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JulijaS [17]
2 years ago
12

Negative numbers have positive square roots. O A. True B. False

Mathematics
2 answers:
melamori03 [73]2 years ago
8 0

Answer:

false

Step-by-step explanation:

negative numbers can't have square roots

musickatia [10]2 years ago
7 0

Answer:

false

Step-by-step explanation:

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Need help with AP CAL
anzhelika [568]

Answer: Choice C

\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve y = e^{-x}

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is e^{-x} where 0 < x < 1

Let's compute the area of each general cross section.

\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

\displaystyle \int_{0}^{1}e^{-2x}dx\\\\

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

  • If x = 0, then u = -2x = -2(0) = 0
  • If x = 1, then u = -2x = -2(1) = -2

This means,

\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\

I used the rule that \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

In short,

\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

This points us to choice C as the final answer.

5 0
1 year ago
Consider the line y=-4/7x+4.
Wittaler [7]

Answer:

1). y = -4/7x         2). y = 7/4x - 65/4

Step-by-step explanation:

1). When a line is parallel, the slope remains the same.

y = -4/7x + b

-4 = -4/7(7) + b

-4 = -4 + b

0 = b

The equation is simply y = -4/7x.

2). When a line is perpendicular, the slope becomes the exact opposite.

y = 7/4x + b

-4 = 7/4(7) + b

-4 = 49/4 + b

-65/4 = b

The equation is y = 7/4x - 65/4.

7 0
2 years ago
Please help i need the answer asap ill give brainliest
timofeeve [1]
80.1 years, im not 100% sure of my answer though
6 0
2 years ago
6x(0,5x+3)+3x(1-x)-(1-10x)=7
Eddi Din [679]

Answer:

answer<em> </em><em>is</em><em> </em>

Step-by-step explanation:

ok ok ok ok ok ok ok ok ok ok ok ok

7 0
3 years ago
Lawrence wants to drive from Durban to Johannesburg 550km. If he travels at an average speed of 100km/hr, how long does he tale
Dafna1 [17]

Answer:

5.5hr

Step-by-step explanation:

Distance=550Km

Speed=100Km/hr

Speed=(Distance/Time)

Time=(Distance/Speed)

Time=550/100=5.5hr

8 0
3 years ago
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