Does 3,4,7 make a right triangle

If x-y=9 and xy=2,find the value of (x square + y square)

kati45 [8]

Answer:

x² + y² = 85

Step-by-step explanation:

Using the expansion

(x - y)² = x² + y² - 2xy , then

x² + y² - 2xy = (x - y)² ( add 2xy to both sides )

x² + y² = (x - y)² + 2xy ← substitute given values

= 9² + 2(2)

= 81 + 4

= 85

3 0

3 years ago

The length of some fish are modeled by a von Bertalanffy growth function. For Pacific halibut, this function has the form L(t) =

Dafna1 [17]

Answer:

a) L'(t) = 34.416*e^(-0.18*t)

b) L'(0) = 34 cm/yr , L'(1) =29 cm/yr , L'(6) =12 cm/yr

c) t = 10 year

Step-by-step explanation:

Given:

- The length of fish grows with time. It is modeled by the relation:

L(t) = 200*(1-0.956*e^(-0.18*t))

Where,

L: Is length in centimeter of a fist

t: Is the age of the fish in years.

Find:

(a) Find the rate of change of the length as a function of time

(b) In this part, give you answer to the nearest unit. At what rate is the fish growing at age: t = 0 , t = 1, t = 6

c) When will the fish be growing at a rate of 6 cm/yr? (nearest unit)

Solution:

- The rate of change of length of a fish as it ages each year can be evaluated by taking a derivative of the Length L(t) function with respect to x. As follows:

dL(t)/dt = d(200*(1-0.956*e^(-0.18*t))) / dt

dL(t)/dt = 34.416*e^(-0.18*t)

- Then use the above relation to compute:

L'(t) = 34.416*e^(-0.18*t)

L'(0) = 34.416*e^(-0.18*0) = 34 cm/yr

L'(1) = 34.416*e^(-0.18*1) = 29 cm/yr

L'(6) = 34.416*e^(-0.18*6) = 12 cm/yr

- Next, again use the derived L'(t) to determine the year when fish is growing at a rate of 6 cm/yr:

6 cm/yr = 34.416*e^(-0.18*t)

e^(0.18*t) = 34.416 / 6

0.18*t = Ln(34.416/6)

t = Ln(34.416/6) / 0.18

t = 10 year

7 0

3 years ago

find the missing angle and side measures of the triangle. The triangle has one angle that measures 90 degrees, and the other two

Tamiku [17]

Since we know that the measure of one of the angles is 90°, we know that we have a right triangle with legs 1 and $\sqrt{3}$ . Now lets apply the Pythagorean theorem: $hypotenuse= \sqrt{leg^{2}+leg^{2} }$ , to find our hypotenuse:
$h= \sqrt{1^{2}+ \sqrt{3}^{2} }$
$h= \sqrt{1+3}$
$h= \sqrt{4}$
$h=2$

Now that we know that the measure of the hypotenuse is 2, lets use the trig function sine to find one of the angles that we are going to call $x$ .
Remember that $sin(x)= \frac{opposite.side}{hypotenuse}$ , so:
$sin(x)= \frac{1}{2}$
$x=sin^{-1} ( \frac{1}{2} )$
$x=30$
Now that we have two angles, remember that the sum of the interior angles of a triangle is 180°; lets use that to find our final angle $y$ :
$y=180-(90+30)$
$y=180-120$
$y=60$

We can conclude that the measure of the hypotenuse of our triangle is 2, and the measure of its missing angles are 30° and 60° respectively.

5 0

3 years ago

Miranda wants to buy as many collectible dolls as possible for $2.50 each if she has $45 to spend how many dolls can she buy. wh

julsineya [31]

Let the number of collectible dolls she can buy be x.

x ≤ 45/2.5

x ≤ 18

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Answer:She can buy at most 18 dolls.
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7 0

3 years ago

Read 2 more answers

Sid says 26 is a multiple of 3. Is Sid correct? Why or why no?

Romashka-Z-Leto [24]

Answer:

The answer to your question is: Incorrect

Step-by-step explanation:

Sid is wrong because 26 is not a multiple of 3.

A number is multiple of three if the sum of its digits is multiple of three.

Example:

24 = 2 + 4 = 6 6 is a multiple of 3

27 = 2 + 7 = 9 9 is multiple of 3

but 26 = 2 + 6 = 8 8 is not a multiple of 3

8 0

3 years ago