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3 years ago

Find the average rate of change of the function between the given values of x. y = 9+ 5x + 0.5x2 between x = 2 and x = 4.

Mathematics

1 answer:

svet-max [94.6K]3 years ago

3 0

Answer:

The average rate of change is 8.

Step-by-step explanation:

The formula to calculate the average rate of change of a function F(x) is:

$\frac{F(b)-F(a)}{b-a}$

In this case, F(x) = $0.5x^{2} +5x+9$

a=2 and b=4

You have to evaluate x=2 (which is a in the formula) and x=4 (which is b in the formula) in the function.

In order to obtain F(b) and F(a) you have to replace x=4 and x=2 in the given function:

F(b) = $(0.5)4^{2} + 5(4) +9= 37$

F(a) = $(0.5)2^{2} + 5(2)+9=21$

$\frac{F(b)-F(a)}{b-a} = \frac{37-21}{4-2}=\frac{16}{2} = 8$

The answer is 8.

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Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet,

babunello [35]

Answer:

15 feet

Step-by-step explanation:

It is given that Quadrilateral ABCD is similar to Quadrilateral EFGH. This means that the corresponding sides of these two quadrilateral will be in the same proportion.

i.e.

Ratio of two corresponding sides would be the same. We are given longest three sides of ABCD and shortest two sides of EFGH. Let the 4th sides of ABCD i.e. the shortest side be x.

So, the ratio of the shortest sides of two quadrilaterals would be the same as the ratio of second shortest sides.

So,

$x:6=30:12\\\\\frac{x}{6}=\frac{30}{12}\\\\ x=\frac{30}{12} \times 6\\\\ x = 15$

So, the 4th side on quadrilateral ABCD would be 15 feet. None of the options match with the answer.

8 0

3 years ago

Let S be the universal set, where:

kolezko [41]

A' = {7,8,10}

B' = {1,3,59}

Given,

Let S be the universal set, where:

S = {1,2,3,4,5,6,7,8,9,10}

Let sets A and B be subsets of S, where:

Set A = {1,2,3,4,5,6,9}

Set B = {2,4,6,7,8,10}

We need to find the elements in the set (A') and (B)'

<h3>What is a complement of a set?</h3>

A compliment of a set D is denoted by D' or D bar.

It means the set contains all elements in the universal set U other than the elements in set D.

Example:

U = {1,2,3,4,5,6,7,8,9}

D = {1,2,3,4,5}

D' = {6,7,8,9}

Find A' and B'

S = {1,2,3,4,5,6,7,8,9,10}

A = {1,2,3,4,5,6,9}

B = {2,4,6,7,8,10}

A' = {7,8,10}

B' = {1,3,59}

Thus,

A' = {7,8,10}

B' = {1,3,59}

Learn more about the complement of sets here:

brainly.com/question/20319548

#SPJ1

3 0

2 years ago

A water tank is in the shape of a right circular Austin simulato water tank is in the shape of a right circular Cylinder with a

Burka [1]

⓵ To calculate the volume of a right circular cylinder, the formula is π times the radius of the circular base² time the height of the cylinder.

⓶ Now that we know that the equation to calculate the volume of a right circular cylinder is :

V = π x (r²) x h

You need to find the numbers to replace the volume (V) and the height (h) in the formula.

We already know that the volume is 320 square feet and that the height is 20 feet.

So we are left with a formula looking like this :

320 = π x (r²) x 20

⓷ Now we need to find the radius of the circular base! To do so, you need to solve this equation and isolate the “r”. Start by simplifying the right side :

320 = π x (r²) x 20
÷20 ÷20

↓

16 = π x r²
÷π ÷π

↓

5,09 ⋍ r²
√ √

↓

2,26 feet ⋍ r

⓸ Now that we knoe the value of the radius of the circular base, all there’s left to do is multiply this number by two in order to find the diameter of the water tank :

2,26 x 2 = d

↓

4,51 feet ⋍ d

So your final answer is : the diameter of the water tank is about 4,51 feet.

** Since I devided by “π”, all the answers I wrote from that point are rounded to the nearest hundredths just to make things easier to visualize, but I kept all of the decimals when doing the calculations. So it is possible that your answer might differ slightly from mine if you use the rounded numbers to calculate everything. Just keep that in mind!

I hope this helped, if there’s anything just let me know! ☻

4 0

4 years ago

Help needed ASAP will give BRAINLIEST

grin007 [14]

Answer:

Step-by-step explanation:

Recall that the sum of the (3) interior angles of a triangle <em>must</em> equate to 180.

In other words:

$(55)+(20)+(x)=180$