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jonny [76]
3 years ago
7

If the sphere shown above has a radius of 5 units, then what is the approximate volume of the sphere? (Use 3.14 for .) A. 261.67

cubic units B. 523.33 cubic units C. 314 cubic units D. 654.17 cubic units
Mathematics
1 answer:
Olenka [21]3 years ago
8 0

Answer:

B. 523.33 cubic units

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 (3.14) 5^3

V =523.3333333

V = 523.33 units^3

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Answer:

Month 5 is when it will be at $100

I hope this helps!

Step-by-step explanation:

x---0-----1-----2-----3----4-----5

y-300-260-220-180-140-100

y=40x+300

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3 years ago
Find the equation of a line that passes through the point (0,1) and has a gradient of 2.
Usimov [2.4K]

Answer:

  • y = 2x + 1

Step-by-step explanation:

Given point (0, 1) and the slope m = 2

<u>Use point- slope form to find the equation of the line:</u>

  • y - y₁ = m(x - x₁)
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6 0
2 years ago
What’s the area of this figure?
Ivan

Answer:

C. 155.5 cm2

Step-by-step explanation:

area = 5*15 + (15+8)*7/2 = 75 + 80.5 = 155.5 cm2

3 0
3 years ago
How do u simplify this expression |-7|
snow_tiger [21]
The absolute value is 7.
7 0
3 years ago
Read 2 more answers
Derivative of tan(2x+3) using first principle
kodGreya [7K]
f(x)=\tan(2x+3)

The derivative is given by the limit

f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h

You have

\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}

By this identity, you have

\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}

So in the limit you get

\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}
\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}

The first two limits are both 1, and the single term in the last limit approaches 0 as h\to0, so you're left with

f'(x)=\dfrac12\sec^2(2x+3)

which agrees with the result you get from applying the chain rule.
7 0
3 years ago
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