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2 years ago

Can anyone help? Will give Brainly + 22 pts.

Mathematics

1 answer:

Volgvan2 years ago

4 0

Answer:

4 and 19

Step-by-step explanation:

One number : 4x+3 (this is 3 more than 4 times x)

Another number: x This is tricky because the main number for comparison is "another number", which is x

Sum of the #s is 23: Means add them and = 23, so

x+(4x+3) = 23

5x+3=23

5x=20

x=4 and the other # is 4x+3, so 4(3)+3=19

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Which equation matches the given points? (0, 7.6), (1, 6.2), (2, 4.8), (3, 3.4), (4,2)

Cerrena [4.2K]

The equation that matches the given points is g(x) = -1.4x + 7.6

The standard form of a linear equation is expressed as $g(x)=mx + b$

m is the slope of the line

b is the y-intercept:

Using the coordinate points (3, 3.4), (4,2)

$m=\frac{2-3.4}{4-3}\\m=\frac{-1.4}{1}\\m=-1.4$

Substitute m = -1.4 and the coordinate (4, 2) into the formula:

$2=4(-1.4)+b\\2=-5.6+b\\b=2+5.6\\b=7.6$

Get the required equation:

$g(x)=mx+b\\g(x)=-1.4x+7.6$

Hence the equation that matches the given points is g(x) = -1.4x + 7.6

Learn more on equation of a line here; brainly.com/question/9351428

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2 years ago

Find the function r that satisfies the given condition. r'(t) = (e^t, sin t, sec^2 t): r(0) = (2, 2, 2) r(t) = ()

lesantik [10]

Answer:

r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2)

Step-by-step explanation:

A primitive of e^t is e^t+c, since r(0) has 2 in its first cooridnate, then

e^0+c = 2

1+c = 2

c = 1

Thus, the first coordinate of r(t) is e^t + 1.

A primitive of sin(t) is -cos(t) + c (remember that the derivate of cos(t) is -sin(t)). SInce r(0) in its second coordinate is 2, then

-cos(0)+c = 2

-1+c = 2

c = 3

Therefore, in the second coordinate r(t) is equal to -cos(t)+3.

Now, lets see the last coordinate.

A primitive of sec²(t) is tan(t)+c (you can check this by derivating tan(t) = sin(t)/cos(t) using the divition rule and the property that cos²(t)+sin²(t) = 1 for all t). Since in its third coordinate r(0) is also 2, then we have that

2 = tan(0)+c = sin(0)/cos(0) + c = 0/1 + c = 0

Thus, c = 2

As a consecuence, the third coordinate of r(t) is tan(t) + 2.

As a result, r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2).

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Answer:

Step-by-step explanation:

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