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3 years ago

Find the surface area of the rectangular prism

Mathematics

1 answer:

grin007 [14]3 years ago

7 0

Answer:

23 units²

Step-by-step explanation:

height = 2

length = 4

width = 2.5

Formula = 2(wl + lh + hw) ⇒ 2 [(2.5 × 4) + (4 × 2) + (2 ×2.5)] = 23 units²

Hope this helps.

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Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)

Citrus2011 [14]

Answer:

It is 3y = 4x + 10

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

${x}^{2} - xy + {y}^{2} = 7$

introduce dy/dx :

$\frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0$

make dy/dx the subject:

$2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1}$

At point (-1, 2):

$\frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3}$

but a tangent has the same slope as the curve:

$y = mx + c$

m is the slope

c is the y-intercept

At (-1, 2):

$2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3}$

equation:

$y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}$

8 0

3 years ago

Read 2 more answers

Scientific notation pls help me read the instructions

zubka84 [21]

Answer:

Standard Notation -> Scientific Notation

11) 2.2 × 10^1

13) 6.9 × 10^1

15) 6 × 10^-1

17) 1.8 × 10^0

19) 6.14 × 10^1

Scientific Notation -> Standard Notation

1) 0.0894

3) 44.6

5) 3.2

7) 120

9) 4.23

5 0

3 years ago

The population of a town can be represented by the formula P(t) = 67.35 -

Vera_Pavlovna [14]

Answer:

B. -⅜ and 67.35

Step-by-step explanation:

An equation can be given in the slope-intercept form such as y = mx + b, where,

m is the slope and b is a constant which is the y-intercept.

In the case of the formula, P(t) = 67.35 - 3t/8,

The constant, 67.35, in the equation, is the y-intercept (b)

The number multiplying the variable, t, which is -⅜, is the slope (m) of the equation.

Slope = -⅜, y-intercept = 67.35

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4 years ago

Walters weekly take home pay is $354.90, which is 78% of his gross pay (before deductions). what is Walter's weekly gross pay?

Butoxors [25]

$432.978 or $432.98 is the answer

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4 years ago

Does this graph represent a function?

taurus [48]

Yeas it does represent a function

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