Can someone please help me ASAP?

A point P(x,y) moves along the graph of the equation y = x3 + x2 + 2. The x-values are changing at the rate of 2 units per secon

CaHeK987 [17]

Using implicit differentiation, it is found that y is changing at a rate of 10 units per second.

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The equation is:

$y = x^3 + x^2 + 2$

Applying implicit differentiation in function of t, we have that:

$\frac{dy}{dt} = 3x^2\frac{dx}{dt} + 2x\frac{dx}{dt}$

x-values changing at a rate of 2 units per second means that $\frac{dx}{dt} = 2$
Point Q(1,4) means that $x = 1, y = 4$ .

We want to find $\frac{dy}{dt}$ , thus:

$\frac{dy}{dt} = 3x^2\frac{dx}{dt} + 2x\frac{dx}{dt}$

$\frac{dy}{dt} = 3(1)^2(2) + 2(1)(2) = 6 + 4 = 10$

y is changing at a rate of 10 units per second.

A similar problem is given at brainly.com/question/9543179

5 0

2 years ago

[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?

Nitella [24]

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

$\log_4x+\log_4(x-3)=\log_4(-7x+21)$

First, notice that

$x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x$

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

$\log_4x+\log_4(x-3)=\log_4x(x-3),$

then

$\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3$

Hence, $x=3$ and $x=-7$ are extraneous solutions

6 0

2 years ago

Drake wants to save $750 so that he can take a class on computer analysis for cars. The class is being held on various dates ove

STatiana [176]

C. Both options A and B will allow him to meet his goal.

Looking at Drake's situation after 4 weeks, he only has $470 saved. By his original plan, he should have had $500 saved. So he's $30 short of his goal and has 2 weeks until his originally planned class. If he goes with option A and takes the later class, he will save an additional $125 which is more than enough to make up the $30 short fall. So option A will work for him to save enough money for his class. With option B, he will save $140 for the last 2 weeks of his plan giving him a savings of $280 for the last 2 weeks. Adding the $470 he's already saved will give him a total savings of $470 + $280 = $750 which is enough for him to attend his class. So option B will also allow Drake to attend his desired class. Both options A and B allow him to meet his goal. Hence, the answer is "c".

8 0

2 years ago

Equation A: a=5b + 1

lukranit [14]

ANSWER:

a = 11

b = 2

Explaination:

We have two equations:

a = 5b + 1 .....................(1)

a = 3b + 5.....................(2)

Here we use substitution method in order to solve the set of equations.

put a=3b+1 to equation (1)

3b + 5 = 5b + 1

Solve for b

5 = 5b -3b + 1

5-1 =2b

4 = 2b

b = 2

Now put the value of b = 2 into the equation (1) or (2)

a = 5b + 1

a = 5(2) + 1

a = 10 + 1

a = 11

5 0

2 years ago

My teacher didn’t have have to explain the decimal place value can you guys help?

Vlad1618 [11]

Answer:

Step-by-step explanation:

See attachment

7 0

1 year ago