The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is
given by x = 5 + t , y = 4 + 1 4 t, where x and y are measured in centimeters. The temperature function satisfies Tx(3, 5) = 1 and Ty(3, 5) = 1. How fast is the temperature rising on the bug's path after 4 seconds? (Round your answer to two decimal places.)
1 answer:
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Answer:
- <u>5</u><u> </u>is the value which makes the equation true .
Step-by-step explanation:
In this question we have provided an equation that is <u>9</u><u> </u><u>(</u><u> </u><u>3x</u><u> </u><u>-</u><u> </u><u>1</u><u>6</u><u> </u><u>)</u><u> </u><u>+</u><u> </u><u>1</u><u>5</u><u> </u><u>=</u><u> </u><u>6</u><u>x</u><u> </u><u>-</u><u> </u><u>2</u><u>4</u><u> </u>. And we are asked to <u>write </u><u>the </u><u>steps </u><u>to </u><u>solve </u><u>the </u><u>equation </u><u>with </u><u>explanation </u> and <u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>X </u><u>.</u>
<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>
<u>Step </u><u>1</u><u> </u><u>:</u> Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :
<u>Step </u><u>2</u><u> </u><u>:</u> Solving like terms on left side that are -144 and 15 :
<u>Step </u><u>3 </u><u>:</u> Adding 129 on both sides :
Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :
<u>Step </u><u>4</u><u> </u><u>:</u> Subtracting with 6x on both sides :
On calculating further, We get :
<u>Step </u><u>5</u><u> </u><u>:</u> Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :
Now , by cancelling 21 with 21 on left side , We get :
<u>Step </u><u>6</u><u> </u><u>:</u> Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>x </u><u>is </u><u>5</u>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
Now we are verifying our answer by substituting value of x in the given equation . So ,
- 9 ( 3x - 16 ) + 15 = 6x - 24
- 9 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 24
- 9 ( 15 - 16 ) + 15 = 30 - 24
- 9 ( -1 ) + 15 = 6
- -9 + 15 = 6
- 6 = 6
- L.H.S = R.H.S
- Hence , Verified .
<u>Therefore</u><u>,</u><u> our</u><u> value</u><u> for</u><u> x</u><u> is</u><u> correct</u><u> </u><u>that </u><u>means</u><u> </u><u>it'll</u><u> </u><u>makes</u><u> </u><u>the </u><u>equation</u><u> true</u><u> </u><u>.</u>
<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>