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3 years ago

Helpppppppppppppppppp What does the statement ∣

Mathematics

1 answer:

Xelga [282]3 years ago

7 0

Answer:

b is 7 units from 0.

Step-by-step explanation:

$|b|$ = 7 means that the absolute value of b is 7. This means that b can be -7 or 7, so it will always be 7 units from 0.

Hope this helps!

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The volume of a pyramid with a square base where the area of the base is 8.7m^2 and the height is 10

MrMuchimi

Answer:

29 m³

Step-by-step explanation:

The applicable formula is ...

V = (1/3)Bh

Assuming the height is 10 m, the volume is ...

V = (1/3)(8.7 m²)(10 m) = 29 m³

_____

The shape of the base is irrelevant.

5 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

2 years ago

An acorn falls from the branch of a tree to the ground 25 feet below. The distance, S, that the acorn is from the ground as it f

sukhopar [10]

The distance ( S ) is represented by the equation:
S ( t ) = - 16 t² + 25
- 16 t² + 25 = 0
- 16 t² = - 25 / · ( - 1 )
16 t² = 25
t ² = 25 / 16
t = √( 25/16) = 5/4 = 1.25 s ( we will not accept the negative value )
Answer:
The acorn is moving trough the air for 1.25 seconds.

6 0

3 years ago

Read 2 more answers

a boat travels x miles per hour upstream on the mississippi river. The trip takes 3 hours. On the return trip, the boat travels

bogdanovich [222]

Multiply by the reciprocal by 3 and divide the common denominator by 14

6 0

3 years ago

X+2=x+10<br><br>I need to set them equal to each other. Please show workk

soldi70 [24.7K]

These cannot be set equal to each other. you know this because of the following: x + 2 = 10 + x. subtract x from both sides to get 2 = 10, which is not true. they cannot be set equal to each other.

4 0

3 years ago