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3 years ago

F(x)=x^+4x+2 what is the average rate of change from x=3 to x=5

Mathematics

1 answer:

mars1129 [50]3 years ago

8 0

Answer:

Step-by-step explanation:

f(x)=x^+4x+2 First, let's evaluate when x=3, x=4 and x=5.

f(3) = 3²+4(3)+2 = 9 + 12 + 2 = 23

f(4) = 4²+4(4)+2 = 16 + 16 + 2 = 34

f(5) = 5²+4(5)+2 = 25 + 20 + 2 = 47

Now, let's find the rate of change.

34 - 23 = 11

47 - 34 = 13

Finally, the average rate of change.

(11 + 13) / 2 = 12

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the area of the curved surface of a solid cylinder is equal to 2/3 of the total area of the same cylinder . If the total surface

zheka24 [161]

Answer:

Sa = 36 circumference per meter square

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7 0

2 years ago

Help with 21 would be much appreciated.

umka2103 [35]

Answer:

$\large\boxed{x=2\sqrt{21}\ and\ y=4\sqrt3}$

Step-by-step explanation:

Look at the picture.

ΔADC and ΔCDB are similar. Therefore the sides are in proportion:

$\dfrac{AD}{CD}=\dfrac{CD}{DB}$

We have

$AD=14-8=6\\CD=y\\DB=8$

Substitute:

$\dfrac{6}{y}=\dfrac{y}{8}$ cross multiply

$y^2=(6)(8)$

$y^2=48\to y=\sqrt{48}\\\\y=\sqrt{16\cdot3}\\\\y=\sqrt{16}\ cdot\sqrt3\\\\\boxed{y=4\sqrt3}$

For x use the Pythagorean theorem:

$x^2=6^2+(4\sqrt3)^2\\\\x^2=36+48\\\\x^2=84\to x=\sqrt{84}\\\\x=\sqrt{4\cdot21}\\\\x=\sqrt4\cdot\sqrt{21}\\\\\boxed{x=2\sqrt{21}}$

3 0

3 years ago

What is the vertex of g(x) = –3x2 + 18x + 2?

blsea [12.9K]

Answer:

$(3,29)$

Step-by-step explanation:

There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is $x=\frac{-b}{2a}$

We have the function $g(x)=-3x^2+18x+2$

From this function, we can find that

$a=-3\\b=18\\c=2$

We can plug in our know values into the formula to get

$x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3$

Then we can plug in our x-value to find the y-value of the vertex

$g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29$

This means that the vertex would be $(3,29)$

6 0

3 years ago

Rafeeq bought a field in the form of a quadrilateral (ABCD)whose sides taken in order are respectively equal to 192m, 576m,228m,

Valentin [98]

Answer:

a. 85974 m²

b. 17,194,800 AED

c. 18,450 AED

Step-by-step explanation:

The sides of the quadrilateral are given as follows;

AB = 192 m

BC = 576 m

CD = 228 m

DA = 480 m

Length of a diagonal AC = 672 m

a. We note that the area of the quadrilateral consists of the area of the two triangles (ΔABC and ΔACD) formed on opposite sides of the diagonal

The semi-perimeter, s₁, of ΔABC is found as follows;

s₁ = (AB + BC + AC)/2 = (192 + 576 + 672)/2 = 1440/2 = 720

The area, A₁, of ΔABC is given as follows;

$Area\, of \, \Delta ABC = \sqrt{s_1\cdot (s_1 - AB)\cdot (s_1-BC)\cdot (s_1 - AC)}$

$Area\, of \, \Delta ABC = \sqrt{720 \times (720 - 192)\times (720-576)\times (720 - 672)}$

$Area\, of \, \Delta ABC = \sqrt{720 \times 528 \times 144 \times 48}$ = 6912·√(55) m²

Similarly, area, A₂, of ΔACD is given as follows;

$Area\, of \, \Delta ACD= \sqrt{s_2\cdot (s_2 - AC)\cdot (s_2-CD)\cdot (s_2 - DA)}$

The semi-perimeter, s₂, of ΔABC is found as follows;

s₂ = (AC + CD + D)/2 = (672 + 228 + 480)/2 = 690 m

We therefore have;

$Area\, of \, \Delta ACD = \sqrt{690 \times (690 - 672)\times (690 -228)\times (690 - 480)}$

$Area\, of \, \Delta ACD = \sqrt{690 \times 18\times 462\times 210} = \sqrt{1204988400} = 1260\cdot \sqrt{759} \ m^2$

Therefore, the area of the quadrilateral ABCD = A₁ + A₂ = 6912×√(55) + 1260·√(759) = 85973.71 m² ≈ 85974 m² to the nearest meter square

b. Whereby the cost of 1 meter square land = 200 AED, we have;

Total cost of the land = 200 × 85974 = 17,194,800 AED

c. Whereby the cost of fencing 1 m = 12.50 AED, we have;

Total perimeter of the land = 576 + 192 + 480 + 228 = 1,476 m

The total cost of the fencing the land = 12.5 × 1476 = 18,450 AED

4 0

3 years ago

Find the median of the data set: 3, 7, 3, 2, 7, 9. A: 7 B: 5 C: 5.3 D: 3

harina [27]

To find the median, you order the numbers from least to greatest, then find the middle number.

3,7,3,2,7,9

2,3,3,7,7,9

There are two middle numbers, so we have to find the middle of the two.

3,4,5,6,7

5 is the median, so the answer is B.

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hope it helps

5 0

3 years ago

Read 2 more answers