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3 years ago

3

Explain the difference between finding the volume of this right rectangular prism with whole unit cubes and with 1/2 -unit cubes

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Pls do not give me a bad answer

1 answer:

pogonyaev3 years ago

5 0

Finding volume by multiplying

Finding volume with unit cubes

you take base one and mulitiply it by the number its beside. then multiply by the height

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What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

7 0

3 years ago

Evaluate x2/y + x2/z for x = 6, y = -4, and z = -2.<br> -27<br> -9<br> 9<br> 27

Orlov [11]

<h2>Answer:</h2>

The value of the given expression is -27.

<h2>Given: </h2>

$\frac{x^{2}}{y}+\frac{x^{2}}{z}$

<h2>Step-by-step explanation: </h2>

In this problem, we need to solve the given expression in which we need to find the values of the variables. Since, the values of the variables are given, we can substitute the values and solve the equation as numerical calculation.

On substituting the values,

$\Rightarrow \frac{x^{2}}{y}+\frac{x^{2}}{z}=\frac{(6)^{2}}{-4}+\frac{(6)^{2}}{-2}$

On squaring the values in the numerator,

$\Rightarrow \frac{x^{2}}{y}+\frac{x^{2}}{z}=-\frac{36}{4}-\frac{36}{2}$

On cancelling the numerator and denominator,

$\Rightarrow \frac{x^{2}}{y}+\frac{x^{2}}{z}=-9-18$

On adding,

$\Rightarrow \frac{x^{2}}{y}+\frac{x^{2}}{z}=-27$

7 0

3 years ago

This is a little difficult for me! Can someone explain?

ch4aika [34]

Answer:

We can write sin 21° as 1200 / x and also 0.36 so we can write:

1200 / x = 0.36

1200 = 0.36x

x = 1200 / 0.36

x ≈ 3333 ft

5 0

4 years ago

Find the slope and y-intercept of the graph of x-2y = 4.

lions [1.4K]

Answer:

The slope is 1/2 and the y - intercept is (0, -2)

Step-by-step explanation:

Use the slope - intercept form y = mx + b to find the slope m and y - intercept b .

6 0

3 years ago

Work out the value of x

Korvikt [17]

Answer:

117 degrees

Step-by-step explanation:

So we already know that one angle is 38 degrees, so we have that one. The angle, 101 is exterior, and we have to subtract 180 from that to get the interior angle. We get a difference of 79. Since the sum of a triangle's interior angles are 180, we have to add 38+79 to get 117. Then, we have to subtract it from 180 to get the value of the interior angle as 63 degrees. Because x is on the outside, we have to again subtract 63 from 180 to get the missing value of x as 117.

6 0

3 years ago

Read 2 more answers