−8/9 ⋅ 5/6 What is the product in simplest form? Fractions btw

Anika [276]

The change would start off as a negative and end as a positive she would end up with $425

3 0

3 years ago

For an activity in class, students used pieces of string to measure roads on a map. They used a map scale to determine the

Elina [12.6K]

Answer:

The real-life distance to the nearest mile between Tampa and Orlando is 88 miles

Step-by-step explanation:

String distance between Fort Myers and Miami = 7 inches

A real life distance between Fort Myers and Miami = 154 miles

So, 7 inches = 154 miles

$1 inch = \frac{154}{7}=22 miles$

Scale : 1 inch = 22 miles

String distance between Tampa and Orlando = 4 inches

Using scale

The real-life distance to the nearest mile between Tampa and Orlando = $4 \times 22 = 88 miles$

Hence The real-life distance to the nearest mile between Tampa and Orlando is 88 miles

6 0

3 years ago

Find the missing measure for a right circular cone TA is 12 pi and LA is 8 pi

salantis [7]

Answer:

The radius of the base of the cone is 2 units

The slant height of the cone is 4 units

The height of the cone is 2√3 units

The volume of the cone is $\frac{8\sqrt{3}\pi}{3}$ units³

Step-by-step explanation:

* Lets revise the total surface area and the lateral area of a cone

- The lateral area of cone = π r l , where r is the radius of the base

and l is the slant height of the cone

- The surface area of the cone = π r l + π r², where π r l is the lateral

area and π r² is the base area

- The cone has three dimensions radius (r) , height (h) , slant height (l)

- r , h , l formed right triangle, r , h are its legs and l is its hypotenuse,

then l² = r² + h²

- The volume of the con = $\frac{1}{3}$ (π r² h)

* Now lets solve the problem

- We will use the total area to find the radius of the base

∵ TA = 12π

∵ TA = LA + πr²

∵ LA = 8π

- Substitute the value of the lateral area in the total area

∴ 12π = 8π + π r² ⇒ subtract 8π from both sides

∴ 12π - 8π = π r²

∴ 4π = π r² ⇒ divide both sides by π

∴ r² = 4 ⇒ take square root for both sides

∴ r = 2

* The radius of the base of the cone is 2 units

- We will use the lateral area to find the slant height

∵ LA = π r l

∵ LA = 8π

∵ r = 2

∴ π (2) l = 8π ⇒ divide both sides by π

∴ 2 l = 8 ⇒ divide both sides by 2

∴ l = 4

* The slant height of the cone is 4 units

- Use the rule l² = r² + h² to find the height of the cone

∵ r = 2 and l = 4

∵ l² = r² + h²

∴ (4)² = (2)² + h²

∴ 16 = 4 + h² ⇒ subtract 4 from both sides

∴ 12 = h² ⇒ take square root for both sides

∴ h = √12 = 2√3

* The height of the cone is 2√3 units

∵ The volume of the con = $\frac{1}{3}$ (π r² h)

∵ r = 2 and h = 2√3

∴ V = $\frac{1}{3}$ (π × 2² × 2√3) = $\frac{1}{3}$ (π × 4 × 2√3) = $\frac{1}{3}$ (π × 8√3)

∴ V = $\frac{8\sqrt{3}\pi}{3}$

* The volume of the cone is $\frac{8\sqrt{3}\pi}{3}$ units³

4 0

4 years ago

Help please!!!!!!!!!!!!!!!!!!!!!!!!!

slava [35]

The answer is -5.
Steps:
1. I multiplied the top equation by 2 and the bottom equation by 3 and then added them together.
2. 24x=72 is what you should have now. I divided each side by 24 to get x=3.
3. I plugged 3 in for x in one of the equations to get y=-8.
4. -8+3=-5.

4 0

4 years ago

The speed of a tidal wave in meters/second is given by the square root of the product of the acceleration due to gravity on Eart

fredd [130]

Answer:

70 m/s

Step-by-step explanation:

"The speed of a tidal wave in meters/second is given by the square root of the product of the acceleration due to gravity on Earth (9.8 meters/second2) and the depth of the ocean in meters":

The sentence above can be interpreted into the equation shown below (letting speed of tidal wave be "s", acceleration due to gravity be "g", and depth be "d"):

$s=\sqrt{g*d}$

Given d = 500 and g = 9.8, we find speed (s):

$s=\sqrt{g*d} \\s=\sqrt{(9.8)*(500)} \\s=\sqrt{4900}\\ s=70$

Hence, the speed is 70 meters per second.

6 0

3 years ago