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3 years ago

5

The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more t

han the width, x, which interval can be the possible widths?

1 answer:

Margarita [4]3 years ago

6 0

X(x+18) <= 175
<span>x^2+18x-175 <= 0 </span>
<span>(x+25)(x-7) <= 0 </span>
<span>So, -25 <= x <= 7 </span>
<span>Or, for real-world tables, </span>

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A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

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2 years ago

The least common multiple of two numbers is 60, and one of the numbers is 7 less than the other number. What are the numbers? Ju

Aleks [24]

To do this we need to find the factors of 60 these are:
1 and 60
2 and 30
3 and 20
4 and 15
5 and 12
6 and 10
There is 1 pair that have a difference of 7 and that is 5 and 12

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3 years ago

Is the variable qualitatie or quantitive? Distance in miles to nearest school.

Naddik [55]

<span>It's quantitative, you can measure it by a specific quantity, which is the number of miles. If it was qualitative, you would be measuring how uncomfortable the ride to the nearest school is.</span>

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3 years ago

A = 12 cm, b = 15 cm, and c = 6 cm<br> whats the area?

elena-s [515]

Answer:

1080

Step-by-step explanation:

just multiply all the numbers to get the area of the whole shape.

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3 years ago

A trapezoid has a base of two and six and an area of 24 square units. What is the height?

Nezavi [6.7K]

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=&\stackrel{bases}{parallel}\\ &sides\\ h=&height\\ \cline{1-2} a=&2\\ b=&6\\ A=&24 \end{cases}\implies 24=\cfrac{h(2+6)}{2}\implies 24=\cfrac{h(8)}{2} \\\\\\ 24=4h\implies \cfrac{24}{4}=h\implies 6=h$

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3 years ago