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4 years ago

Using two or more complete sentences, describe how you can find a vector parallel to b=-2,3

Mathematics

1 answer:

Romashka-Z-Leto [24]4 years ago

8 0

Answer:

The answer is not unique.

$^{\rightarrow}_a=\binom{-6}{9}$

is a possible correct answer

Step-by-step explanation:

Two vectors are parallel if one is a scalar multiple of the other.

The given vector is $^{\rightarrow}_b=\binom{-2}{3}$

To find another vector that is parallel to $^{\rightarrow}_b=\binom{-2}{3}$ , we multiply by any non-zero scalar not equal to 1, to obtain;

$^{\rightarrow}_a=3^{\rightarrow}_b$

This implies that;

$^{\rightarrow}_a=3\binom{-2}{3}$

$^{\rightarrow}_a=\binom{-6}{9}$

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A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

Area of the field with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the same perimeter, but change the area, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the longest side of the rectangle while width is the shorter side. Therefore, we should choose:

decrease the width and increase the length by the same amount.

Define the variables:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

Example 1:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

Example 2:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

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2 years ago

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What is the expeson of allen is shipping a gift to his cousin. the gift weighs 4 pounds. the box and shipping materials weigh 9

inn [45]

The answer is 73 ounces. the gift weights 64 ounces ( 4 pounds ) alone and 64+9=73. *1 pounds = 16 ounces

4 0

3 years ago

Will mark as brainliest if correct

stepladder [879]

Answer:

1.2

Step-by-step explanation:

5*1.2=6

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4 years ago

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Is this the right answer!! :)

beks73 [17]

Answer:

Option D). Quadrant V is the correct answer.

Step-by-step explanation:

Your answer is correct.

Hope this helps!

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Kevin is designing a logo in the shape of a trapezoid for his company. The longer of the two parallel sides is twice as long as

satela [25.4K]

P = distance all around

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3 years ago