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3 years ago

Simplify. log412 + log47

Mathematics

1 answer:

VikaD [51]3 years ago

6 0

Answer:4.28699507397

Step-by-step explanation:

log412

+ log470

It equals=log4.28699507397

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Dmitriy789 [7]

On the line segment $x=2$ , $f$ depends only on $y$ :

$f(2,y) = g(y) = 4y^2 - 4y - 4$

Find the critical points of $g$ .

$\dfrac{dg}{dy} = 8y - 4 = 0 \implies y = \dfrac12$

At this critical point, we have

$g\left(\dfrac12\right) = f\left(2,\dfrac12\right) = 3$

Check the value of $f$ at the endpoints of the line segment.

$f\left(2,0\right) = 4$

$f\left(2,2\right) = 12$

So we have

$\min\left\{f(x,y) \mid x=2 \text{ and } 0 \le y \le 2\right\} = \boxed{3} \text{ at } (x,y) = \left(2,\dfrac12\right)$

7 0

1 year ago

Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every

aksik [14]

Given:

Principal value = $65,550

Rate of interest = 3% compounded every six month

To find:

The taken to have $100,000 in Jack's account.

Solution:

The formula for amount is

$A=P(1+\dfrac{r}{n})^{nt}$

where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.

Interest compounded every six month. It means, interest compounded 2 times in an year.

Substitute A=100000, r=0.03 and n=2 in the above formula.

$100000=65550(1+\dfrac{0.03}{2})^{2t}$

$\dfrac{100000}{65550}=(1+0.015)^{2t}$

$1.525553=(1.015)^{2t}$

Taking log on both sides.

$\log (1.525553)=\log (1.015)^{2t}$

$\log (1.525553)=2t\log (1.015)$

$\dfrac{\log (1.525553)}{2\log (1.015)}=t$

$t=14.1838928$

$t\approx 14.18$

Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.

3 0

3 years ago

Solve the following <br> 19.2<br> x 1.5

k0ka [10]

Answer:

no value of X so no answer

Step-by-step explanation:

6 0

4 years ago

What's the answer to this 94<-2(1+6b)

tigry1 [53]

Answer:

-8 > b

Step-by-step explanation:

94<-2(1+6b)

Distribute

94<-2-12b

Add 2 to each side

94+2<-2-12b +2

96 < -12b

Divide each side by -12, remembering to flip the inequality since we divide by a negative

96/-12 > -12b/-12

-8 > b

5 0

3 years ago

For conducting a two-tailed hypothesis test with a certain data set, using the smaller of n1minus−1 and n2minus−1 for the degr

Schach [20]

Answer:

D. Using the critical values of t=±2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of ±2.093.

Step-by-step explanation:

solution is solved below,

8 0

3 years ago