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3 years ago

Find the missing dimension of the cylinder. Round your answer to the nearest hundredth.

Mathematics

1 answer:

ivann1987 [24]3 years ago

6 0

Answer:

The missing dimension, radius = 6.00 m

Step-by-step explanation:

We are given the following things:

Height of cylinder, $h$ = 15 m

Radius of cylinder, $r = z$ m (Labelled as $z$ )

Volume of cylinder, $V = 1696.5\ m^{3}$

Please refer to the image attached for the dimensions of cylinder as given.

We know that the volume of a cylinder can be given as:

$V = \pi r^{2} h$

Where $r$ is the radius of cylinder

$h$ is the height of cylinder

Putting the values of $V, r \text{ and } h$ :

$1696.5 = \pi z^{2} \times 15\\\Rightarrow z^{2} = 36.01\\\Rightarrow z = 6.00\ m$

Hence, The missing dimension, radius = 6.00 m

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How many blocks fill this prism?

zaharov [31]

Answer : 72 blocks

To find the answer, you have to find the volume of the prism. To find the volume you multiply the length, width, and height.

6 x 3 x 4 = 72

This gives you 72 blocks.

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3 years ago

Sandra normally takes 2 hours to drive from her house to her grandparents' house driving her usual speed. However, on one partic

Rudiy27

Answer:

Her usual driving speed is 38 miles per hour.

Step-by-step explanation:

We know that:

$s = \frac{d}{t}$

In which s is the speed, in miles per hour, d is the distance, in miles, and t is the time, in hours.

We have that:

At speed s, she takes two hours to drive. So

$s = \frac{d}{2}$

$d = 2s$

However, on one particular trip, after 40% of the drive, she had to reduce her speed by 30 miles per hour, driving at this slower speed for the rest of the trip. This particular trip took her 228 minutes.

228 minutes is 3.8 hours. So

$0.4s + 0.6(s - 30) = \frac{d}{3.8}$

$3.8(0.4s + 0.6s - 18) = d$

$3.8s - 68.4 = 2s$

$1.8s = 68.4$

$s = 38$

Her usual driving speed is 38 miles per hour.

3 0

3 years ago

A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of material t

Mila [183]

Answer:

The short side is _15___ft and the long side is ___30___ ft.

Step-by-step explanation:

As fence is built in a rectangular area, so we can consider

Let

x be the length of the rectangle

y be width of the rectangle

Given area of rectangle is = 450 ft²

Formula for area of rectangle = Length x width

450 ft² = xy

Solve for y

y = 450/x

now according to given condition

three sides of the fence costs $5 per foot and for the fourth side costs$15 per foot.

We have two condition either the fourth side be x or y

So condition 1: Three sides =(x,y,x) 4-th side = y.

So we can write as 5x,5y,5x and 15 y

Cost C = 5x +5y+5x+15y

= 10x+ 5y+15y

= 5(2x+y) +15y----------------equation 1

= 10x +20y

Adding value of y 450/x

= 10x + 20(450/x)

= 10x + 9000/x

For minimum cost, we can consider the cost to be 0

0 = 10x + 9000/x

Dividing and multiplying by -x/x

0 = -10 +9000/x²

10 = 9000/x²

10x² = 9000/

x²= 900

x = 30

so y = 450/x = 450/30= 15 ft

so adding the values of x and y in equation 1 we will have

cost C= 5(2x+y) +15y----------------equation 1

cost is = 5(2(30)+15) +15(15)

= $600 is the cost

X= 30 y =15

So condition 2: Three sides =(y,x,y) 4-th side = x.

So we can write as 5y,5x,5y and 15 x

Cost C = 5y +5x+5y+15x

= 5x+ 10y+15x

= 5(x+2y) +15x----------------equation 2

= 20x +10y

Adding value of y= 450/x

= 20x + 10(450/x)

= 20x + 4500/x

For minimum cost, we can consider the cost to be 0

0 = 20x + 4500/x

Dividing and multiplying by -x/x

0 = -20 +4500/x²

20 = 4500/x²

20x² = 4500

x²= 4500/20= 225

x = 15

so y = 450/x = 450/15= 30 ft

so adding the values of x and y in equation 2 we will have

cost C= = 5(x+2y) +15x----------------equation 2

cost is = 5(15+2(30) +15(15)

= $600 is the cost

y= 30 x=15

so from both conditions satisfy the cost and the two sides are known as length and width

so dimension will be 15 ft by 30 ft

7 0

2 years ago

PWEASE HELP, AREA OF A TRAPEZOID

sdas [7]

Answer:

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Step-by-step explanation:

4 0

2 years ago

Perform the indicated operation. PLEASEE HELPP HURRYY!! (3 + i) + (5 + 7i) = A) -2 + 6i B) 2 + i C) 8 + 6i D) 8 + 8i

Dovator [93]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{8 + 8i}}}}}$

Option D is the correct option.

Step-by-step explanation:

$\sf{(3 + i) + (5 + 7i)}$

When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign.

That means, the expression remains the same.

Just remove the unnecessary parentheses

⇒ $\sf{3 + i + 5 + 7i}$

Collect like terms and simplify

⇒ $\sf{3 + 5 + i + 7i}$

⇒ $\sf{8 + 8i}$

Hope I helped!

Best regards!!

7 0

2 years ago