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4 years ago

Tom began a savings account with $120

1 answer:

6 0

The answer is D because he initially put in $120 and x is the number of months. It can’t be a or b because x already represent months. It can’t be c because $120 was the initial deposit. So the answer is D.

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The angle of depression is 11° from the bottom of a boat to a deep sea diver at a depth of 120 feet. Find the distance x the div

balu736 [363]

Answer: 629 ft

Step-by-step explanation:

$\sin 11^{\circ}=\frac{120}{x} \\ \\ x(\sin 11^{\circ})=120 \\ \\ x=\frac{120}{\sin 11^{\circ}}\approx \boxed{629}$

5 0

2 years ago

Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x)

Allisa [31]

Part A:

Given the function $f(x)=x+2\cos(x)$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow1-2\sin{x}=0 \\ \\ \Rightarrow2\sin{x}=1 \\ \\ \Rightarrow\sin{x}= \frac{1}{2} \\ \\ \Rightarrow x=\sin^{-1}{\frac{1}{2}}= \frac{\pi}{6}$

Using the second derivative test,

$f''(x)=-2cosx \\ \\ \Rightarrow f''\left( \frac{\pi}{6} \right)=-2\cos{\left( \frac{\pi}{6} \right)}=-1.732$

Since the second derivative gives a negative number, the given function has a maximum point at $x=\frac{\pi}{6}$ .

And the maximum point is given by:

$f\left( \frac{\pi}{6} \right)=\frac{\pi}{6}+2\cos\left( \frac{\pi}{6} \right) \\ \\ =0.5236+2(0.8660)=0.5236+1.732 \\ \\ =\bold{2.256}$

i.e. $\left(\frac{\pi}{6},\ 2.256\right)$

Part B:

Given the function $f(x)=e^{-x}-e^{-2x}$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow-e^{-x}+2e^{-2x}=0 \\ \\ \Rightarrow2e^{-2x}=e^{-x} \\ \\ \Rightarrow2e^{-x}=1 \\ \\ \Rightarrow e^{-x}=\frac{1}{2} \\ \\ \Rightarrow-x=\ln \frac{1}{2}=-0.6931 \\ \\ \Rightarrow x=0.6931$

Using the second derivative test,

$f''(x)=e^{-x}-4e^{-2x} \\ \\ \Rightarrow f''(0.6931)=e^{-0.6931}-4e^{-2(0.6931)} \\ \\ =0.5-4e^{-1.386}=0.5-4(0.25)=0.5-1 \\ \\ =-0.5$

Since the second derivative gives a negative number, the given function has a maximum point at $x=0.6931$ .

And the maximum point is given by:

$f(0.6931)=e^{-0.6931}-e^{-2(0.6931)} \\ \\ =0.5-e^{-1.386}=0.5-0.25=\bold{0.25}$

i.e. (0.693, 0.25)

3 0

3 years ago

Use the quadratic formula to solve<br> 2x^2 = 5x + 6

Vikentia [17]

16 answer .............

8 0

3 years ago

Read 2 more answers

Question 9

NeX [460]

It should be 40 ~
6*10=60
5*4=20
60-20=40

5 0

3 years ago

Read 2 more answers

In which funtion is x=2 mapped to 32?

prisoha [69]

The function g(x)=4(x+3)² - 68 is mapped to 32.

<h3>What is equation?</h3>

An equation is a mathematical expression in terms of one or more unknown variable.

Given are the following functions:

f(x)= - 3x² - 4

g(x)= 4(x+3)²-68

f(x)= 3x

f(x)= 2x-62

To get the mapped function, we substitute the value of x in all function,

a) f(x)=-3x²- 4

Put x=2,

f(2)= -3 (2)² - 4

f(2)= -16

It is not mapped.

b) g(x)=4(x+3)² - 68

Put x=2,

g(2) = 4(2+3)² - 68

g(x) =32

It is mapped to 32.

c) f(x)=3x

Put x=2,

f(2) = 3 x 2 =6

It is not mapped.

d) f(x)=2x - 62

Put x=2,

f(2) =2x2 -62

f(2) = -58

It is not mapped.

Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.

Learn more about equations.

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5 0

2 years ago