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3 years ago

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A tumor is injected with 10 grams of Iodine-125, which has a half-life of 76 days. Write an exponential model representing the a

mount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 20 days.

1 answer:

ipn [44]3 years ago

8 0

Answer:

so you want to find the tumer after 20 days right

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

3(2y + 3) = 1(y + 1)

777dan777 [17]

Answer:

= − 8/5

Step-by-step explanation:

Distribute

3

(

2

+

3

)

=

1

(

+

1

)

6

+

9

=

1

(

+

1

)

Multiply by 1

6

+

9

=

1

(

+

1

)

6

+

9

=

+

1

Subtract

9

9

9

from both sides of the equation

6

+

9

=

+

1

6

+

9

−

9

=

+

1

−

9

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3 years ago

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How are the side-splitter theorem and the angle bisector theorem similar?

mart [117]

The side-splitter theorem is basically bisecting a side of a shape.

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3 years ago

QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The ratio of the hours the Teenage Mutant Ninja Turtles spend training,

kicyunya [14]

Answer:

6 hours

The difference between the ratio numbers is 8-3 = 5. That corresponds to the 10-hour difference between training hours and pizza-eating hours. Thus, each ratio unit stands for 2 hours. The 3 ratio units spent eating pizza stand for ...

3×2 hours = 6 hours eating pizza

Step-by-step explanation:Hopefully this helped, if not HMU and I will get u a better answer!

and get i get brainliest plz, im trying to upgrade my statis

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2 years ago

Pls owrk out the missing angle

Alik [6]

Answer:

125

Step-by-step explanation:

A full circle is 360°

80+85+70=235

360-235=125

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3 years ago