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3 years ago

What is the center and radius of the circle with equation x2 + y2 + 6x + 16y + 64 = 0?

Mathematics

1 answer:

almond37 [142]3 years ago

5 0

Hello,

By making factors:
$x^2+y^+2+6x+16y+64=0\\
x^2+6x+9+y^2+16y+64-9=0\\
(x+3)^2+(y+8)^2=9\\
radius=3

$

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Steve drove at a constant rate to the beach for a vacation. In the equation below, t is the time in hours it took Steve to drive

Sindrei [870]

9514 1404 393

Answer:

A. 64 miles per hour

Step-by-step explanation:

In a linear equation, the "unit rate" is generally the coefficient of the variable. The units of the unit rate depend on the definition of the relationship.

Here, the time t is in hours, so the "unit rate" will be <something> per hour. The answer choices suggest that the <something> is "miles". That is, the units of the equation are ...

(miles/hour) × (hours) = miles

With numbers/variables, that is ...

(64 miles/hour) × (t hours) = 384 miles

The unit rate is 64 miles per hour.

6 0

2 years ago

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

7 0

2 years ago

Read 2 more answers

(3x-4y)^2-(3x-4y)(3x+4y)

zheka24 [161]

Answer:

$-24xy + 32y^2$

Step-by-step explanation:

Hello!

We can use the special binomial product formulas:

$(a + b)^2 = a^2 + 2ab + b^2$
$(a + b)(a - b) = a^2 - b^2$

<h3>Simplify</h3>

$(3x - 4y)^2 - (3x - 4y)(3x + 4y)$
$(9x^2-24xy+16y^2) - (9x^2 - 16y^2)$
$9x^2 - 9x^2 - 24xy + 16y^2 + 16y^2$
$-24xy + 32y^2$

The simplified form is $-24xy + 32y^2$

6 0

1 year ago

Consider U = {x|x is a negative real number} which is an empty set?

gavmur [86]

I am not sure exactly what you are looking for is this problem. Are you given choices from which to choose?

The empty set is a set with no numbers. Therefore, you should look for a set that doesn't have any elements.

6 1

2 years ago

Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?

sveta [45]

Answer:

$-\frac{2}{3}i - \frac{13}{5}j$