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3 years ago

H(y)=9/5 • 2y at y=-2

Mathematics

1 answer:

Deffense [45]3 years ago

6 0

Answer:

$H( - 2) = - 7 \frac{1}{5}$

Step-by-step explanation:

We want to evaluate the equation

$H(y) = \frac{9}{5} \times 2y$

at y=-2

We just have to substitute to obtain;

$H( - 2) = \frac{9}{5} \times 2 \times - 2$

We now multiply to get:

$H( - 2) = \frac{9}{5} \times - 4$

This is the same as:

$H( - 2) = \frac{9}{5} \times \frac{ - 4}{1}$

We multiply the numerators separately and denominators separately to get:

$H( - 2) = \frac{9 \times - 4}{5 \times 1}$

$H( - 2) = \frac{ - 36}{5}$

This implies that

$H( - 2) = - 7 \frac{1}{5}$

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If a = √3-√11 and b = 1 /a, then find a² - b²

Serga [27]

If $b=\frac1a$ , then by rationalizing the denominator we can rewrite

$b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8$

Now,

$a^2 - b^2 = (a-b) (a+b)$

and

$a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8$

$a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8$

$\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}$

5 0

2 years ago

Match the numbers with the correct label

mr_godi [17]

Answer:

see below

Step-by-step explanation:

In decimal, the values of the fractions are ...

-0.2 = -0.200

-3/7 = -0.429

-2/8 = -0.250

So, in a, b, c order, they are ...

a = -3/7

b = -2/8

c = -0.2

3 0

3 years ago

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)

vichka [17]

Answers:

a = -6/37

b = -1/37

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

Explanation:

Let's start things off by computing the derivatives we'll need

$y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\$

Apply substitution to get

$y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\$

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0

3 years ago

How would I figure this out ?

Anit [1.1K]

They get paid $22 a hour, so ur answer would be 374÷22=$17

3 0

3 years ago

Read 2 more answers

What would be the value of $150 after eight years if you earn 12 percent interest per year? A. $371.39 B. $415.96 C. $465.88

salantis [7]

<h3>What would be the value of $150 after eight years if you earn 12 % interest per year? A. $371.39 B. $415.96 C. $465.88 </h3>

<em>The compound interest is applied, that is to say, each year the interest produced is accumulated to the outstanding capital and the interest of the next period is calculated on the new outstanding capital.</em>

The formula for calculating compound interest is:

Compound interest = Total amount of Principal and interest in future less Principal amount at present = [P(1 + i)ⁿ] – P

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods)

[P(1 + i)ⁿ] – P = P[(1 + i)ⁿ – 1] = $150[(1 + 12/100)⁸ – 1] = $150[(1.12)⁸ – 1] = $150[2.47596317629 - 1] = $150[1.47596317629] = $221.39

Total amount = $150 + $221.39 = $371.39

Answer : A.) $371.39

$\textit{\textbf{Spymore}}$

5 0

4 years ago