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2 years ago

13 9/10 divided by 3 1/2

Mathematics

1 answer:

Arlecino [84]2 years ago

8 0

Answer:

$3 \frac{13}{44}$

Step-by-step explanation:

First let's write our equation

$13 \frac{9}{10} \div 3 \frac{1}{2}$

Now let's make them improper fractions

$\frac{139}{10} \div \frac{7}{2}$

Now since we're dividing we with fractions we do the reciprocal and multiply

$\frac{139}{10} \times \frac{2}{7}$

$\frac{139}{5} \times \frac{1}{7} = \frac{139}{42} = 3 \frac{13}{42}$

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Andreyy89

Answer:

C. Marie should make sure she surveys both the fathers and mothers.

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2 years ago

Calculate the total area of the shaded region.

LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

$\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}$

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

$\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill$

$\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}$

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2 years ago

Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros -4,-2,5. write the functio

OLga [1]

Answer:

Step-by-step explanation:

This is a third degree polynomial since we have 3 zeros. We find these zeros by factoring the given polynomial. The zeros of a polynomial are where the graph of the function goes through the x-axis (where y = 0). If x = -4, the factor that gives us this value is (x + 4) = 0 and solving that for x, we get x = -4. If x = -2, the factor that gives us that value is (x + 2) = 0 and solving that for x, we get x = -2. Same for the 5. The way we find the polynomial that gave us these zeros is to go backwards from the factors and FOIL them out. That means that we need to find the product of

(x + 4)(x + 2)(x - 5). Do the first 2 terms, then multiply in the third.

$(x+4)(x+2)=x^2+2x+4x+8$ , which simplifies to

$x^2+6x+8$

No we multiply in the final factor of (x - 5):

$(x^2+6x+8)(x-5)=x^3+6x^2+8x-5x^2-30x-40$ which simplifies to

$f(x)=x^3+x^2-22x-40$

If you are aware of the method for factoring higher degree polymomials, which is to use the Rational Root Theorem and synthetic division, you will see that this factors to x = -4, -2, 5. If you know how to use your calculator, you will find the same zeros in your solving polynomials function in your apps.

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3 years ago

Which of the following is not a geometric sequence?

Leviafan [203]

A.

Because in mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

3 0

3 years ago

the population P (t) of a culture of bacteria is given by P (t) =-1710t +92,000t+10,000, where t is the time in hours since the

Akimi4 [234]

The question might have some mistake since there are 2 multiplier of t. I found a similar question as follows:

The population P(t) of a culture of bacteria is given by P(t) = –1710t^2+ 92,000t + 10,000, where t is the time in hours since the culture was started. Determine the time at which the population is at a maximum. Round to the nearest hour.

Answer:

27 hours

Step-by-step explanation:

Equation of population P(t) = –1710t^2+ 92,000t + 10,000

Find the derivative of the function to find the critical value

dP/dt = -2(1710)t + 92000

= -3420t + 92000

Find the critical value by equating dP/dt = 0

-3420t + 92000 = 0

92000 = 3420t

t = 92000/3420 = 26.90

Check if it really have max value through 2nd derivative

d(dP)/dt^2 = -3420

2nd derivative is negative, hence it has maximum value

So, the time when it is maximum is 26.9 or 27 hours

5 0

3 years ago