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1 year ago

C Expressions

Mathematics

1 answer:

Alinara [238K]1 year ago

6 0

Answer:

16a+32b-8c

Step-by-step explanation:

Distribute the 8 to all the terms in the parenthesis.

8(2a + 4b − c) = 16a+32b-8c

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A paper clip is dropped from the top of a 144‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = −

hoa [83]

To calculate the velocity, we use the given expression above which is s(t) = −16t^2 + 144. First, we calculate the time it takes to reach the ground. Then, differentiate the expression and substitute time to the differentiated expression.

s(t) = −16t^2 + 144
0 = -16t^2 + 144
t = 3

s'(t) = v = -32t
v = -32(3)
v = -96

Note: negative sign signifies that the object is going down

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2 years ago

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The sum of 9and -16 increased by 4

LenaWriter [7]

Answer:

-3

Step-by-step explanation:

The statement is,

→ Sum of 9 and -16 increased by 4

The equation will be,

→ {9 +(-16)} + 4

→ (9 - 16) + 4

→ -7 + 4

→ [ -3 ]

Hence, the solution is -3.

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2 years ago

Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to

prohojiy [21]

Answer:

$300000= 100000 e^{0.12 t}$

We divide both sides by 100000 and we got:

$3 = e^{0.12 t}$

Now we can apply natural logs on both sides;

$ln(3) = 0.12 t$

And then the value of t would be:

$t = \frac{ln(3)}{0.12}= 9.16 years$

And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

$A =P e^{rt}$

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means $A= 300000$ and we want to find the value for t.

$300000= 100000 e^{0.12 t}$

We divide both sides by 100000 and we got:

$3 = e^{0.12 t}$

Now we can apply natural logs on both sides;

$ln(3) = 0.12 t$

And then the value of t would be:

$t = \frac{ln(3)}{0.12}= 9.16 years$

And rounded to the nearest tenth would be 9.2 years.

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3 years ago

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murzikaleks [220]

Answer:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$\boxed{y=mx+b}$

where:

m is the slope.
b is the y-intercept (where the line crosses the y-axis).

Slope formula

$\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}$

Equation 1

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(-1, 6)$

$\textsf{Let }(x_2,y_2)=(0, 1)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5$

From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=-5x+1$

Equation 2

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(1, 1)$

$\textsf{Let }(x_2,y_2)=(0, -4)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5$

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=5x-4$

Conclusion

Therefore, the system of linear equations shown by the graph is:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Learn more about systems of linear equations here:

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If f(x) = x + 4 and g(x)=x^2-1, what is m(g o f)(x)?

Andreas93 [3]

Until now, given a function f(x), you would plug a number or another variable in for x. You could even get fancy and plug in an entire expression for x. For example, given f(x) = 2x + 3, you could find f(y2 – 1) by plugging y2 – 1 in for x to get f(y2 – 1) = 2(y2 – 1) + 3 = 2y2 – 2 + 3 = 2y2 + 1.

In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points:

Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and

let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.

Find (i) f (1), (ii) g(–1), and (iii) (g o f )(1).

(i) This type of exercise is meant to emphasize that the (x, y) points are really (x, f (x)) points. To find f (1), I need to find the (x, y) point in the set of (x, f (x)) points that has a first coordinate of x = 1. Then f (1) is the y-value of that point. In this case, the point with x = 1 is (1, –1), so:

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3 years ago

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