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4 years ago

Solve the following inequality for b in terms of a: 3a +7b > 2a - 8b

Mathematics

1 answer:

12345 [234]4 years ago

5 0

Answer:

Step-by-step explanation:

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assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28

melomori [17]

Given:

x and y are both differentiable functions of t.

$4x^2+3y^3=28$

$x=-1\text{ and }\dfrac{dy}{dt}=8$

To find:

The value of $\dfrac{dx}{dt}$ .

Solution:

We have,

$4x^2+3y^3=28$ ...(i)

At x=-1,

$4(-1)^2+3y^3=28$

$4+3y^3=28$

$3y^3=28-4$

$3y^3=24$

Divide both sides by 3.

$y^3=8$

Taking cube root on both sides.

$y=2$

So, y=2 at x=-1.

Differentiate (i) with respect to t.

$4(2x\dfrac{dx}{dt})+3(3y^2\dfrac{dy}{dt})=0$

Putting x=-1, y=2 and $\dfrac{dy}{dt}=8$ , we get

$4(2(-1)\dfrac{dx}{dt})+3(3(2)^28)=0$

$-8\dfrac{dx}{dt}+9(4)(8)=0$

$-8(\dfrac{dx}{dt}-9(4))=0$

Divide both sides by -8.

$\dfrac{dx}{dt}-36=0$

$\dfrac{dx}{dt}=36$

Therefore, the value of $4x^2+3y^3=28$ is 36.

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3 years ago

Two studies were completed in California. One study in northern California involved 1,000 patients; 74% of them experienced flul

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The study has the smallest margin of error for a 98% confidence interval is <span>The northern California study with a margin of error of 3.2%.

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3 years ago

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The following data points represent the number of holes that moths ate in each of Grandma Marion's

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Answer:

1, 0, 2, 3

Step-by-step explanation:

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Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to increasing

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Step-by-step explanation:

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4 years ago

You have 16 yellow beads, 20 red beads, and 24 orange beads to make identical bracelets. What is the greatest number of the brac

zzz [600]

Answer:

4 bracelets

Step-by-step explanation:

We have been given that you have 16 yellow beads 20 red beads and 24 orange beads to make identical bracelet. We are asked to find the greatest numbers of bracelets you can make using all the beads.

To solve our given problem, we need to find greatest common factor of 16, 20 and 24.

Factors of 16: 1, 2, 4, 8, 16.

Factors of 20: 1, 2, 4, 5, 10, 20.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

We can see that greatest common factor of 16, 20 and 24 is 4, therefore, you can make 4 bracelets using all the beads.

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3 years ago