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Georgia [21]
3 years ago
6

Verify the property: a x ( b + c ) = a x b + a x c by taking a = −5 /2,b= 11/8​

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Answer:

True

Step-by-step explanation:

a x ( b + c ) = a x b + a x c  Substitute

-5 x ( 11/8 + c ) = -5 x 11/8 + -5 x c

-5 ( c + 11/8) = - 5c - 55/8

- 5c - 55/8 = - 5c - 55/8

True

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A sine function increasing through the origin can be used to model light waves. Violet light has a wavelength of 400 nanometers.
andrew11 [14]

Answer:

(2) (100, 300)

Step-by-step explanation:

One wave can be divided on 4 parts, as show on the picture.

Since a length of one whole wave equals 400, a length of each part is 400:4=100 nanometers.

The height of the wave is decreasing on the second and on the third part, hence over the interval (100, 300).

3 0
3 years ago
Find the tangent line approximation for 10+x−−−−−√ near x=0. Do not approximate any of the values in your formula when entering
Svetllana [295]

Answer:

L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x

Step-by-step explanation:

We are asked to find the tangent line approximation for f(x)=\sqrt{10+x} near x=0.

We will use linear approximation formula for a tangent line L(x) of a function f(x) at x=a to solve our given problem.

L(x)=f(a)+f'(a)(x-a)

Let us find value of function at x=0 as:

f(0)=\sqrt{10+x}=\sqrt{10+0}=\sqrt{10}

Now, we will find derivative of given function as:

f(x)=\sqrt{10+x}=(10+x)^{\frac{1}{2}}

f'(x)=\frac{d}{dx}((10+x)^{\frac{1}{2}})\cdot \frac{d}{dx}(10+x)

f'(x)=\frac{1}{2}(10+x)^{-\frac{1}{2}}\cdot 1

f'(x)=\frac{1}{2\sqrt{10+x}}

Let us find derivative at x=0

f'(0)=\frac{1}{2\sqrt{10+0}}=\frac{1}{2\sqrt{10}}

Upon substituting our given values in linear approximation formula, we will get:

L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}(x-0)  

L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}x-0

L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x

Therefore, our required tangent line for approximation would be L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x.

8 0
3 years ago
A car can go from 0 m/s to 27 m/s in 4.5 seconds. If a net force of 6600 N acted on
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Step-by-step explanation:

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8 0
3 years ago
If Sonja deposits $1,000 into a savings account at 4% simple interest, how long will it
Galina-37 [17]

Given:

Principal (P)= $1,000

Rate of interest (R)= 4% = 0.04

Simple interest (I)= $100

To find:

The time for which she deposits $1000 into a savings account at 4% simple interest.

Solution:

The formula for simple interest is

I=P\times R\times T

On substituting P=1000, R=0.04 and I=100 in the above formula, we get

100=1000\times 0.04\times T

100=40T

Divide both sides by 40.

\dfrac{100}{40}=T

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Therefore, the required time is 2.5 years.

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