels each day is A. d = rt & the total distance that Eric travels each day is C. 112.5 miles.

Speed is measured as distance moved over time.

here, given that,

He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.

so, the linear equation that can be used to find the distance that Eric travels each day is A. d = rt

i.e. d= 75*1.5

      =112.5

& the total distance that Eric travels each day is C. 112.5 miles.

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Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.

Expand the tan expression using the angle sum identities for sin and cos :

tan(u + v) = sin(u + v) / cos(u + v)

tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]

Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.

Recall that for all x,

cos²(x) + sin²(x) = 1

and it follows that

cos(u) = - √(1 - sin²(u)) = -12/13

sin(v) = - √(1 - cos²(v)) = -3/5

Then putting everything together, we have

tan(u + v)

= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]

= 56/33

(or, if sin(u) = -12/13, then tan(u + v) = -63/16)

Answer:

And great great the owner is 44

Step-by-step explanation:

or 36 because you have to add all sides