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~/1 pointsSCalcET8 3.9.021.My NotesAsk Your TcacherThe altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a ...

Question

~/1 pointsSCalcET8 3.9.021.My NotesAsk Your TcacherThe altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of cr? /min, At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 150 cm"? cm/minNced Help?RendMhkchillHTalk laluiTular

~/1 points SCalcET8 3.9.021. My Notes Ask Your Tcacher The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of cr? /min, At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 150 cm"? cm/min Nced Help? RendM hkchill HTalk laluiTular



Answers

The altitude of a triangle is increasing at a rate of $ 1 cm/min $ while the area of the triangle is increasing at a rate of $ 2 cm^2/min. $ At what rate is the base of the triangle changing when the altitude is $ 10 cm $ and the area is $ 100 cm^2? $

Test.

Oh this is a question in which will be using the concept of increasing and decreasing our application of derivative. We should say if this is triangle abc, this is the altitude and this is the base so Area is 1/2 and two. Base into the altitude question number one. Now various things we have been given ah that altitude is increasing at a rate of one centimeter per minute. So D. H by DT is one cm/min. An area is increasing at the rate of two centimeters Squire per minute. So we need to find the raid outfits. The basis is changing when altitude is 10 centimeter and base area and the area is 100 centimeters square. So let us differentiate equation number eight with respect to T so dear by duty is half since be an edge all our variables. So you'll be using the concept of the differentiation of the product. So be the H by DT place DB by DT into at Disability is 2 1 x two B. What should be base should be taken as okay. At what rate is the base of the triangle is changing when altitude? Okay no problem. Be into DHB oddity we have one place delivery T. We need to find out and altitude is 10 cm we have to find the value of B when area is and the centimeter and ah Altitude is 10 cm 8800 centimeter square half into base into altitude 10. So the system. So BB. is 20 cm so we'll be plugging in value of 20 over here. So this will be to equal to one x 2, 22 and 20 plus DB by detained 2 10. So this will be four Equal to 20 plus and D. V by DT So D V. But it will be cool too, -16 x 10 -8 x five. So the rate of change of the base will be minus 85 centimeter permit on minus one point six centimeter per minute. Now this negative science shows that the base is decreasing with time. Thank you.

So we know that the area of a triangle is 1/2 base times height and we know that the area is 100 centimeters squared and we know that the height it's 10 centimeters so we can sell for the base. We get that 10 centimeters equals 1/2 B. So the base must be 20 centimeters Now if we take the derivative with respect to time, we get t a d t. Because 1/2 times be th tt plus h DBT. And now we have an expression where we can plug in are known values. So we know that the A t T is going to be two centimeters squared per minute equals 1/2 times. But we just figured out that the basis 20 centimeters and we know that the height is increasing at a rate of one centimeter. Her minute. We know that the height is 10 centimeters and we're trying to find the rate at which the base is changing. So now we can just simplify and sell for DBT. So we have two centimeters squared per minute equals 1/2 of 20 centimeters squared, permitted plus 10 centimeters times DBT. And if we multiply both sides by two. We're going to get four centimeters squared permanent because 27 meters squared per minute plus 10 centimeters times dp DT. And if we subtract 20 centimeters squared permitted from both sides will get negative 16 centimeter squared per minute. He goes 10 centimeters times DBT And now if we just divide both sides by 10 centimeters, we're going to get negative 1.6 seven meters permitted equals TB DT and we have the rate at which the base is changing with respect to time at negative 1.67 years.

We know the formula for the area of a triangle with based B and high age is a equals 1/2 the age differentiating using the product rule. If I split this up into two components 1/2 B and H using the product rule day over DT, I got 1/2 times D B that indicates base times age plus B times D H you can probably in furnace indicates height changing height so h and B just using those with derivatives. You know dp over. Dt is negative. One d h over dt is five. B is 10 and ages 22 So plugging him, we end up with D A over DT equals 14 centimeters per minute.


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