help 10 points to solve please

I think how you approach this depends on your knowledge of calculus.

If you don't know how to compute definite integrals yet, but you do know that they represent signed areas under curves, then you can plot both curves |x - 4| and √(36 - x ²), then recognize that the areas represented by these integrals are areas of geometric shapes. (See attached images)

First integral: if you plot |x - 4| on the interval [3, 6], you'll see that the integral corresponds to the area of two triangles. One of them has base = height = 1, and the other has base = height = 2. Then

[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac12\times1\times1+\frac12\times2\times2=\frac52[/tex]

Second integral: if [tex]y=\sqrt{36-x^2}[/tex], then [tex]x^2+y^2=6^2[/tex], meaning this curve is the upper half of a circle with radius 6. On the interval [-6, 0], the area amounts to 1/4 of the total area of such a circle, so that

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\frac{\pi\times6^2}4=9\pi[/tex]

* * *

If you already know a few things about calculus and integration, you can compute these areas directly.

First integral:

[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\int_3^4(4-x)\,\mathrm dx+\int_4^6(x-4)\,\mathrm dx[/tex]

[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(4x-\frac{x^2}2\right)\bigg|_{x=3}^{x=4}+\left(\frac{x^2}2-4x\right)\bigg|_{x=4}^{x=6}[/tex]

[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(\left(4\times4-\frac{4^2}2\right)-\left(4\times3-\frac{3^2}2\right)\right)+\left(\left(\frac{6^2}2-4\times6\right)-\left(\frac{4^2}2-4\times4\right)\right)[/tex]

[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac52[/tex]

Second integral:

Substitute x = 6 sin(t ) and dx = 6 cos(t ) dt, then

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\int_{-\frac\pi2}^0\sqrt{6^2-(6\sin(t))^2} (6\cos(t))\,\mathrm dt[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{1-\sin^2(t)} \,\mathrm dt[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{\cos^2(t)} \,\mathrm dt[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) |\cos(t)| \,\mathrm dt[/tex]

For t ∈ [-π/2, 0], cos(t ) > 0, so |cos(t )| = cos(t ) :

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos^2(t)\,\mathrm dt[/tex]

Recall the half-angle identity,

cos²(t ) = (1 + cos(2t )) / 2

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\int_{-\frac\pi2}^0(1+\cos(2t))\,\mathrm dt[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(t+\frac{\sin(2t)}2\right)\bigg|_{t=-\frac\pi2}^{t=0}[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(\left(0+\frac{\sin(2\times0)}2\right)-\left(-\frac\pi2+\frac{\sin\left(2\times\left(-\frac\pi2\right)\right)}2\right)\right)[/tex]

[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=9\pi[/tex]

Answer:

D) {-5,1}

R) {-4,7}

x (-31/11,0)

y (0,31/6)

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

9514 1404 393

Answer:

Step-by-step explanation:

a) The fraction is ...

  2(5 1/4)/(15 2/3) = (21/2)/(47/3) = 63/94

Two streamers will require 63/94 of the original material.

__

b) $4800 is 70% of Sara's salary, so that salary is ...

  4800 = 0.70s

  4800/0.70 = s = 6857.14

Sara's salary is about $6857.14.

Answer:

6n + 20

Step-by-step explanation:

10 + 2n + 10 +4n

6n +20

Answer:

[tex]10 + 2n + 10 + 4n \\ 6n + 20 \\ 2(3n + 10)[/tex]

it's 158 inches

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

Answer:

10

Step-by-step explanation:

Answer:

I’m sorry, can you please tell me the options for the drop down menu. Thanks, I will edit my answer when you do.

Step-by-step explanation:

Answer/Step-by-step explanation:

1. <A = <B (alternate angles theorem)

90° = 2x (substitution)

Divide both sides by 2

90/2 = 2x/2

45 = x

x = 45

2. <3 = <5 (corresponding angles theorem)

½x = 60 (substitution)

Multiply both sides by 2

x = 60*2

x = 120

3. Based on supplementary bangle theorem, sum of supplementary angles = 180°. Therefore:

m<LFG + m<ABC = 180°

2.5x + x + 33 = 180 (substitution)

Add like terms

3.5x + 33 = 180

3.5x = 180 - 33

3.5x = 147

x = 147/3.5

x = 42

3a. m<LFG = 2.5x

Plug in the value of x

m<LFG = 2.5(42)

m<LFG = 105°

3b. m<ABC = x + 33

Plug in the value of x

m<ABC = 42 + 33

m<ABC = 75°

Answer:

20

Step-by-step explanation:

Because this angle is 90 and we have 70

Answer:

x = 17

Step-by-step explanation:

Use the interior angle sum theorem which says:

if n is the number of sides the sum of the interior angles is 180(n-2)

there are 6 sides, so the interior angle sum is 180(6 - 2) = 180 * 4 = 720.

This means that if you add all the angles you will get 720, so:

[tex]110 + 8x - 1+5x+36+116+7x+19+6x-2=720[/tex]

[tex]26x+278=720\\26x = 442\\x = 17[/tex]

Answer:

11 3/4

31 5/8

Step-by-step explanation:

1. 54 1/2 - 42 3/4

= 109/2 -171/4

= 218-171/4

= 47/4

= 11 3/4

2. 45 3/8 - 11 3/4

= 363/8 -55/4

= 363-110/8

= 253/8

= 31 5/8

Answer:

The slope is -4 and the y-intercept is 8.

Step-by-step explanation:

y+4x=8

y=8-4x

y=-4x+8

y=mx+b where m=slope and b=y-intercept.

Hello!

The equation of this line is written in slope-intercept form (y=mx+b)

Where

m is the slope

b is the y-intercept

m is 4

b is 8

Hope it helps!

If you have any questions, feel free to ask! :)

~An excited gal

[tex]MagicalNature[/tex] here to help

Answer:

ab=a×b

cb=c×b

ad=a×d

cd=c×d

Answer:

well the factor: Add and subtract the second term to the expression and factor by grouping.     (a+c)(b+d)

Step-by-step explanation:

Hope this is helpful! God Bless you !

Answer:

0.43ᵣ = 0.1 + 0.33ᵣ = 1/10 + 1/3 = 3/30 + 10/30 = 13/30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

x = 0.43333......

Multiply the equation by 10 on both sides, then we have

10x = 10 × 0.43333......

10x = 4.33333......                        ...1

Multiply the equation by 100 on both sides, then we have

100x = 100 × 0.43333......

100x = 43.33333......                     ...2

Subtract equation 1 from equation 2, then we have

100x - 10x = 43.3333.... - 4.3333.....

90x = 39

x = 39 / 90

x = 13 / 30

The expression 0.43333... is equivalent to the fraction number 13/30. And it is proved below.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

Step-by-step explanation:

tan B=372/279=(31×12)/(31×9)=12/9=4/3

Answer:

mean.

Step-by-step explanation:

since this is a math question i'm assuming you want a mathematical term. the mean of a set of data represents the entire set of data.

Answer:

1. C. x^8

2. C. 3^9

3. D. 12x^7

Step-by-step explanation:

1.

x^6 * x^2 = x^(6 + 2) = x^8

Answer: C. x^8

2.

3^2 * 3^3 * 3^4 = 3^2 + 3 + 4) = 3^9

Answer: C. 3^9

3.

3x^2 * 4x^5 = 3 * 4 * x^2 * x^5 = 12x^(2 + 5) = 12x^7

Answer: D. 12x^7

Answer:

True

Step-by-step explanation:

Answer:

m = 2

The slope of the line through (1, 3) and (-2, -3) is 2!

The formula to find the slope is attached below.

Hope I was of help. Have a good new year!

Answer:

false, it would be 8,000

Answer:

4 5/6 + 5 7/8= 10 17/24

Step-by-step explanation:

pretty sure I answered this exact question like minutes ago

Answer: 257/24, or 10 and 17/24.

Step-by-step explanation:

First, we need to turn the fractions into improper fractions and then find the common denominator.

4 and 5/6 = 29/6

5 and 7/8 = 47/8

The common denominator is 24. Now, we convert the fractions and add. Hope this helps!