MATHEMATICS HIGH SCHOOL

Order of operations question

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Answer 1

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Answer:

165 po ang sagot

Kung Hindi po tama sorry

I try my best

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Which two solid figures have the same volume?A. A rectangular solid with a base of 6 cm2 and a height of 12 cm B. An oblique solid with a base of 6 cm2 and a slant height of 12cm C. A cone with a base of 6 cm2 and a height of 12 cm D. An oblique solid with a base of 6 cm2 and a height of 12 cm

. For vectors B⃗ =−iˆ−4jˆB→=−i^−4j^ and A⃗ =−3iˆ−2jˆA→=−3i^−2j^ , calculate (a) A⃗ +B⃗ A→+B→ and its magnitude and direction angle, and (b) A⃗ −B⃗ A→−B→ and its magnitude and direction angle.

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(a) A + B: The result is -4i - 6j, with a magnitude of 2√13 and a direction angle of arctan(3/2).

(b) A - B: The result is -2i + 6j, with a magnitude of 2√10 and a direction angle of arctan(-3).

The given vectors are:

B = -i - 4j

A = -3i - 2j

(a) A + B:

To add two vectors,

Simply add their corresponding components.

So, A + B = (-3i - 2j) + (-i - 4j)

Combining the i-components, we get:

-3i - i = -4i.

And combining the j-components, we get:

-2j - 4j = -6j.

Therefore, A + B = -4i - 6j.

To find the magnitude of A + B,

Use the Pythagorean theorem:

|A + B| = $√((x^2 + y^2))$ ,

Where x is the magnitude of the i-component and y is the magnitude of the j-component.

In this case,

x = -4 and y = -6,

So: |A + B| = $√((-4)^2 + (-6)^2)$

|A + B| = 2√13

To find the direction angle of A + B,

Use the arctan function:

θ = arctan(y / x),

Where y is the j-component and x is the i-component.

In this case,

x = -4 and y = -6,

so: θ = arctan(-6 / -4)

θ = arctan(3/2)

Therefore, the magnitude of A + B is 2√13 and the direction angle is arctan(3/2).

(b) A - B:

To subtract two vectors,

Subtract their corresponding components.

So, A - B = (-3i - 2j) - (-i - 4j).

Combining the i-components, we get:

-3i + i = -2i.

And combining the j-components, we get:

-2j - (-4j) = 2j + 4j = 6j.

Therefore, A - B = -2i + 6j.

To find the magnitude of A - B,

Use the Pythagorean theorem:

$|A - B| = √((x^2 + y^2))$ ,

Where x is the magnitude of the i-component and y is the magnitude of the j-component.

In this case,

x = -2 and y = 6,

so: $|A - B| = √((-2)^2 + 6^2)$

|A - B| = 2√10

To find the direction angle of A - B,

Use the arctan function:

θ = arctan(y / x),

Where y is the j-component and x is the i-component.

In this case, x = -2 and y = 6,

so:

θ = arctan(6 / -2)

θ = arctan(-3)

Therefore,

The magnitude of A - B is 2√10 and the direction angle is arctan(-3).

To learn more about vectors visit:

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The complete question is:

For vectors B =−i −4j and A =−3i −2j ,

Calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.

The resulting vectors after adding and subtracting vectors A and B are A + B = -4i - 6j with a magnitude of 7.21 and A - B = -2i + 2j with a magnitude of 2.83. The direction angle for the vectors are calculated using arctan of the absolute value of the components' ratios.

For vectors B = -i - 4j and A = -3i - 2j, you first need to add and subtract these vectors component-wise to get the resulting vectors. Addition gives A + B = -i + (-3i) + -4j + (-2j) = -4i - 6j, whereas subtraction gives A - B = -3i - (-i) + -2j - (-4j) = -2i + 2j.

The magnitude of a vector is calculated by the Pythagorean theorem: (magnitude of A+B) = sqrt((-4)^2 + (-6)^2) = 7.21 and (magnitude of A-B) = sqrt((-2)^2 + 2^2) = 2.83.

Learn more about Vectors here:

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Victoria needs material for her sewing project. She buys 4.50 yards of material at $4.30 per yard. What is the total cost of the material? You must show your work to receive all possible points. es )

Answers

Answer:

Unit price= $4.30 create equation x= 4.50y

where x= total cost and y= $4.30

solve by multiplying $4.30x 4.50

x=$19.35

final answer: the total cost of the material was $19.35

Step-by-step explanation:

At Noise Pollution Cellular, plan A is $30.00 per month and $5.00 for every gigabyte of data. Plan B is $50.00 per month and $2.00 for every gigabyte of data used. Irfan wants to find out which plan is the best choice for him. On average, he uses five to eight GB of data per month.How much data would Irfan need to use for both plans to cost the same?

Answers

Answer:

Part 1) The best choice is Plan A

Part 2) The data is $6(2)/(3)\ GB$

Step-by-step explanation:

Part 1)

Let

y ----> the cost per month

x ----> the number of GB of data per month

we know that

Plan A

$y=5x+30$

Plan B

$y=2x+50$

Find out which plan is the best choice if he uses five to eight GB of data per month

Plan A

For x=5 GB -----> y=5(5)+30=$55

For x=8 GB -----> y=5(8)+30=$70

with Plan A the cost is between $55 and $70 -----> average $62.5

Plan B

For x=5 GB -----> y=2(5)+50=$60

For x=8 GB -----> y=2(8)+50=$66

with Plan B the cost is between $60 and $66 ----> average $63

therefore

The best choice is Plan A

Part 2) How much data would Irfan need to use for both plans to cost the same?

we have

y=5x+30 ----> equation A

y=2x+50 ----> equation B

Solve the system of equations by elimination

Subtract equation B from equation A

0=5x-2x+30-50

0=3x-20

3x=20

$x=(20)/(3)\ GB$

Convert to mixed number

$x=6(2)/(3)\ GB$ ----> for this data the cost is the same in both plans

In rectangle KLMN, KM =6x + 16, and LM =49. find the value of x

Answers

The rectangle is a figure with opposite sites equal in length.
Also, the diagonals in a rectangle have equal length.
KM and LN are the diagonals and they are equal by definition.
So, we can write the equation: KM=LM
6x+16=49
6x=49-16
6x=33
x=5.5

a jar containing only nickels an dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. What is the number of nickels and dimes in the jar?