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Schach [20]
3 years ago
12

Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the l

ake, the rock's distance from the lake's surface changes at a rate of -5 inches per second. If lisa holds her hand 5 feet above the lake's surface, how far from Lisa's hand is the rock 4 seconds after it hits the surface? Please show how you arrive at your answer
Mathematics
1 answer:
yawa3891 [41]3 years ago
5 0
Well, it goes 5 inches per second so after 4 seconds it is 4 times 5 =20 inches under the surface,  add that to 5 feet and you get 6 ft and 8 inches
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How do you determine where f(x)=cos^(-1)(lnx) is continuous?
olga nikolaevna [1]
\ln x is continuous over its domain, all real x>0.

Meanwhile, \cos^{-1}y is defined for real -1\le y\le1.

If y=\ln x, then we have -1\le \ln x\le1\implies \dfrac1e\le x\le e as the domain of \cos^{-1}(\ln x).

We know that if f and g are continuous functions, then so is the composite function f\circ g.

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7 0
3 years ago
A credit union client deposits $3,300 in an account earning 6.5% interest, compounded annually. What will the balance of the acc
astra-53 [7]

Answer:

The balance of account at the end of 36 years is $31,849.29

Step-by-step explanation:

We are given the following in the question:

P = $3,300

r = 6.5% = 0.065

t = 36 years

The compound interest is given by:

A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}

where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.

Since interest is compounded annualy we use n = 1

A = 3300\bigg(1+\dfrac{0.065}{1}\bigg)^{36}\\\\A = \$31,849.29

Thus, balance of account at the end of 36 years is $31,849.29

6 0
3 years ago
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makkiz [27]

Answer:

Step-by-step explanation:

x + 2y + 3z = 12

z=\frac{12-x-2y}{3}

Volume = V=f(x,y) = xy(\frac{12-x-2y}{3} )

find partial derivatives using product rule

f_x =\frac{y}{3} (12-2x-2y)\\f_y = \frac{x}{3} (12-x-4y)

i.e.

Using maximum for partial derivatives, we equate first partial derivative to 0.

y=0 or x+y =6

x=0 or x+4y =12

Simplify to get y =2, x = 4

thus critical points are (4,2) (6,0) (0,3)

Of these D the II derivative test gives

D<0 only for (4,2)

Hence maximum volume is when x=4, y=2, z= 4/3

Max volume is = 4(2)(4/3) = 32/3

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3 years ago
PLEASE HELP n+5(-n+1)=7
yKpoI14uk [10]

Answer: n= -1/2

Step-by-step explanation:

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