Mathematics College

match the equation with its graph . identify the slope and y-intercept y= -2/3x+1

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Answer 1

Answer:

the slope is -2/3x and the y intercept is 1

Step-by-step explanation:

Related Questions

help again again again

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Answer:

it's the last choice, by process of elimination that's the only one that includes the 4. and of course the math adds up

the answer is the last choice

Evaluate the following expression.
(-5+7 x 1)-9x5

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Answer:

Step-by-step explanation:

The answer is -43 ......

in the equation 80 multiplied by 10 = 8, the number 80 is the

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Answer:

product of 10 and 8

Step-by-step explanation:

8 is the quotient of 80 and 10 (80/10=8)

[tex]\frac{d}{dx} \int t^2+1 \ dt[/tex]
There is a 2x on the bottom and x^2 on top of the integral symbol
Please help me my teacher did not teach us this:(

Answers

Answer:

[tex]\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2[/tex]

Step-by-step explanation:

[tex]\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?[/tex]

We can use Part I of the Fundamental Theorem of Calculus:

[tex]\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}[/tex]

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

[tex]\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}[/tex]

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

[tex]\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}[/tex]

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

[tex]\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}[/tex]

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

[tex]\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}[/tex]

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

[tex]\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u][/tex]where u represents any function other than a variable

For the first term, replace [tex]\text{t}[/tex] with [tex]2x[/tex], and apply the chain rule to the function. Do the same for the second term; replace

[tex]\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)[/tex]

Simplify the expression by distributing [tex]2[/tex] and [tex]2x[/tex] inside their respective parentheses.

[tex][-(8x^2 +2)] + (2x^5 + 2x)[/tex] [tex]-8x^2 -2 + 2x^5 + 2x[/tex]

Rearrange the terms to be in order from the highest degree to the lowest degree.

[tex]\displaystyle2x^5-8x^2+2x-2[/tex]

This is the derivative of the given integral, and thus the solution to the problem.

Identify the graph that displays the depth of water in a swimming pool after the drain is opened.

Answers

Answer:

option b is the answer because if we open drain then depth of water will decrease continuously with time and in option b graph it is clearly visible that depth and time are inversely proportional to each other so if time increases then depth of water decrease.

Answer:

Step-by-step explanation:

Evaluate 32 divided by 1.6
show work long division