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3 years ago

Please someone help!!!

Mathematics

1 answer:

kari74 [83]3 years ago

6 0

Answer:

0.001189 x 10^7

Step-by-step explanation:

4.1 x 10^7 gallons of water

2,900 gallons of water = 2.9 x 10^3

Balance the 10th power with the first one.

2,900 = 0.00029 x 10^7

Multiply only the decimal number...

4.1 x 0.00029 = 0.001189

The answer is...

0.001189 x 10^7

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What is the derivative of 1/square root 4x.

Bumek [7]

Answer:

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$

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Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

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Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]$

Step 2: Differentiate

Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'$
Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'$
Derivative Rule [Basic Power Rule]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)$
Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

5 0

3 years ago

during the new year celebration there are orange, green purple, and blue fireworks. In how many different orders can the differe

WINSTONCH [101]

There are 256 possible combinations of fireworks, if they can be repeated in each 4 firework combinations.
If they cannot be repeated, there are 24 possible combinations.

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3 years ago

A brace for a shelf has the shape of a right triangle. Its hypotense is 16 incges long and the two legs are equal in length. How

Len [333]

We use trigonometry because we know an angle and a side length.

We are looking for one of the sides that isn't the hypotenuse:
As illustrated by the picture I made below:

We know both unknown angles will be 45 degrees, as there are 180 degrees in a triangle, we know the triangle is a right angle triangle (has 90 degrees) so, (180-90)/2 = 45

Using SOH CAH TOA, short for : SIN- OH COS- AH TAN- OA

We are looking for the one with H, as we know what H is.
I am picking "SIN- OH", but we could use "COS- AH"

The formula for this is: Sin(angle) = O/H
We substitute the angle (45) and the length for H (16)

Sin(45)= O/16 <- rearrange it
Sin(45)*16= O <- Solve in the calculator
13.6145 (4 DP)= O
The legs = O

The legs have a length of "13.6145 (4 DP)" each