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sertanlavr [38]

4 years ago

10

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what i

s the value of b, if a=2 (root of)3 and c=2b

1 answer:

Mekhanik [1.2K]4 years ago

5 0

Use the Pythagorean Theorem.

c^2 = a^2 + b^2. Thus, (2b)^2 = (2√3)^2 + b^2

Simplifying, we get: 4b^2 = 4(3) + b^2, or 3b^2 = 4(3). Then b^2 = 4, and b = +2

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10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.

Gre4nikov [31]

Answer:

$\large\boxed{x\in(-2,\ 2)}$

Step-by-step explanation:

$f(x)=12x-x^3$

Calculate the derivative of the function:

$f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2$

Calculate the zeros of the derivative:

$f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2$

Let's check the derivative sign:

$f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2$

Sketch a parabola open down

(before the brackets there is the number -3 < 0)

Look at the picture.

Where the derivative is negative, the function decreases.

Where the derivative is positive, the function increases.

Therefore your answer is:

$x\in(-2,\ 2)$

3 0

4 years ago

Average Daily Temperature in August

timurjin [86]

Answer:

The range for the average low temperatures for the states listed in the chart is B) 24.

Step-by-step explanation:

Low temperatures are:

56, 55, 65, 64, 55, 44, 54, 55, 68

First we put them in order from least to greatest

44, 54, 55, 55, 55, 56, 64, 65, 68

Range is maximum - minimum

68 is maximum and 44 is minimum

68 - 44 =

24

Hope this helps you! (:

-Hamilton1757

6 0

3 years ago

a onion is 0.6 pounds and the cost of that onion is $0.48 what is independent and dependent variables

Vsevolod [243]

Independent = weight
Dependent = cost
I believe

4 0

3 years ago

Equation where slope = 7/2 and y-intercept is -15

matrenka [14]

Answer:

y = 7/2x - 15

Step-by-step explanation:

y = mx + b

if slope is 7/2, m= 7/2

y = 7/2x + b

if y-intercept is -15, y = -15, x = 0

-15 = 7/2(0) + b

b = -15

then

y = 7/2x - 15

6 0

2 years ago

Solve the equation. <br><br> -4.6p - 6.3p + 3.9= -9.18

KiRa [710]

Answer: P=1.2

Step-by-step explanation:

-4.6p-6.3p+3.9=-9.18

simplify

-10.9p+3.9=-9.18

-10.9p=-13.08

p=1.2

4 0

3 years ago

Read 2 more answers