Estimate the solution to the equation 3.1g = 20.9 to the nearest whole number.

Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 8 terms

arlik [135]

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
15 = -3 r^(2-1)
-5 = r
r = -5

Then, we can find the sum by the expression:

S(n) = a(1) ( 1 - r^n) / 1-r
S(8) = -3 (1 + 5^8) / 1+5
S(8) = -195313

3 0

3 years ago

You are a young entrepreneur who ventures into selling milk tea. On the soft opening day, you sold all 50 glasses of classic and

shutvik [7]

Answer:

35 glasses of classic milk tea

15 glasses of flavored milk tea

Step-by-step explanation:

You sold 50 glasses of classic and flavored milk tea.

c + f = 50

You made 4700 when classic tea costs 100 and flavored tea costs 80.

100c + 80f = 4700

Use this system of equation to solve. Use substitution. Rearrange the first equation so that it is equal to c. Then, plug the c-value into the second equation.

c + f = 50

c = 50 - f

100c + 80f = 4700

100(50 - f) + 80f = 4700

5000 - 100f + 80f = 4700

5000 - 20f = 4700

-20f = -300

f = 15

Plug the f-value into one of the equations and solve for c.

c + f = 50

c + 15 = 50

c = 35

35 glasses of classic milk tea and 15 glasses of flavored milk tea were sold.

4 0

3 years ago

Three students are arguing over who can run the fastest. Student A says that she can run 2/3 mile in six minutes. Student B says

harkovskaia [24]

1/10

..............................

8 0

3 years ago

If the length of side a is 12 centimeters, measure of angle B = 36 degrees and measure of angle C = 75 degrees , what is the len

Fofino [41]

The length of side b is 7.61 m.

Here's how the length was calculated:

Let:

length of side a = 12 centimeters
B = 36 degrees
C = 75 degrees

In order to solve an AAS triangle, use the three angles, add to 180 degrees to find the other angle, then, use The Law of Sines to find each of the other two sides.

A = 180 - (36 + 75) = 69 degrees

by using the law of sines:

a / sin A = b / sin B = c/ sin C

we will substitute the given values:

12 / sin (69) = b / sin (36)

b = unknown

12 / 0.93 = b / 0.59

12.9 = b / 0.59

b = 12.9 * 0.59

b =7.61 cm (length of side b)

6 0

3 years ago

Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4

ad-work [718]

Answer:

$f''(x)=36x^2+4$

Step-by-step explanation:

Let's start by finding the first derivative of $f(x)= 3x^4+2x^2-8x+4$ . We can do so by using the power rule for derivatives.

The power rule states that:

$\frac{d}{dx} (x^n) = n \times x^n^-^1$

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

$\frac{d}{dx} (3x^4+2x^2-8x+4)$

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)$

Simplify the equation.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)$
$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)$

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)$
$f'(x)=12x^3+4x-8$

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

$\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)$

$\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)$

Simplify the equation.

$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )$

Therefore, this is the 2nd derivative of the function f(x).

We can say that: $f''(x)=36x^2+4$

6 0

2 years ago

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