A triangular prism was sliced parallel to its base. What is the shape of the Cross section shown in the figure?

H(x)=1/8x^3-x^2<br><br> Over which interval does h have a positive average rate of change?

lara31 [8.8K]

Answer:

$(-\infty,0)\cup(\frac{16}{3},\infty)\\That \ is x\frac{16}{3}$

Step-by-step explanation:

$h(x)=\frac{1}{8}x^{3} -x^{2} \\\\Differentiate \ h(x) \ with \ respect \ to \ x\\h'(x)=\frac{3}{8}x^{2} -2x$

For positive rate of change $h'(x)>0$

$\frac{3}{8} x^{2} -2x>0\\x(\frac{3}{8}x-2)>0\\\\ When \ x0 \ (multiplication \ of \ two \ positives \ is \ positive)\\\\h'(x)>0 \ when \ x\frac{16}{3} \\\\$

6 0

3 years ago

Use the distance formula to calculate the length of the leg CD

Karo-lina-s [1.5K]

To calculate the distance between two points on the coordinate system you have to use the following formula:

$d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}$

Where

d represents the distance between both points.

(x₁,y₁) are the coordinates of one of the points.

(x₂,y₂) are the coordinates of the second point.

To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph

C(2,-1)

D(-1,-2)

Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)

$\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}$

The length of CD is √10 units ≈ 3.16 units

6 0

1 year ago

The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to

Mariana [72]

Answer:

The answer to your question is The cost to raise a child from birth to 17 years in a household is $194119.

Step-by-step explanation:

Equation

y = 1.55x + 110,419

Annual income = $54,000

To solve this problem just substitute the annual income and simplify to find the cost.

y = 1.55(54,000) + 110419

Simplify

y = 83700 + 110419

Result

y = $194119

3 0

3 years ago

What is the circumference of a circle with a radius of eight inches

stira [4]

Answer:

50.24 inches

$\:$

Step-by-step explanation:

It is given that, the radius of a circle is 8 inches and we are to find the circumference of the circle.

$\:$

To find the circumference of the circle we must know this formula first :

$\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Circumference_{(circle)}= 2 \pi r}}}}}} \: \: \bigstar \\ \\$

Where

r is the radius of the circle.

We'll take the value of π as 3.14

Now substituting the values in the formula :

$\\{ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 2 \times 3.14 \times 8}}}}}} \: \: \\ \\$

${ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 3.14 \times 16}}}}}} \: \: \\ \\$

${ \longrightarrow \qquad{ { \pmb{\frak{{ \: Circumference_{(circle)}= 50.24}}}}}} \: \: \\ \\$

Therefore,

The circumference of the circle is 50.24 inches

7 0

2 years ago

Read 2 more answers

Find the lateral area of the regular pyramid<br><br> L.A. =

Arisa [49]

Answer:

FOR REGULAR PYRAMID with those dimension.

L.A = 96

FOR HEXAGONAL PYRAMID with those dimension

L.A = 171.71

Step-by-step explanation:

Please the question asked for L.A of a REGULAR PYRAMID, but the figure is a HEXAGON PYRAMID.

Hence I solved for both:

FOR REGULAR PYRAMID

Lateral Area (L.A) = 1/2* p * l

Where p = Perimeter of base

P = 4s

P = 4 * 6

P = 24cm

l = slanted height

l = 8cm

L.A = 1/2 * 24 * 8

L.A = 1/2 ( 192)

L.A = 96cm ^ 2

FOR AN HEXAGONAL PYRAMID

Lateral Area = 3a √ h^2 + (3a^2) / 4

Where:

a = Base Edge = 6

h = Height = 8

L.A = 3*6 √ 8^2 + ( 3*6^2) / 4

L.A = 18 √ 64 + ( 3 * 36) / 4

L.A = 18 √ 64 + 108/4

L.A = 18 √ 64+27

L.A = 18 √ 91

L.A = 18 * 9.539

L.A = 171.71

8 0

3 years ago