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USPshnik [31]
3 years ago
11

How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between

x=1 and x=b is equal to 240?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
6 0
The Fundamental Theorem of Calculus regarding geometry states that 
\int\limits^b_a g{(x)} \, dx = F(b)-F(a)

Where F is the indefinite integral of g(x)

The first step is to integrate g(x)
\int\ {4x} \, dx = \frac{4x^{1+1} }{1+1} = \frac{4x^{2} }{2} =2 x^{2}

Then substitute the value of b and a=1 into 2x^{2}

[2 (b)^{2}]-[2 (1)^{2}] = 240
2b^{2} -2=240
2b^{2}=240+2
2b^{2}=242
b^{2}= \frac{242}{2}
b^{2}=121
b=11

Hence the limit of the area under g(x) is between a=1 and b=11

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Type the correct answer in the box. Use numerals instead of words.
KIM [24]

Answer:

y = -.05x + 6

Step-by-step explanation:

Plug in your x and y coordinates

1 = -.05(10) + b

1 = -5 + b

6 = b

3 0
3 years ago
Tito drives his car and covered a distance of 225 kilometers in 7.5 hours. What is the average in kilometers per hour?
Eva8 [605]

Step-by-step explanation:

I hope u are asking for average speed

average speed = total distance/total time

= 225/7.5

= 30 km/h or 30 km per hour

6 0
2 years ago
Read 2 more answers
2. How many real number solutions are there to the equation 0 =-3x2 + x - 4?
goblinko [34]

For this case we have the following quadratic equation:

-3x ^ 2 + x-4 = 0

Where:

a = -3\\b = 1\\c = -4

By definition, the discriminant of a quadratic equation is given by:

d = b ^ 2-4 (a) (c)

We have to:

d> 0: Two different real roots

dTwo different complex roots

d = 0: Two equal real roots

Substituting the values we have:

d = 1 ^ 2-4 (-3) (- 4)\\d = 1-48\\d = -47

So, we have two different complex roots

Answer:

Two different complex roots

7 0
3 years ago
Someone help please i am so bad at point slope stuff
Fynjy0 [20]
<span>1) Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). y = 1/2x

2)Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). 
m = (-9 - 1) / (6 - 7) = -10/-1 = 10
y + 9 = 10 (x - 6)
y = 10x - 69

3) A line passes through the point (-6, 6) and (-6, 2). In two or more complete sentences, explain why it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line. 

4)Write the point-slope form of the equation of the line that passes through the points (-3, 5) and (-1, 4).
m = (5 - 4) / (-3 - -1) = 1/-2
y - 5 = (-1/2) (x +3)
y = (-1/2)x + 7/2

5) Write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1).
m = (6-1)/(6 - -6) = 5 / 12
y - 6 = (5/12) (x-6)
y = (5/12)x + 17 / 2

6) Write the point-slope form of the equation of the line that passes through the points (-8, 2) and (1, -4).
m = (2 - -4)  / (-8 -1) = 6 / -7
y - 2 = (-6/7) (x + 8)
y = (-6/7)x - 50 / 7


7) Write the point-slope form of the equation of the line that passes through the points (5, -9) and (-6, 1).
m = (-9 - 1) / (5 - -6) = -10 / 11
y + 9 = (-10 / 11) (x - 5)
y = (-10 / 11)x -49/11

</span>
3 0
4 years ago
a cone with a radius of 3” has a total area of 24pie square inches. Find the volume of the cone. 12pie, 24 pie or 15 pie
Ratling [72]

Answer:

12\pi (inches)^{2}

Step-by-step explanation:

Given:

radius of cone = 3 inch

Total area of cone = 24\pi (inch)^{2}

Find the volume of the cone?

We know the area of cone = \pi r(r+s) -------(1)

Where r = radius

Ans s = side of the cone

Put the area value in equation 1

24\pi=\pi r(r+s) -------(1)

\frac{24\pi }{\pi r} =r+s

\frac{24}{ r}-r =s

Put r value in above equation.

s =\frac{24}{ 3}-3

s=8-3

s=5

The side s = 5 inches

We know the side of the cone formula

s^{2}=r^{2}+ h^{2}

h^{2}=s^{2}- r^{2}

Put r and s value in above equation.

h^{2}=5^{2}- 3^{2}

r^{2} = 25-9

r^{2} = 16

r = 4

The volume of cone is

V = \frac{1}{3} \pi r^{2} h

Put r and h value in above equation.

V = \frac{1}{3} \pi (3)^{2}\times 4

V = 12\pi (inches)^{2}

The Volume of the cone is 12\pi (inches)^{2}

7 0
3 years ago
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