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3 years ago

I need help on this please

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

8 0

Since these equations are consecutive interior angles, they will add up to 180.
The equation will be (x+20)°+(4x-5)°=180.

(x+20)+(4x-5)=180
5x+15=180
5x=165
165/5x
=33°

You can make sure your answer is correct by putting your x back into the equation.
(33+20)+(4•33-5)
53+132-5
53+127
180

harina [27]3 years ago

6 0

Answer:

25/3

Step-by-step explanation:

Set the equations equal to each other since the lines are parallel.

(x+20)=(4x-5)

-x +5 -x +5

25/3 = 3x/3

x = 25/3

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What the * stands for ?

TEA [102]

Depends. It’s called an asterisk.
In math it’s used for multiplying.
So 5*5= 25

5 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Find the area of cross section,the lateral surface area,the total surface area and volume of the following prisms.

FinnZ [79.3K]

Answer:

don't

Step-by-step explanation:

please send me only

7 0

3 years ago

on a scale drawing, 5 metres is represented by 4 centimetres. write the scale as a ratio in it's simplest form.

ryzh [129]

Answer:

<em>The scale factor is 1:125</em>

Step-by-step explanation:

<u>Scaling</u>

Objects can be represented in a reduced or augmented size by using scaling which consists of multiplying or dividing by a constant factor. We use scaling when representing geographic locations on a map.

On a scale drawing, a distance of 5 meters = 500 cm is represented by 4 centimeters. The scale factor is usually represented as a ratio of the smallest to the biggest magnitude:

$\frac{4}{500}=\frac{1}{125}$

The scale factor is 1:125

8 0

3 years ago

Which is bigger? 30% or 1/3?

aalyn [17]

Convert them to comparable thingummys

convert to fraction

percent means parts out of 100
30%=30/100=3/10

3/10 vvs 1/3
make bottom number 30

3/10 times 3/3=9/30

1/3 times 10/10=10/30
10/30>9/30

1/3 is bigger

8 0

4 years ago