in the diagram above,PQR=125°, QRS=r,RST=80°and STU=44°. Calculate the value of r​

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]

use constant integration rule which yields:

[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]

notice that we can rewrite √x using Law of exponent therefore we obtain:

[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]

once again use law of exponent which yields:

[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]

use exponent integration rule which yields;

[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]

simplify which yields:

[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]

recall fundamental theorem:

[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]

simplify:

[tex] \displaystyle 2 [/tex]

hence

our answer is A

Answer:

The population of Fun City after 171 years would be 214563.

Step-by-step explanation:

The statement depicts a case of exponential growth, whose model is described below:

[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)

Where:

[tex]p_{o}[/tex] - Initial population, no unit.

[tex]p(t)[/tex] - Current population, no unit.

[tex]r[/tex] - Growth rate, no unit.

[tex]t[/tex] - Time, in years.

[tex]T[/tex] - Growth period, in years.

If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:

[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]

[tex]p(t) = 214563[/tex]

The population of Fun City after 171 years would be 214563.

Answer:

67

Step-by-step explanation:

log(3t+9)-log21 = 1

Applying, the law of logarithm,

log(3t+9)/21 = 1

converting the log into index

(3t+9)/21 = 10

solving for t

3t+9 = 21×10

3t+9 = 210

3t = 210-9

3t = 201

t = 201/3

t = 67

Answer:

please mark me brainlist

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

tangent is opp/ad

so that is 15/20, or 3/4

Answer:

I think B

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]\sqrt{y^3} +\sqrt{9y^3} -3y\sqrt{y} \\=\sqrt{y^2 *y} +\sqrt{9*y^2*y} -3y\sqrt{y} \\=y\sqrt{y} +3y\sqrt{y} -3y\sqrt{y} \\=y\sqrt{y}[/tex]

Answer:

The answer is C.) m∠RCD = m∠ACD ÷ 2

RCD = ACD divided by two.

RCD = 90 degrees

ACD ÷2 = 180÷2 = 90 degrees.

So, your answer is C.

Hope this helped. Have a grey day!

Answer:

C. m∠RCD = m∠ACD ÷ 2

Hope this helps!

Step-by-step explanation:

I got it right.

Answer:

x-4y=8

Step-by-step explanation:

y=mx+c comparing with given eq

we get slope(m1)=-4

since both are prependicular

m1×m2=-1

-4×m2=-1

m2=1÷4

eq:-y-y1=m2 (x-x1)

y-1=(1÷4)(x-8)

x-4y=4

Answer:

someone help call the police candice just got shot

Step-by-step explanation:

ahahahahahahahhahaa

Answer:

3m

Step-by-step explanation:

1 month =3 movies

m month =3*m movies

Slope Formula: y2 - y1 / x2 - x1

(m and slope represent the same quantity)

m = 1 - - 5 / -4 - 0

m = 1 + 5 / -4

m = 6 / -4

m = -3/2

Now that we know the slope, we can plug the slope and one of our points into slope-intercept form (y = mx + b) and solve for b. I will be using the point (-4,1).

y = -3/2x + b

1 = -3/2(-4) + b

1 = 6 + b

b = -5

In point form, the y-intercept is (0, -5).

Therefore, to get the equation all we need to do is plug in our slope and b-value to slope-intercept form.

Equation: y = -3/2 x - 5

To check the point (-6, -14) we plug it into our equation and see if the two sides are equal.

-14 = -3/2(-6) - 5

-14 = 9 - 5

-14 = 4

-14 does not equal 4, therefore the point is NOT on the line.

Hope this helps!

Answer:

-25.2

Step-by-step explanation:

by replacing -6 on the place of x we get4.2(-6)=-25.2

Hello,

[tex]\begin{array}{c|c|c|}&x&f(x)\\1&-4&-10\\2&-3&0\\3&-2&0\\4&-1&-4\\5&0&-6******\\6&1&0\\\end{array}\\[/tex]

y-intercept is -6

If x=0 then y=-6

Answer:

P = 157.5 units

Step-by-step explanation:

Answer: b and c

a) 5x + 5 = -4x - 5

9x = - 10

x = -10/9

-

b) - 4x + 5 = -4x - 4

0x = -9 (no solution)

-

c) -4x + 5 = -4x - 5

0x = -10 (no solution)

-

d) 4x + 5 = -4x + 5

8x = 0

x = 0

-

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Answer:

Below.

Step-by-step explanation:

15+10+8=33.

Answer:

13 meters

Step-by-step explanation:

It went 15 meters, but then it went back 10 meters.

[tex]15-10=5[/tex]

Then it went 8 more meters.

[tex]5+8=13[/tex]

Hope this helped! Please mark brainliest :)

Answer:

hope that is helpful

Step-by-step explanation:

W= VI

W= VI

I. I

V= W

I

Answer:

V = [tex]\frac{W}{I}[/tex]

Step-by-step explanation:

Given

W = VI ( isolate V by dividing both sides by I )

[tex]\frac{W}{I}[/tex] = V

Answer:

7500 m

Step-by-step explanation:

5500 is the initial height. It increased by 1500, so 5500 + 1500 = 7000. Then it went down 2000 meters, so 7000 - 2000 = 5000. It went up 2500 again. 5000 + 2500 = 7500

Answer:

a) 4-5 = -1

b) -6+6 = 0

c) 6+(-4) = 2

Answer:

50 cu ft

Step-by-step explanation:

The volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.

Boyle's Law states that If the temperature is constant, the volume of a  gas is inversely proportional to the absolute pressure.

V 1/V2 =P2/P1

V2 = P1 x V1 /P2

Substitute 60 psi for P2, 14.7 psi for P1 and 40cu.ft for V1, we get the volume V2

V2 = 40 x 14.7 / 60

V2 = 9.8 cu.ft

Volume is approximately 10 cu.ft.

Thus, the volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.

Learn more about Boyles law.

https://brainly.com/question/1437490

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Answer:

x=12 is the answer

Step-by-step explanation:

[tex] \frac{5}{2} x - 7 = \frac{3}{4} x + 14[/tex]

[tex] \frac{5}{2} x - \frac{3}{4} x = 14 + 7[/tex]

[tex] \frac{10}{4} x - \frac{3}{4} x = 21[/tex]

[tex] \frac{7}{4} x = 21[/tex]

[tex]x = 21 \div \frac{7}{4} [/tex]

[tex]x = 21 \times \frac{4}{7} [/tex]

[tex]x = 3 \times 4[/tex]

[tex]x = 12[/tex]

Answer:

prime number between 1 to7

The description of set P is the set of prime numbers less than or equal to 7 and the rule is {x | x is a prime number less than or equal to 7}

The set P is given as:

P = {2,3,5,7}

Note that the numbers are prime numbers.

This means that the description of set P is the set of prime numbers less than or equal to 7

The rule form of the set would be:

P = {x | x is a prime number less than or equal to 7}

Read more about sets at:

https://brainly.com/question/1563195

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Answer:

Explanation is in the attachment

hope it is helpful to you

Answer:

f) 11

g) 75

please correct me if I am wrong

Answer:

80in 2

Step-by-step explanation:

Answer:

a=(d1×d2)÷2

(20×12)÷2

240/2

120

The choose (C) 60

The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°