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2 years ago

Calculate f(4) for each function below

Mathematics

1 answer:

jeka57 [31]2 years ago

5 0

Subtitute x = 4 to the equations:

$b)\ f(x)=\left(\dfrac{1}{5}\right)^x\to f(4)=\left(\dfrac{1}{5}\right)^4=\dfrac{1^4}{5^4}=\dfrac{1}{625}\\\\c)\ f(x)=3x-12\to f(4)=3\cdot4-12=12-12=0\\\\d)\ f(x)=(x-2)^3\to f(4)=(4-2)^3=2^3=8$

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3. start fraction x over 5 end fraction + 6 = 10 (1 point) 44 30 20 –20 4. 3(4 – 2x) = –2x (1 point) –1 1 2 3

max2010maxim [7]

Answer:

3.x=20

Step-by-step explanation:

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3 years ago

Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x

lutik1710 [3]

Rotating the graph of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ with $B\ne0$ counterclockwise by $\theta$ eliminates the $xy$ term, where $\cot2\theta=\frac{A-C}{B}.$ Plugging in, we have $\cot2\theta=\frac{7}{24},$ since $C=0.$ Solving, we have $\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.$

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3 years ago

Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)

aleksandr82 [10.1K]

$\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}$

Notice that if $f(x)=e^{\sin x}$ , then $f(\pi)=e^{\sin\pi}=e^0=1$ . Recall the definition of the derivative of a function $f(x)$ at a point $x=c$ :

$f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$

So the value of this limit is exactly the value of the derivative of $f(x)=e^{\sin x}$ at $x=\pi$ .

You have

$f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1$

4 0

3 years ago

The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that

tekilochka [14]

Answer:

a) P(X∩Y) = 0.2

b) $P_1$ = 0.16

c) P = 0.47

Step-by-step explanation:

Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.

So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67

Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:

P(X∩Y) = P(X) + P(Y) - P(X∪Y)

P(X∩Y) = 0.36 + 0.51 - 0.67

P(X∩Y) = 0.2

On the other hand, the probability $P_1$ that he must stop at the first signal but not at the second one can be calculated as:

$P_1$ = P(X) - P(X∩Y)

$P_1$ = 0.36 - 0.2 = 0.16

At the same way, the probability $P_2$ that he must stop at the second signal but not at the first one can be calculated as:

$P_2$ = P(Y) - P(X∩Y)

$P_2$ = 0.51 - 0.2 = 0.31

So, the probability that he must stop at exactly one signal is:

$P = P_1+P_2\\P=0.16+0.31\\P=0.47$

7 0

2 years ago

What is 9x-5-8+x= what

Elanso [62]

Hi there!

First you simplify.

Simplified = 9x+(−5)+(−8)+x

Then you combine the like terms.

9x+(−5)+(−8)+x (*-5 and -8 are like terms) (9x and x are like terms)

Combined it's~ (9x+x)+(−5+−8)

Solve and that comes to 10x+−13 which is your answer. :)

Hope this helps.

3 0

2 years ago