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Verdich [7]
3 years ago
10

The temperature in the morning was -2 degrees. The temperature is dropping at a constant rate, and 4 hours later the temperature

is now -22 degrees. How many degrees did the temperature change each hour?
Mathematics
1 answer:
lisov135 [29]3 years ago
6 0

Given:

Temperature in the morning = -2 degrees.

Temperature is dropping at a constant rate.

Temperature after 4 hours = -22 degrees.

To find:

The rate of change of temperature.

Solution:

Let y be the temperature after x hours from the morning.

Temperature in the morning is -2 degrees. It means, the ordered pair is (0,-2).

4 hours later the temperature is now -22 degrees. It means, the ordered pair is (4,-22).

Now, formula for average rate of change or slope is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{-22-(-2)}{4-0}

m=\dfrac{-22+2}{4}

m=\dfrac{-20}{4}

m=-5

Therefore, the change in temperature is -5 per hour. It means the permutate is decreasing by 5 degrees per hour.

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BartSMP [9]

Answer: The required conclusion is

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Step-by-step explanation:  Given that in triangle ABC,  AB ≅ AC, implies that AB = AC must be true. We are given to assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other.

If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.

For the same reason, if m∠B < m∠C, then AC < AB.

This is a contradiction to the given information.

We are to state the conclusion.

Since in the beginning, it is given that AB ≅ AC and we have assumed that ∠B and ∠C are not congruent, so

our assumption must be wrong.

That is, ∠B and ∠C must be congruent.

Thus, the required conclusion is

if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent.

5 0
3 years ago
Read 2 more answers
Find the polynomial of minimum degree, with real coefficients, zeros at
drek231 [11]

Answer:

\huge\boxed{p(x)=4x^3-20x^2+4x+300}

Step-by-step explanation:

\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has  a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)

\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300

7 0
3 years ago
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Ugo [173]
Hello Friend,here is the solution for your question


<span>so the given function is </span>
y= √(-2cos²x+3cosx-1)
 i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)

Now here  in this equation is this quantity :-
<span>(cosx=3/4)²----------------(2)   is to it's minimum value then the whole equation </span>
<span>i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa </span>


And we know that cosx-3/4 will be minimum if cosx=3/4
<span>therefore put this in (1) we get </span>
(cosx=3/4)²=0    [ cosx=3/4]
<span>hence the minimum value of the quantity (cosx=3/4)² is 0 </span>

<span>put this in equation (1) </span>
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
   =√[1/8-3(0)]        [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
     =√1/8
      =1/(2√2)

<span>this is the maximum value now to find the minimum value </span>

<span>since this is function of root so the value of y will always be ≥0 </span>

<span>hence the minimum value of the function y is 0 </span>


<span>Therefore, the range of function </span>y is [0,1/(2√2)]


__Well,I have explained explained each and every step,do tell me if you don't understand any step._

8 0
3 years ago
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evablogger [386]

Answer:

x  = 8

Step-by-step explanation:

you have similar triangles here

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2/4 =  4/x

x = 8

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