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4 years ago

15

It takes a submarine 11 minutes to dive 154 meters below sea level. If the submarine dives at a constant speed, how much does it

s depth change per minute

1 answer:

professor190 [17]4 years ago

7 0

Its depth increases 14 meters every minute since its traveling 14m a min, which can be found by divding the distance and time by 11 reducing it to the distance traveled in a min<span />

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Consider the quadratic equation x squared = 4x - 5. how many solutions does the equation have?

snow_lady [41]

Answer:

The quadratic equation has two complex solutions

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}=4x-5$

Equate to cero

$x^{2}-4x+5=0$

so

$a=1\\b=-4\\c=5$

substitute in the formula

$x=\frac{4(+/-)\sqrt{-4^{2}-4(1)(5)}} {2(1)}$

$x=\frac{4(+/-)\sqrt{16-20}} {2}$

$x=\frac{4(+/-)\sqrt{-4}} {2}$

Remember that

$i^{2}=-1$

so

$x=\frac{4(+/-)2i} {2}$

$x=2(+/-)i$

therefore

The quadratic equation has two complex solutions

5 0

3 years ago

Which sequence shows the numbers in the order least to greatest 1/2 , -2/3 , -3/4

torisob [31]

Order least to greatest -3/4 , -2/3 ,1/2

3 0

3 years ago

12598 round to the nearest thousand

MakcuM [25]

12598 rounded to the nearest thousands is 1260

5 0

3 years ago

Read 2 more answers

The perimeter of the first rectangle below is 120 inches. The perimeter of the second rectangle is 180 inches. What are the valu

8_murik_8 [283]

Answer:

A

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

when the polynomial f(x) is divided by (x-2) the remainder is 4, and when it is divided by (x-3) the remainder is 7. Given that

natima [27]

$f(x)=(x-2)(x-3)Q(x)+ax+b$

Recall the polynomial remainder theorem: the remainder upon dividing a polynomial $p(x)$ by $x-c$ is equal to $p(c)$ . This means that $f(2)=4$ and $f(3)=7$ , which tell us

$4=2a+b$

$7=3a+b$

From here we can solve for $a,b$ :

$4=2a+b\implies b=4-2a$

$7=3a+b=3a+(4-2a)\implies a=3\implies b=-2$

so that

$f(x)=(x-2)(x-3)Q(x)+3x-2$

Now,

$\dfrac{f(x)}{(x-2)(x-3)}=Q(x)+\dfrac{3x-2}{(x-2)(x-3)}$

so the remainder upon dividing $f(x)$ by $(x-2)(x-3)$ is $3x-2$ .

Next, if $f$ is a cubic function, then $Q(x)$ is a linear polynomial that can be written as $Q(x)=cx-d$ . The coefficient of $x^3$ in $f(x)$ is 1 (unity), so that expanding $f(x)$ gives us

$f(x)=(x-2)(x-3)(cx-d)+3x-2$

$f(x)=(cx^3-(5c+d)x^2+(6c+5d)x-6d)+3x-2$

$f(x)=cx^3-(5c+d)x^2+(6c+5d+3)x-(6d+2)$

$\implies c=1$

and we also have that $f(1)=1$ , so that

$1=1-(5+d)+(6+5d+3)-(6d+2)$

$\implies2d=2\implies d=1$

so that

$Q(x)=x-1$

4 0

3 years ago