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3 years ago

If (42)^p = 41^4, what is the value of p?

Mathematics

1 answer:

babymother [125]3 years ago

4 0

First you need to make both bases the same:

Lets remove the ^p and ^4

To make the base of 42 equal to 41, you would have 41^x = 41

X - ln(42) / ln(41) = 1.00648904

Now you have 41^1.00648904(p) = 41^4

Now the bases are equal so we need to set the exponents to equal:

1.00648904(p) = 4

Divide both sides by 1.00648904 to solve for P

P = 4 / 1.00648904

P = 3.97421114

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A recursive rule for a geometric sequence is a1=2; an= 4/9 an-1

Oxana [17]

A recursive rule for a geometric sequence:

$a_1\\\\a_n=r\cdot a_{n-1}$

---------------------------------------------------

$a_1=2;\ a_n=\dfrac{4}{9}a_{n-1}\to r=\dfrac{4}{9}$

---------------------------------------------------

The exciplit rule:

$a_n=a_1r^{n-1}$

Substitute:

$a_n=2\left(\dfrac{4}{9}\right)^{n-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\left(\dfrac{4}{9}\right)^{-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\dfrac{9}{4}\\\\\boxed{a_n=\dfrac{9}{2}\cdot\left(\dfrac{4}{9}\right)^n}$

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3 years ago

5y + 3 = 8y − 5 + 2y

DIA [1.3K]

Answer:

$\fbox{y = 8/5 }$

Explanation:

[to solve for y, first use the properties of equality to simplify the equation]

5y + 3 = 8y − 5 + 2y

5y + 3 = (8y + 2y) – 5

[regroup the like terms of y together: commutative property of equality ; adding in a different order will still give you the same result]

5y + 3 = 10y – 5

[combine like terms]

5y + 3 = 10y – 5

$\: \: \: \: \: \: -3 \: \: \: \: \: \: \: \: \: \: \: -3$

[subtract 3 from both sides in order to eliminate the constant term on the left side: subtraction property of equality]

5y = 10y – 8

–10y –10y

[subtract 10 from both sides in order to eliminate the variable term: subtraction property of equality]

-5y = -8

÷(-5) ÷(-5)

[divide both sides by -5 to cancel out the coefficient of y: division property of equality]

y = 8/5

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2 years ago

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Geometry question need help finding the answer.

Xelga [282]

Answer: 1208.96

Step-by-step explanation:

The volume of the cylinder is $(\pi)(4^2)(4)=64\pi$

The volume of the prism is $(6)(12)(14)=1008$

So, the total volume is $1008+64\pi=\boxed{1208.96}$

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1 year ago

In the figure shown to the right, two angle measurements are given. Determine the others.

creativ13 [48]

The figure is shown below

From the figure

Angle 150 degree and angle p forms angles on a straight

Since the sum of angles on a straight line equals 180 degrees

Hence

$150^{\circ}+p=180^{\circ}$

Solve for p in the equation

$\begin{gathered} p=180^{\circ}-150^{\circ} \\ p=30^{\circ} \end{gathered}$

Hence, p = 30

From the figure

Angle p and angle q are vertically opposite angles

Since vertically opposite angles are equal then

$p=q=30^{\circ}$

Hence, q = 30

Applying the rule of angles on a straight line

This implies

$q+w+60=180$

Substitute q = 30 into the equation

$30+w+60=180$

Solve for w

$\begin{gathered} w+90=180 \\ w=180-90 \\ w=90 \end{gathered}$

Hence, w = 90

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1 year ago

HELP PLS IM TIMED What is the result of 96 divided by 6? Use the model to find the answer.

jeka94

Answer:

Step-by-step explanation:

9 divided by 6 is 1 but leaves 3 leaving 36 divide that by 6 so 16

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2 years ago

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