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3 years ago

The question is 7a +10 = 2a

2 answers:

8 0

7a + 10 = 2a subtract 2a from both sides
-2a -2a
5a + 10 = 0 subtract 10 from both sides
-10 -10
5a = -10 then divide both sides by 5
/5 /5
a = - 2

Sergeeva-Olga [200]3 years ago

4 0

7a+10=2a
Subtract 7a from both sides.
10=-5a
Divide 10 by -5.
-2=a or a=-2

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Experimental data are collected as:

aliina [53]

Answer:

$y = 1.00114x + 1.75243$

Step-by-step explanation:

Given

The x and y values

Required

The regression line equation

Because of the length of the given data, I will run the analysis using online tools, then analyze the result.

From the analysis, we have:

$\sum x = 5050$

$\sum y = 5231.1011$

$\bar x = 50.5$

$\bar y = 52.311$

$SSX = 83325$ --- Sum of squares

$SP = 83419.7626$ --- Sum of products

The regression equation is calculated as:

$y = ax + b$

Where:

$a = \frac{SP}{SSX}$

So, we have:

$a = \frac{83419.76}{83325}$

$a = 1.00114$

$b = \bar y - a * \bar x$

$b = 52.31 - (1.00114*50.5)$

$b = 1.75243$

So:

$y = ax + b$ becomes

$y = 1.00114x + 1.75243$

6 0

3 years ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

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3 years ago

Kim has read 42 pages of a book. That is 20% of the total number of pages. How many pages long is Kim's book?

ki77a [65]

Hi there! The answer is 210 pages.

We can find our answer by looking at the proportions:
20 % is 42 pages.
10 % is 21 pages (42 / 2).
100% is 210 pages. (21 × 10).

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Answer:

Step-by-step explanation:

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