General house cleaning (sweeping the floors, vacuuming, laundry etc.)

The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of

Dovator [93]

Answer:

The height of the cone is 10.9 cm

Step-by-step explanation:

step 1

Find the height of the cone

Applying the Pythagoras Theorem

$12^{2}=5^{2}+h^{2}$

$144=25+h^{2}$

$h^{2}=144-25$

$h^{2}=119$

$h=10.9\ cm$

therefore

The height of the cone is 10.9 cm

6 0

3 years ago

What divides each median into two sections at a 2:1 ratio? Question 6 options: a) circumcenter b) incenter c) centroid d) orthoc

allochka39001 [22]

Answer:

C. Centroid

Step-by-step explanation:

The circumcenter is the center of a triangle's circumcircle (circumscribed circle over triangle). It can be found as the intersection of the perpendicular bisectors.

The incenter is the center of the incircle (inscribed circle into a triangle) of a triangle. The incenter can be constructed as the intersection of angle bisectors.

Centroid is the point where the three medians of the triangle intersect.

The intersection of the three altitudes of a triangle is called the orthocenter.

Since three medians intersect at point which divides each median into 2:1 ratio, the answer is centroid.

6 0

3 years ago

Read 2 more answers

Someone help me solve please !!

Tresset [83]

Answer:

-2.9

Step-by-step explanation:

It's in the picture.

3 0

3 years ago

A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

3 years ago

Mr Ahmad bought 2 fans and 3 table lamps for $540. Each fan cost 3 times as much as a table lamp. (a) Find the cost of each tabl

sergey [27]

Answer:

(a) $60

(b) $180

Step-by-step explanation:

Let the price of 1 table lamp be t.

Then the price of a fan is 3t.

2(3t) + 3t = 540

6t + 3t = 540

9t = 540

t = 60

A table lamp costs $60.

3($60) = $180

A fan costs $180.

4 0

2 years ago