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3 years ago

Can lengths 7,1,7 form a triangle

Mathematics

1 answer:

Vadim26 [7]3 years ago

4 0

Answer:

Yes

Step-by-step explanation:

There is no unclosable gap. 7+1>7. 7+7>1. An isosceles triangle would be formed.

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Elisa withdrew $20 at a time from her bank account and withdrew a total of $140.francis withdrew $45 at a time from his bank acc

solmaris [256]

Elisa made more withdrawals because when you divide Elisa's total withdrawal by the amount of cash she withdrew at a time would be 140/20=7. When you compare that to Francis's withdrawal which would be 270/45=6. 7>6 so Elisa made more withdrawals than Francis.

7 0

3 years ago

Read 2 more answers

Match each polynomial with its degree

slega [8]

Answer:

Step-by-step explanation:

degree 1 - 5x+5 - d.

degree 2- 3x^2-2x+4- b.

degree 3 - 1/2x^3+8x^2-3- a.

degree 4 - x^4+(x+4)^2- c

5 0

3 years ago

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving

harina [27]

Answer:

The volume of the solid is 714.887 units³

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

rectangle

- If each vertical rectangle is revolved about the y-axis, we

obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

of the cylinder times the thickness of the cylinder

- The formula for the volume will be: V = $\int\limits^a_b {2\pi xf(x)} \, dx$ ,

where 2πx · f(x) is the surface area of the cylinder shell and

dx is its thickness

* Lets solve the problem

∵ y = $x^{\frac{5}{2}}$

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ $y = x^{\frac{5}{2}}$

∵ y = 32

∴ $32=x^{\frac{5}{2}}$

- We will use this rule to find x, if $x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}}$ , where c

is a constant

∴ $x=(32)^{\frac{2}{5}}=4$

∴ The definite integral are x = 0 , x = 4

- Now we will use the rule

∵ $V = \int\limits^a_b {2\pi}xf(x) \, dx$

∵ y = f(x) = x^(5/2) , a = 4 , b = 0

∴ $V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx$

- simplify x(x^5/2) by adding their power

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{7}{2}}} \, dx$

- The rule of integration of $x^{n} is ==== \frac{x^{n+1}}{(n+1)}$

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}]$ from x = 0 to x = 4

∴ $V=2\pi[\frac{2}{9}x^{\frac{9}{2}}]$ from x = 0 to x = 4

- Substitute x = 4 and x = 0

∴ $V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]$

∴ $V=\frac{2048}{9}\pi=714.887$

* The volume of the solid is 714.887 units³

5 0

3 years ago

Evaluate sin^2 (pi/4) + cos^2(pi/4) + cos.

mart [117]

The answer of $sin^2 (pi/4) + cos^2 (pi/4)$ is √ 2

<u>Step-by-step explanation:</u>

The value of $sin^2 (pi/4)$ = √2/ 2

The value of $cos^2 (pi/4)$ = √2/ 2

= √2/ 2 + √2/ 2

= √2 + √2 / 2

= 2 √2 / 2

Dividing √2 by 1

= √2

3 0

3 years ago

2 a square root of 2 b square root 3 parentheses for a square root 2 + 380 square root 2 - 80 parentheses equal

velikii [3]

2√2

= 2√2

√3(√2+380√2-80)

= -80√3+381√6

I hope that's help and sorry for the late answer !

5 0

3 years ago