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2 years ago

Dominique decided to build his sons a fort in the backyard. He put a roof on the fort in the shape of a triangular prism.

Mathematics

2 answers:

jekas [21]2 years ago

7 0

It should be 216ft^2 (B)

VARVARA [1.3K]2 years ago

4 0

Answer:

B. 216 ft

Step-by-step explanation:

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Differentiate Vx(x + 2) with respect to x.

Travka [436]

Answer:

$y'= \frac{3x+2}{2\sqrt{x} }$

General Formulas and Concepts:

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$y=\sqrt{x} (x+2)$

Step 2: Rewrite

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

Step 3: Differentiate

Product Rule [Basic Power/Chain Rule]: $y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)$
Simplify: $y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}$
Rewrite: $y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}$
Add: $y'= \frac{3x+2}{2\sqrt{x} }$

7 0

3 years ago

Complete the point-slope equation of the line through (-8,-1)(−8,−1)left parenthesis, minus, 8, comma, minus, 1, right parenthes

ratelena [41]

Answer:

- y=(−112)x−52. Explanation: (−10,3) and (−8,−8) The slope of the line between A(x1,y1) and B(x2,y2) is: m=y2−y1x2−x1.

Step-by-step explanation:

4 1

3 years ago

Read 2 more answers

Find the area of the figure, in square meters, to 1 decimal place.

alukav5142 [94]

Answer:

Where is the picture of the figure

Step-by-step explanation:

6 0

3 years ago

F(x) = -7x^2+8x+2f(x)=−7x 2 +8x+2

MaRussiya [10]

Answer:5

Step-by-step explanation:

6 0

3 years ago

The base of 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)

Nina [5.8K]

Given:

The base of 40-foot ladder is 8 feet from the wall.

To find:

How high is the ladder on the wall (round to the nearest foot).

Solution:

Ladder makes a right angle triangle with wall and ground.

We have,

Length of ladder (hypotenuse)= 40 foot

Base = 8 foot

We need to find the perpendicular to get the height of the ladder on the wall.

Let h be the height of the ladder on the wall.

According to the Pythagoras theorem,

$Hypotenuse^2=Base^2+Perpendicular^2$

$(40)^2=(8)^2+(h)^2$

$1600=64+h^2$

$1600-64=h^2$

$1536=h^2$

Taking square root on both sides.

$\pm \sqrt{1536}=h$

$\pm 39.1918358=h$

Height cannot be negative. Round to the nearest foot.

$h\approx 39$

Therefore, the height of the ladder on the wall is 39 foot.

5 0

3 years ago