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KengaRu [80]
3 years ago
6

Find the cube root(s): ∛1

Mathematics
1 answer:
Over [174]3 years ago
7 0

Answer:

1

Step-by-step explanation:

1 times 1 times 1 = 1

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T what point does the curve have maximum curvature? Y = 7ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
Nookie1986 [14]

Formula for curvature for a well behaved curve y=f(x) is


K(x)= \frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}


The given curve is y=7e^{x}


{y}''=7e^{x}\\ {y}'=7e^{x}


k(x)=\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}


{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}

For Maxima or Minima

{k(x)}'=0

7(e^x)(1+49e^{2x})(98e^{2x}-1)=0

→e^{x}=0∨ 1+49e^{2x}=0∨98e^{2x}-1=0

e^{x}=0  ,  ∧ 1+49e^{2x}=0   [not possible ∵there exists no value of x satisfying these equation]

→98e^{2x}-1=0

Solving this we get

x= -\frac{1}{2}\ln{98}

As you will evaluate {k(x})}''<0 at x=-\frac{1}{2}\ln98

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[-\frac{1}{2}\ln98,1/√2]

k(x)=\lim_{x\to\infty } \frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}

k(x)=\frac{7}{\infty}

k(x)=0







5 0
3 years ago
Three boxes of cereal cost $9.57. How much do five boxes cost
KengaRu [80]

Answer:

$15.95

Step-by-step explanation (without words):

9.57/3= 3.19

3.19*5= $15.95

7 0
3 years ago
Please help. What is the circumference of the circle? <br><br> (X+4)^2+(y-5)^2=81
PIT_PIT [208]

the radius: r^2 = 81

r =9

c = 2*pi*r

 = 2 * pi * 9

 = 18 *pi

Answer: 18*pi or approximately 56.62

8 0
3 years ago
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Jasmine runs 13kilometers and 76 minutes. how long woukd it take to run 1 kilometers​
k0ka [10]

Answer:

It would take her 5.85 minutes to run 1 kilometer.

Step-by-step explanation:

76/13= 5.846

5 0
3 years ago
Use the following function rule to find f(0).<br> f(x)=3(8)^x + 6<br> f(0)=
Anestetic [448]

Answer:

Answer: 9

Step-by-step explanation:

{ \tt{f(x) = 3( {8)}^{x} + 6 }}

• For f(0), substitute x with zero:

{ \tt{f(0) = 3( {8)}^{0}  + 6}} \\  \\ { \tt{f(0) = (3 \times 1) + 6}} \\  \\ { \tt{f(0) = 3 + 6}} \\  \\ { \boxed{ \tt{ \: f(0) = 9 \: }}}

6 0
2 years ago
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