Daniaal Sanchez
2021-02-12
Answered

How do you solve this using completing the square? $-16{t}^{2}+32t=-5-16{t}^{2}+32t=-5-16{t}^{2}+32t=-5$

You can still ask an expert for help

krolaniaN

Answered 2021-02-13
Author has **86** answers

To solve an equation by completing the square, you need to rewrite the expression to have a leading coefficient of 1.

Since the leading coefficient of

To complete the square for an expression of the form

For

Adding 1 on both sides of

Now that the left side is a perfect square, you need to factor. Since

The factored equation is then

Square rooting both sides gives

Adding 1 on both sides then gives

asked 2022-05-20

Given: For some $X$, $Var(X)=9$, $E(X)=2$, $E({X}^{2})=13$

Problem: $Pr[X=2]>0$

The solution in my book says to construct a r.v. to satisfy the above conditions and confirm or deny the statement from there. For simplicity, assume $X$ can take on two values $Pr[a]=\frac{1}{2}$ and $Pr[b]=\frac{1}{2}$. Finding that $a$ and $b$ are not $2$ is enough to disprove the statement. We can apply the constraints:

$\frac{1}{2}a+\frac{1}{2}b=2$

$\frac{1}{2}{a}^{2}+\frac{1}{2}{b}^{2}=13$

So I did this:

$a=4-b$ from the first equation

${b}^{2}-4b-5=0$ by substituting $a$

The above quadratic has two solutions, $b=-1$ and $b=5$ which happen to be the same solutions the book got for $a$ and $b$ respectively.

I'm not sure if this is the right way to solve this problem since I never explicitly solved for $a$ and the two solutions for $b$ may coincidentally be the same.

Problem: $Pr[X=2]>0$

The solution in my book says to construct a r.v. to satisfy the above conditions and confirm or deny the statement from there. For simplicity, assume $X$ can take on two values $Pr[a]=\frac{1}{2}$ and $Pr[b]=\frac{1}{2}$. Finding that $a$ and $b$ are not $2$ is enough to disprove the statement. We can apply the constraints:

$\frac{1}{2}a+\frac{1}{2}b=2$

$\frac{1}{2}{a}^{2}+\frac{1}{2}{b}^{2}=13$

So I did this:

$a=4-b$ from the first equation

${b}^{2}-4b-5=0$ by substituting $a$

The above quadratic has two solutions, $b=-1$ and $b=5$ which happen to be the same solutions the book got for $a$ and $b$ respectively.

I'm not sure if this is the right way to solve this problem since I never explicitly solved for $a$ and the two solutions for $b$ may coincidentally be the same.

asked 2022-06-20

$P+Q=\sqrt{5}.$

Where $P$ is a rational number and $Q$ is an irrational number. Give possible values of $P$ and $Q$.

Where $P$ is a rational number and $Q$ is an irrational number. Give possible values of $P$ and $Q$.

asked 2021-03-06

Cramer’s Rule to solve (if possible) the system of linear equations.

$-8{x}_{1}+7{x}_{2}\mid -10{x}_{3}=-151$

$12{x}_{1}+3{x}_{2}-5{x}_{3}=86$

$15{x}_{1}-9{x}_{2}+2{x}_{3}=187$

asked 2021-08-19

The function $A=7.7{\left(0.92\right)}^{t}$ represents an exponential growth or decay function.

A.

Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?

a.

Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

b.

Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08

c.

Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08

d.

. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

e.

None of these

A.

Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?

a.

Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

b.

Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08

c.

Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08

d.

. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

e.

None of these

asked 2021-12-20

Write the trigonometric expression as an algebraic expression in u.

$\mathrm{sec}\left({\mathrm{cos}}^{-1}u\right)$

asked 2020-12-03

Evaluate the limit.

$\underset{x\to \mathrm{\infty}}{lim}\frac{7({x}^{9}-4{x}^{5}+2x-13}{-3{x}^{9}+{x}^{8}-5{x}^{2}+2x}$

asked 2021-06-18

I need answer on it ASAP
A bacteria population is growing exponentially with a growth factor of 18 each hour. By what growth factor does the population change each half hour?