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3 years ago

Assume a and b are whole numbers, and a>b. Which expression has the least value?

Mathematics

1 answer:

dedylja [7]3 years ago

8 0

a > b

A . a^5b^3/ab^4 = a^4/b

B. a^4 / a*a*a*a = a^4 / a^4 = 1

C. ab^2 / a^2b = b/a

D. b*b*b/b^3 = b^3/b^3 = 1

B and D, doesn't matter what values of a and b it's always equal 1

Lets say a = 2 and b = 1

A. a^4/b = 2^4 / 1 = 16/1 = 16

C. b/a = 1/2 = 0.5

So C has the least value

Answer:

ab^2 / a^2b

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If y varies directly as x, and y is 16 when x is 4, when y= 24 what is the value of x?

sergejj [24]

Answer:

x = 6 possibly

Step-by-step explanation:

I am just an algebra student, but if I am correct I would appreciate a crown.

16/4 is 4, so i assumed that was the geometric pattern, so i divided 24 by 4 and got 6.

Hoped this helped.

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3 years ago

Jane and Sammie are making decisions about their bank accounts. Jane wants to deposit

prisoha [69]

Answer:

Sammie

Step-by-step explanation:

Jane

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 550.00(1 + 0.05/4)(4)(10)

A = 550.00(1 + 0.0125)(40)

A = $903.99

Sammie

First, convert R as a percent to r as a decimal

r = R/100

r = 7/100

r = 0.07 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 550.00(1 + 0.07/12)(12)(10)

A = 550.00(1 + 0.005833333)(120)

A = $1,105.31

3 0

2 years ago

Find the missing length of the triangle b 0.3 cm 0.5 cm

Juli2301 [7.4K]

Answer:

I'm assuming that it is a right angle triangle.

Step-by-step explanation:

0.3x0.5=0.15

0.15/2=0.075

missing length is 0.075

6 0

3 years ago

Select the postulate of equality or inequality that is illustrated.

Zanzabum

The symmetric property of equality.

This property states that: if a = b, b = a.

4 0

3 years ago

Read 2 more answers

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago