Ask question

Ask question

All categories

DanielleElmas [232]

3 years ago

7

The base of a pyramid is a rectangle with a width of 4.6cm and a length of 9cm.What is the height,in centimeters of the pyramid

if it's volume is 82.8cm^3

1 answer:

den301095 [7]3 years ago

4 0

Answer:

Step-by-step explanation:

The formula for determining the the volume of a rectangular base pyramid is expressed as

Volume = 1/3 × base area × height

From the information given,

Length of base = 9 cm

Width of base = 4.6 cm

Area of base = 9 × 4.6 = 41.4 cm²

Volume of pyramid = 82.8cm³

Therefore

82.8 = 1/3 × 41.4 × height

82.8 = 13.8 × height

Dividing both sides of the equation by 13.8, it becomes

height = 82/13.8

Height = 5.94 8 cm

You might be interested in

Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0

3 years ago

which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

sdas [7]

Answer:

Obtuse triangle.

Step-by-step explanation:

Side a = 5

Side b = 2

Side c = 4

Angle ∠A = 108.21° = 108°12'36" = 1.88862 rad

Angle ∠B = 22.332° = 22°19'54" = 0.38976 rad

Angle ∠C = 49.458° = 49°27'30" = 0.86321 rad

Since one angle is above 90 degrees, the triangle is obtuse triangle.

This cannot be an acute triangle.

6 0

3 years ago

A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20

lisabon 2012 [21]

Answer:

30 square feet.

Step-by-step explanation:

We have to find the main area of the rectangle to determine the changes.

We know, Area of a rectangle = Length × Width

Given,

Length = 12 feet

Width = 5 feet

Therefore, the area of the rectangle = (12 × 5) Square feet.

The area of the rectangle = 60 square feet.

Now, if the length of the rectangle increased by 25%, the new length would be = 12 feet (12 feet × 25%) = 12 feet + 3 feet = 15 feet.

If the width increased by 20%, the latest width would be = 5 feet + (5 feet × 20%) = 5 feet + 1 foot = 6 feet.

The new area of that rectangle = (15 × 6) square feet = 90 square feet.

The changes of area from the previous rectangle is = (90 - 60) square feet = 30 square feet.

5 0

3 years ago

If function F is defined by f(x) = 3x^2 + 5, what is f(x-4)

shepuryov [24]

Answer:

The function f(x) when x=x-4 is $f(x-4)=3x^2-24x+53$ or $f(x-4)=3x(x-8)+53$

Step-by-step explanation:

Given function f is defined by $f(x)=3x^2+5$

Now to find the function f(x-4):

$f(x)=3x^2+5$

Put x=x-4 in the above function we get

$f(x-4)=3(x-4)^2+5$

$f(x-4)=3(x^2-2(x)(4)+4^2)+5$ (using the formula $(a-b)^2=a^2-2ab+b^2$ )

$f(x-4)=3(x^2-8x+16)+5$

$f(x-4)=3x^2-24x+48+5$ (adding the like terms)

$f(x-4)=3x^2-24x+53$

$f(x-4)=3x(x-8)+53$

Therefore $f(x-4)=3x^2-24x+53$ or $f(x-4)=3x(x-8)+53$

The function f(x) when x=x-4 is $f(x-4)=3x^2-24x+53$ or $f(x-4)=3x(x-8)+53$

4 0

3 years ago

During the summer, the height of the water in the pool decreased by 5 inches each week due to evaporation. What is the change in

rjkz [21]

Answer:

40 inches

Step-by-step explanation:

We know that the height of water in a pool decreased 5 inches per week.

This means that we can form the equation $y=-5x$ , since the amount of water remaining is proportionate to the amount of weeks that have passed.

We know $x=8$ , since we need to find the change for 8 weeks.

$y = -5\cdot 8$

$-5 \cdot 8 = -40$

$y=-40$

The change will be the absolute value of -40, which just makes it positive, so 40.

Hope this helped!

8 0

3 years ago

Read 2 more answers