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3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if

Mathematics

1 answer:

abruzzese [7]3 years ago

8 0

Answer:

4 it would go back in order

Step-by-step explanation:

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A school quiz cmon guys

faltersainse [42]

I believe its 16...
48 divided by 3!
hope this helps!

8 0

3 years ago

Brian’s grandmother offered to give him a gift of 50% of the amount of money he saved in one year. His grandmother gave him $60.

Mice21 [21]

Answer:

$120

Step-by-step explanation:

7 0

3 years ago

Kim and Daniel are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of

ivanzaharov [21]

There are two equation:

1) From Kim

2) From Daniel

Let:

x be the cost of rolls of plain wrapping paper

y be the cost of rolls of shiny wrapping paper

Kim:

7x + 8y = 140

Daniel:

14x + 7y = 154

<u>Using elimination method:</u>

(7x + 8y = 140) * -2 (Multiplying the equation by -2)

-14x - 16y = -280

-14x -16y = -280

14x + 7y = 154

------------------------------

0x - 9y = -126

9y = 126 (Negative sign cancels from both sides)

y = 126 /9

y = 14

The cost of each shiny wrapping paper is $14.

Now solve x, you pick any two equation to solve for x.

7x + 8y = 140

7x + 8(14) = 140 (You know from above y =14)

7x + 112 = 140

7x = 28

x = 28/7

x = 4

The cost of each plain wrapping paper is $4.

Solution: (4,14)

4 0

4 years ago

find the coordinates of the point P on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by

coldgirl [10]

Let point P be with coordinates $(x_0,y_0).$ Find the equation of the tangent line.

1. If $y=1-x^2,$ then $y'=-2x.$

2. The equation of the tangent line at point P is

$y-y_0=-2x_0(x-x_0).$

Find x-intercept and y-intercept of this line:

when x=0, then $y=y_0+2x_0^2;$
when y=0, then $x=\dfrac{y_0}{2x_0}+x_0=\dfrac{y_0+2x_0^2}{2x_0}.$

The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

$A=\dfrac{1}{2}\cdot (2x_0^2+y_0)\cdot \left(\dfrac{y_0+2x_0^2}{2x_0}\right)=\dfrac{(y_0+2x_0^2)^2}{4x_0}.$

Since point P is on the parabola, then $y_0=1-x_0^2$ and

$A=\dfrac{(1-x_0^2+2x_0^2)^2}{4x_0}=\dfrac{(1+x_0^2)^2}{4x_0}.$

Find the derivative A':

$A'=\dfrac{2(1+x_0^2)\cdot 2x_0\cdot 4x_0-4(1+x_0^2)^2}{16x_0^2}=\dfrac{12x_0^4+8x_0^2-4}{16x_0^2}.$

Equate this derivative to 0, then

$12x_0^4+8x_0^2-4=0,\\ \\3x_0^4+2x_0^2-1=0,\\ \\D=2^2-4\cdot 3\cdot (-1)=16,\ \sqrt{D}=4,\\ \\x_0^2_{1,2}=\dfrac{-2\pm4}{6}=-1,\dfrac{1}{3},\\ \\x_0^2=\dfrac{1}{3}\Rightarrow x_0_{1,2}=\pm\dfrac{1}{\sqrt{3}}.$

And

$y_0=1-\left(\pm\dfrac{1}{\sqrt{3}}\right)^2=\dfrac{2}{3}.$

Answer: two points: $P_1\left(-\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right), P_2\left(\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right).$

6 0

3 years ago

If the fourth of 5 consecutive numebrs is 15, what is their sum?

Tju [1.3M]

BRAINLIEST PLEASEEEEEEEEEEEEE

Answer:

Step-by-step explanation:

You know the fourth number in this pattern is 15, and that they are all consecutive. With this information you know that the fifth number will be 16, and by counting backwards from 15 you can figure out all of the numbers are 12, 13, 14, 15, and 16. Now, to find the sum of these numbers you must add them together.

This is what it could look like: 12+13+14+15+16

Now to find the answer you need to calculate what the addition would equal, which is 70.

8 0

3 years ago