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2 years ago

HELP PLSSS find f(9) if f(x) = 4^x + 12

Mathematics

2 answers:

8_murik_8 [283]2 years ago

6 0

Answer:

If f(x) = 4ˣ + 12, f(9) = 262156.

Step-by-step explanation:

f(x) = 4ˣ + 12

Substitute input x = 9.

f(9) = 4⁹ + 12

Evaluate 4 to the 9th power.

f(9) = 262144 + 12

Add 262144 and 12.

f(9) = 262156.

Anna35 [415]2 years ago

4 0

Answer:

I think its 262156

Step-by-step explanation:

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a

NARA [144]

$x^3y^2+\sin(x\ln y)+e^{xy}=0$

Differentiate both sides, treating $y$ as a function of $x$ . Let's take it one term at a time.

Power, product and chain rules:

$\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}$

$=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}$

$=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}$

$=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)$

$=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}$

$=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)$

$=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}$

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

$3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0$

Isolate the derivative, and solve for it:

$\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}$

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by $y$ to get rid of that fraction in the denominator.

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}$

3 0

3 years ago

I need help I don't know how to do this

Trava [24]

Answer:

Median = 7

upper quartile = 10

lower quartile is 6

Step-by-step explanation:

The median is the middle line in the box

Median = 7

The upper quartile is the right line of the box

upper quartile = 10

The lower quartile is the left line of the box

lower quartile is 6

4 0

3 years ago

3. Suppose your credit card has a balance of $7800 and an annual interest rate of 16%. You decide

Blizzard [7]

Answer:

$274.22 per month
$2071.92 in total interest
$433.48 more per month
$1379.52 less in interest

Step-by-step explanation:

a) The amortization formula is used to find the monthly payment (A):

A = P(r/n)/(1 -(1 +r/n)^(-nt))

for a loan of a principal amount P at annual rate r compounded n times per year for t years.

For a borrowed amount of $7800 at 16% compounded monthly for 3 years, the payment will be ...

A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·3)) ≈ $274.22

You must pay $274.22 each month to pay off the credit card in 3 years.

b) The total amount repaid is 36 times this monthly payment, so is ...

$274.22 × 36 = $9871.92

The amount by which this exceeds the principal borrowed is ...

$9871.92 -7800 = $2071.92

You will pay $2071.92 in interest.

c) Changing the time period to 1 year gives the payment value ...

A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·1)) ≈ $707.70

The additional amount you must pay is ...

$707.70 -274.22 = $433.48

You must pay $433.48 more each month.

d) Your total interest with the higher payments will be ...

$707.70×12 -7800 = $692.40

The difference in interest amounts is ...

$2071.92 -692.40 = $1379.52

You will pay $1379.52 less in total interest.

_____

<em>Caveat</em>

Here, the monthly amounts are rounded and the total repayment amount is based on that rounded value. In an actual payment situation, the final payment will be adjusted by a small amount to account for the fact that the monthly payment shown is not exact. That will affect the total interest and the difference in interest.

8 0

3 years ago

Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. P

Gemiola [76]

Answer:

Pierre is right

Step-by-step explanation:

The correct formula for Exponential growth rate is given as:

y = a( 1 + r) ^t

Where

y = Amount after time t

a = Initial amount

r = Growth rate

t = time

From the question

a = 300

r = 2% = 0.02

Hence, our exponential growth rate =

y = 300( 1 + 0.02)^t

y = 300( 1.02)^t

Therefore, Pierre is right

5 0

2 years ago

HELP ME ASAP WITH 8! PLS!! I beg u..

lakkis [162]

7. x=3 is the midpoint between the roots. The other root is x = 2*3 -(-5) = 11.

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8b) y = (x+4)^2 -1. The vertex is (-4, -1). The roots are -5, -3.

8c) f(x) = 2(x +3)^2 -34. The vertex is (-3, -34). The roots are -3±√17.

7 0

3 years ago