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2 years ago

Let $f(x) = x^2 + 4x - 31$. for what value of $a$ is there exactly one real value of $x$ such that $f(x) = a$?

1 answer:

7 0

To solve for this, we need to find for the value of x when the 1st derivative of the equation is equal to zero (or at the extrema point).

So what we have to do first is to derive the given equation:

f (x) = x^2 + 4 x – 31

Taking the first derivative f’ (x):

f’ (x) = 2 x + 4

Setting f’ (x) = 0 and find for x:

2 x + 4 = 0

x = - 2

Therefore the value of a is:

a = f (-2)

a = (-2)^2 + 4 (-2) – 31

a = 4 – 8 – 31

a = - 35

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Two boys who live 14 miles apart start at noon to walk toward each other at rates of 3 mph and 4 mph respectively. In how many h

aniked [119]

Since you have the answers given, just track their walking.
After one hour, one guy has covered 3mi and the other 4mi, which is in total 7, not 14
After 2 hours, one guy has covered 6mi and the other 8mi, which is 14mi

The algebraic way would be:
3x +4x = 14 *x being the hour
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2 years ago

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Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial

Elza [17]

9514 1404 393

Answer:

$2838.14

Step-by-step explanation:

Fill in the values and do the arithmetic.

A = 2000e^(0.07·5)

A = 2000e^0.35 ≈ 2838.14

The value of the investment in 5 years will be $2838.14.

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2 years ago

peggy practices her gymnastics routine for a total of 21 hours . each practice session is 1 3/4 hours . how many practice sessio

algol [13]

Peggy has 12 practice sessions

The first step is finding the unit rate. We can do this by evaluating

21/1.75 divided by 1.75/1.75.
When you divide the two, you get 12.

To check your work you do 12(1.75) and you will get 21

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2 years ago

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elena55 [62]

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2 years ago

Lamont works for an electric utility and is installing a 40 foot utility pole as shown. Lamont drills the anchor of a support ca

PIT_PIT [208]

Answer:

Approximately 43 feet of minimum cable is needed.

Step-by-step explanation:

This problem can be solved using Trigonometry and Pythagorean theorem. Pythagorean theorem applies on right-triangles (which are known to have one 90° angle). The theorem states that the square of the Hypotenuse is obtained by the squared sum of the other two sides of the triangle (i.e the two sides forming the 90° angle - with the hypotenuse side being across it as:

$h^2=a^2+b^2$ Eqn. (1)

where

$h$ is the hypotenuse

$a$ is a side

$b$ is a side

Now in this case, the utility pole must be perpendicular to the ground and the anchor being parallel to the ground, and a 90° angle formed between them. Conclusively the cable length will be represented by the hypotenuse in a right triangle. So here we have $a=40ft$ and $b=15ft$ . Plugging in Eqn.(1) and solving for $h$ we have:

$h^2=40^2+15^2\\h=\sqrt{40^2+15^2} \\h=\sqrt{1600+225}\\ h=\sqrt{1825}\\ h=5\sqrt{73}\\ h=42.72ft$

So we conclude that the minimum length of cable needed by Lamont is

≈43 feet (rounded up).

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2 years ago