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2 years ago

How long is a distance of 8 km if measured on a map with a scale of 1:50,000

1 answer:

6 0

Since this is a ratios and proportions problem, you would set up the equation like this:
1/50,000 = x/8 x is the length of the distance on the map

After that, you cross multiply and you will get 50,000x=8
You then solve for x to get 0.00016

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An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units. An oblique c

Vilka [71]

Answer:

The radius of the cone is 3 units

Step-by-step explanation:

An oblique cone is a kind of slanted cone. It is a figure such that the tip of the cone is not directly over the center of the circular base of the cone.

While the method for calculating the area of an oblique and a right-circular cone is different, the method for calculating the volume is the same

Mathematically, the volume of an oblique cone = 1/3 * pi * r^2 * h

in this question, we have the height and the volume but we want to calculate the radius

substituting the value for the volume, the height and radius( radius is half diameter = 2x/2 = x) we have

18 pi = 1/3 * pi * x^2 * 2x

divide through by pi

18 = 1/3 * 2x * x^2

54 = 2x^3

divide both sides by 2

x^3 = 54/2

x^3 = 27

x = cube root of 27

x = 3 units

This is the length of the radius

6 0

2 years ago

In a given course a student receives preliminary examination grades of 81, 85, and 95. The final examination is weighed for one-

Vsevolod [243]

Answer:

B. 96

Step-by-step explanation:

Let x represent score of final third exam.

We have been given that in a given course a student receives preliminary examination grades of 81, 85, and 95.

Let us find average of preliminary scores.

$\frac{81+85+95}{3}=\frac{261}{3}=87$

We have been given that the final examination is weighed for one-third and the average of the preliminary grades is weighed as 2/3 of the final grade. This means that final grade is equally weighed into 3 parts. The two parts are 87 each and third part is x.

Using our given information, we can set an equation as:

$\frac{87+87+x}{3}=90$

$\frac{174+x}{3}=90$

$\frac{174+x}{3}*3=90*3$

$174+x=270$

$174-174+x=270-174$

$x=96$

Therefore, the final examination grade should be 96 for a semester average of 90.

4 0

2 years ago

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27

densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

$y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Step-by-step explanation:

Vertex form of equation : $f (x) = a(x - h)^2 + k,$ where (h, k) is the vertex of the parabola.

$y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Hence, the vertex form of the equation is $y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

8 0

2 years ago

Read 2 more answers

Find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the

11Alexandr11 [23.1K]

Answer:

Here is the continuation to the question ; The buoyant force is the difference between the fluid forces on the top and bottom of the solid. (The weight-density of water is 62.4 pounds per cubic foot.)

Hence, bouyant force is calculated as = 11980.8lb

Step-by-step explanation:

The steps are as shown in the attachment.

3 0

2 years ago

Darcie wants to crochet a minimum of 3 blankets blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a

bearhunter [10]

Answer:

The inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal is:

$s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

Step-by-step explanation:

Question

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Given:

Darcie has a target to crochet a minimum of 3 blankets.

Rate at which Darcie crochets = $\frac{1}{15}$ of a blanket per day.