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Lunna [17]
3 years ago
11

6. Describe the end behavior and determine

Mathematics
2 answers:
baherus [9]3 years ago
8 0

Answer:

6. an odd-degree polynomial function.

    f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7. Length =x+10=8+10=18 inches

   Width=x=8 inches

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7.

The area of a rectangle is given by l×w, where l is length and w is the width

Let=w=x  , l=x+10  and A=144 in² then;

l×w=144

(x+10) × x = 144

x²+10x =144......................complete squares on both sides

x²+10x+25=144+25

x²+10x+25=144+25................factorize

(x+5)²=169.......................square root the right-hand side

x+5= ±√169

x+5=±13.

x+5=13⇒⇒⇒x=8

x+5=-13⇒⇒⇒x= --18

x=8 inches....................value of width should be positive

Length =x+10=8+10=18 inches

Width=x=8 inches

Allisa [31]3 years ago
4 0

Answer:

6. Since, by given graph,

The end behavior of the function f(x),

f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty

f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty

Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )

⇒ The function must has odd number of solutions,

Again by the graph,

Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),

Hence, the total number of real solution of f(x) is 5.

7. Let x represents the width of the rectangle( in inches ),

Given,

The length is 10 inches longer than the width,

⇒ Length of the rectangle = ( x + 10 ) inches

Thus, the area of the rectangle,

A = length × width = x(x+10)

According to the question,

A = 144 in²

⇒ x(x+ 10) = 144

x^2+10x=144

x^2+10x-144=0

x^2+18x-8x-144=0  ( Middle term splitting )

x(x+18)-8(x+18)=0

(x+18)(x-8)=0

⇒ x = -18 or x = 8    ( By zero test property )

The width can not be negative,

Hence, the width of the rectangle would be 8 inches.

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y = 2x + 4

Step-by-step explanation:

First, we need to find out the original equation. On this graph, we can see that the original y-intercept is -1. We can also figure out the slope by counting how many units up on the graph the higher point is from the lower point, in this case, 4, and how many units right it is, in this case, 2, so our slope is 4/2, which can be simplified to 2/1, or a slope of 2. Using the slope and y-intercept, we can create the equation for the original line. The equation will be y = 2x - 1. To get our final answer, we simply need to substitute 4 in the place of -1, and we get our final equation, y = 2x + 4.

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3 years ago
Help with trigonometry​
Oksanka [162]

Answer:

○B. \frac{\sqrt{6}}{2}

Step-by-step explanation:

Trigonometric Identities

\frac{y}{r} = sin\:θ

\frac{x}{r} = cos\:θ

\frac{y}{x} = tan\:θ

\frac{r}{x} = sec\:θ

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{y}^{2} + {x}^{2} = {r}^{2}

{[-\sqrt{15}]}^{2} + {[-\sqrt{10}]}^{2} = {r}^{2} → 15 + 10 = {r}^{2} → 25 = {r}^{2}\\ \\ 5 = r

* Since we are talking about radii, we only want the NON-NEGATIVE root.

In this case, we will not be using the radius in our ratio, according to the trigonometric identity above because we are using the <em>tangent</em><em> </em>ratio:

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Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).
NemiM [27]

Answer:

See verification below

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To obtain the required form, extract a factor in both the numerator and denominator:

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