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3 years ago

Value of x in log5x = 4logx5 is

1 answer:

4 0

Log5 x=4 logx 5
Ln x/ln5=4(ln5 / ln x) logx z=ln x / ln z
least common multiple=ln5 * ln x

ln²x=4ln²5
√(ln² x)=√(4 ln²5)
ln x=2ln 5
x=e^2ln5=25

Answer: x=25.

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Prove that f(x)=x+3/2 and g(x)=2x-3are inverse

goldfiish [28.3K]

Answer:

Proofs

Step-by-step explanation:

$f(x) = x + \frac{3}{2}$

$y = x + \frac{3}{2}$

$x = y + \frac{3}{2}$

$x - \frac{3}{2} = y$

${f}^{ - 1} (x) = x - \frac{3}{2}$

They are not inverse because f^-1(x) = x - 3/2 is not the inverse to g(x) = 2x - 3.

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3 years ago

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius. (Hint: A chord divides a circle into t

almond37 [142]

The answer to the problem "Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius" is A = (160/3 π + 16 √3) inches². Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

3 0

3 years ago

Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1)

e-lub [12.9K]

Answer:

The proof is shown in the explanation below.

Step-by-step explanation:

Analysis:

The proof by induction focuses on n. In this case, let n = 1, and $L^{1}$ will be a linear operator since $L^{1} = L$

The exercise will show that $L^{n}$ is a linear operator on V and that $L^{n+1}$ is also a linear operator on V. This, follows that:

$L^{n+1} (av) = L(L^{m}(v_{1}+v_{2})\\ = L(L^{m} (v_{1} + L^{m}v_{2})\\ = L(L^{m}v_{1} + L(L^{m}v_{2})\\ = L^{m+1}(v_{1}) + L^{m+1}(v_{2})$

6 0

2 years ago

Read 2 more answers

Corey gets paid $6 per hour to work at a snack stand. This weekend , he worked on both Saturday and Sunday. he made total of $48

Dahasolnce [82]

Answer:

5 hours

Step-by-step explanation:

1. Find out how many dollars he earned on Saturday

3 x 6 = 18

He earned 18 dollars on Saturday.

2. Subtract 18 from 48 since that is from Saturday, not Sunday

48 - 18 = 30

3. Divide 30 by 6 to see how many hours he worked on Sunday

30/6 = 5

6 0

3 years ago

A pizza chef begins to spin a constant volume of dough to make a pie by spinning and tossing the dough into the air, such that t

Alexxandr [17]

Answer:

a ) dAt/dt = 50,24 in/min

dh/dt = - 0,125 in/min

Step-by-step explanation:

The area of the top is At :

At = π*r²

a) Tacking derivatives with respect to time:

dAt/dt = 2* π*r * dr/dt

At t = t₁ r = 16 in and dr/dt = 0,5

Then

dAt/dt = 2*3,14*16*0,5 in/min

a ) dAt/dt = 50,24 in/min

b) The volume of the cylinder is:

Vc = π*r²*h ( where h is the heigh of the cylinder )

Tacking derivatives with respect to time

dVc/dt = 2* π*r*h*dr/dt + π*r²*dh/dt

But dVc/dt = 0 since the volume remains constant, then:

π*r²*dh/dt = - 2* π*r*h*dr/dt

r*dh/dt = - 2*h*dr/dt

dh/dt = - 2*0,5*2/16 in/min

dh/dt = - 0,125 in/min

4 0

3 years ago