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sladkih [1.3K]
3 years ago
7

Let f be continuous on [0, a] and differentiable on (0, a), Prove that if f(a)=0 then there is at least one value of x in (0, a)

, such that f(x)= -xf'(x).(5marks) (%4h) 4

Mathematics
1 answer:
asambeis [7]3 years ago
6 0

Answer:

See picture attached

Step-by-step explanation:

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If $1600 earned simple interest of $56.24 in 2 months, what was the simple interest rate? The simple interest rate is % (Do not
Fiesta28 [93]

Answer:

\$21.1

Step-by-step explanation:

We know that for principal amount P , time period T and rate of interest R\% , simple interest is given by S.I. = \frac{P\times R\times T}{100} .

Here ,

P=\$1600\\T=2\,\,months=\frac{2}{12}\,\,years=\frac{1}{6}\,\,years\\S.I=\$56.24

To find :  simple interest rate i.e., R\%

On putting values of P\,,\,T\,,\,S.I in formula , we get S.I. = \frac{P\times R\times T}{100}

56.24 = \frac{1600\times R\times 1}{600}\\R=\frac{56.24\times 600 }{1600}=\frac{703\times 3}{100}=\$21.09

Now we need to round off the answer to the nearest tenth .

So, simple interest rate is % = \$21.09 = \$21.1

8 0
3 years ago
Find the exact value of the given expression.<br> sin(2cos^-1(5/13))
xeze [42]

Answer:

+120/169 or -120/169

Step-by-step explanation:

  • let cos^{-1}[\frac{5}{13}  ] = \alpha

where, alpha is some angle that satisfies the assumed condition.

  • so, cos\alpha= 5/13

[ taking cos to the other side  or applying cos on both sides]

  • now, substitute this in the given expression
  • sin(2cos^-1(5/13)) = sin(2\alpha )

as sin\beta =  + or -\sqrt{1-(cos\beta) ^{2}

[by general trigonometry formula: cos^{2}[\beta]  +sin^{2}[\beta]=1]

so if  cos\alpha= 5/13, we can get sin\alpha from the above formula as + or - 12/13

(because, after taking square root on both sides we keep + or -]

  • as, sin2\beta  = 2*sin[\beta ]*cos[\beta ]

[by general trigonometry formula]

  • here, now sin[2\alpha ]=2*(+or- 12/13)*5/13\\

so, the final value can be 120/169 or -120/169.

4 0
3 years ago
When you flip 1/6 it is?
prohojiy [21]
Reciprocal
1/6 turns into 6/1 which is 6
5 0
3 years ago
Read 2 more answers
Name one possible cross section of a sphere
pishuonlain [190]
Probably a circle. Its the same thing as cutting a cube and getting a square, and cross sectioning a pentagonal prism and getting a pentagon.
7 0
3 years ago
Read 2 more answers
Select the slope of the equation y-7= -4(x+8)
stiks02 [169]

Answer:

Slope is -4

Step-by-step explanation:

y-7=-4(x+8)

y=-4(x+8)+7

y=-4x-32+7

y=-4x-25

7 0
3 years ago
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