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2 years ago

Which mathematical statement matches the vector operation shown in the geometric representation?

Mathematics

2 answers:

statuscvo [17]2 years ago

8 0

1. B. (1/3, -1)

2. C. (3,9)

3. A. (-1,-3)

4. A. (5, 15)

5. A v+w=u

Sunny_sXe [5.5K]2 years ago

7 0

Answer:

First Option $v+w = u$

Step-by-step explanation:

To graphically add two vectors a and b using the -tail and tip-method, you must draw the tail of b at the tip of the vector a. Then you must draw a line that goes from the tail of a to the tip of b. This line represents the sum of $a + b$ .

In this problem, notice that the tail of the vector w is on the tip of the vector v. The line that joins the tail of v with the tip of w is u.

Therefore we can say that $v + w = u$ .

The answer is the first option

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While Flinn was starting the fire, his friends were collecting firewood. Flinn has 5 sticks. If he puts 3 sticks in the fire eve

fomenos

Answer:

Time required to make a pile of 45 sticks next to their fire = 10 minutes

Step-by-step explanation:

This is an example of arithmetic progression.

First term = 5 - 3 + 7 = 9 sticks

Common difference = 7 - 3 = 4 sticks.

So the number of sticks next to their fire is increasing like this

9, 13, 17, 21 .............

$n^{th}$ term of AP = a + (n-1) d, we need to find n

a + (n-1) d = 45

9 + (n-1) x 4 = 45

(n-1) x 4 = 36

n - 1 = 9

n = 10

Time required to make a pile of 45 sticks next to their fire = 10 minutes

4 0

2 years ago

Read 2 more answers

Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much al

eimsori [14]

If it doubles every 4 hours, in 12 hours you will have 3 doublings.
2 * 2 * 2 = 8
90*8 = 720 pounds of algae

7 0

2 years ago

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

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

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

5 0

2 years ago

Read 2 more answers

Three teachers equally shared StartFraction 4 Over 5 EndFraction of a flat of paper that was donated to the school. What fractio

melisa1 [442]

Answer:

$Each = \frac{4}{15}$

Step-by-step explanation:

Given

$Fraction = \frac{4}{5}$

$Teachers = 3$

Required

Determine fraction of each teacher

Each fraction is calculated by dividing total fraction by number of teachers as follows:

$Each = \frac{Fraction}{Teachers}$

$Each = \frac{4}{5}/3$

$Each = \frac{4}{5} * \frac{1}{3}$

$Each = \frac{4}{15}$

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2 years ago

Halle has 36 feathers, 48 acorns, and 60 agates. She wants to put all of these items into bowls with the same number of feathers

sweet-ann [11.9K]

12 Because 36, 60, and 48 are all dividable by 12. Or, it can also be 6, or 2.

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2 years ago