Mari used a thermometer to record temperatures of -3.4 Celsius and 1.6 Celsius . Which temperature in degrees is lower

A rectangular solid with a square base has a volume of 4096 cubic inches - determine the dimensions that yield the minimum surfa

Bumek [7]

Answer:

side of base, a = 10.1 inches, height, h = 40.1 inches

Step-by-step explanation:

Volume of rectangular solid, V = 4096 cubic inches

Let the side of base is a and the height is h.

$V = a^2h\\\\4096 = a^2 h ..... (1)$

surface area of the solid

$S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches$

So, h = 40.2 inches

5 0

3 years ago

What is the slope of the line created by this equation?<br> y-6 = -3(x--8)<br> Help!

aliya0001 [1]

Rewrite the equation in slope intercept form:

Y -6 = -3(x - -8)

Use the distributive property on the right side first:

Y -6 = -3x -24

Add 6 to both sides

Y = -3x -18

The slope is the number in front of the x variable.

Slope = -3

4 0

2 years ago

Use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge t

Oksi-84 [34.3K]

Answer:

- The sum of the series is given as

7/(1 + 7z)

- The series converges for (-1/7, 1/7)

Step-by-step explanation:

Given the geometric series:

7 - 14z + 28z² - 56z³ + ...

The common ratio r is given as

-14z/7 or 28z²/(-14z) or -56z³/(28z²) and so on

r = -7z

The sum of the series is given as

S = a/(1 - r)

Where a is the first term in the series.

S = 7/(1 -(-7z))

= 7/(1 + 7z)

The series converges for |-7z| < 1

That is for -1/7 < z < 1/7

7 0

3 years ago

Read 2 more answers

Giving brainlist for correct answer. :))

AfilCa [17]

Answer:

Here is the steps. 67.5 cm^3

Step-by-step explanation:

4.5 * 6 = 27

27 * 2.5 = 67.5

4 0

2 years ago

Read 2 more answers

21 points!!

Bogdan [553]

Answer:

See attached pictures.

Step-by-step explanation:

The sine and cosine functions have the forms: $f(x) = C+ A sinBx$ and $f(x) = C + A cosBx$ . A is the amplitude for each function. The period is found by dividing 2π the absolute value of B or $\frac{2\pi}{|B|}$ . C shifts the function up and down.

The sine function always starts and ends on the x-axis.

The cosine function always starts and ends at the y=A.

6.) The sine function starts at (0,0) then peaks at 5. Comes down to 0 and down to -5 before returning to 0.

The amplitude is 5.

The period is $\frac{2\pi}{|2|}=\pi$

7.) Here A=3 so the amplitude is 3, B is 1/2 so the period is 4π. Start at (3,0) and descend down to (2π, 0). Go back up to (4π, 3).

8.) Here A = 2 so the amplitude is A. B is 2π so the period is 1. C is 1 so the graph is shifted up a unit.

Start the graph at (0,1) and go up to (0.25,3) and down to (0.5,1) and continue downward to (0.75, -3) then back up to (1,1).

3 0

3 years ago