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3 years ago

Solve using the quadratic formula. 5x^2+x+3=0

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

6 0

Couldn't figure out how to type this out so here's a picture of the thought process.

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.

lora16 [44]

First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.

The sum $x^2+y^2$ can be written as: $x^2+y^2=(x+y)^2-2xy$ ,

from the binomial expansion formula: $(x+y)^2=x^2+2xy+y^2$ .

Thus, substituting y=-3x+18 and simplifying we have

 $x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)$ $=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x$ $=10x^2-108x+18^2$ .

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.

At x=5.4, the expression $10x^2-108x+18^2$ , which is equivalent to $x^2+y^2$ , takes it smallest value.

Substituting, we would find $10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324$ =32.4 This is the smallest value of the expression.

For x=5.4, y=-3x+18=-3(5.4)+18=1.8.

Answer: (5.4, 1.8)

8 0

3 years ago

15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by graph of this equatio

7nadin3 [17]

Answer:

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees... then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.

7 0

3 years ago

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How many digits of pi does it take to add up to 14, 25, 68, 103, and 150? I am being timed, whoever answers this fast or quick I

Mandarinka [93]

Answer:

to get 14 first 5 digits

to get to 25 first 7 digits

to get to 68 first 14 digits

to get to 103 first 21 digits

to get to 150 first 31 digits

Step-by-step explanation:

3 0

3 years ago

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Write an equation of the line with the given slope, m, and y-intercept (0,b). m = 8, b = 9

Advocard [28]

Answer:

Equation: Y=8x+9, y-intercept: (0,9)

Step-by-step explanation:

An equation is set up in the format of y = mx+b, so simply plug the appropriate numbers in for those variables.

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3 years ago

Write a mixed number that is equivalent to 16 3

Darina [25.2K]

Answer:

5 1/3

Step-by-step explanation:

16/3 = 32/6

32/6 = 5 2/6 = 5 1/3

8 0

3 years ago

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