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2 years ago

Evaluate ab - c. If a = 5, b = 3, and c = 4

Mathematics

2 answers:

irina1246 [14]2 years ago

5 0

The answer is 11 The answer is 11 The answer is 11

Orlov [11]2 years ago

4 0

Answer:

Step-by-step explanation:

1st lets plug in ur numbers into the variables

ab - c

5(3) - 4

i put parenthesis because it means multiplication

5 * 3 = 15

15 - 4 = 11

11 is your answer!

High Hopes^^

Barry-

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A hamster wheel has a diameter of 8.5 in. How many inches does the hamster run in one revolution? Use 3.14 to approximate for π

Ahat [919]

As hamster wheel is circular so for revolution we will find the circumference.

Diameter of the Hamster wheel = 8.5 in

One revolution of the wheel = circumference of the wheel

Circumference = π × d

π = 3.14 and d = 8.5

So, Circumference = 3.14 × 8.5

Circumference = 26.69 in

So in one revolution the hamster wheel travels a distance of 26.69 in

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3 years ago

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The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (

kow [346]

Answer:

$\|a\| = 5\sqrt{13}$ .

$\|b\| = 3\sqrt{29}$ .

Step-by-step explanation:

Let $m$ , $n$ , and $k$ be scalars such that:

$\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}$ .

$\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}$ .

$\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}$ .

The question states that $\| a + b \| = 34$ . In other words:

$k\, \sqrt{8^{2} + 15^{2}} = 34$ .

$k^{2} \, (8^{2} + 15^{2}) = 34^{2}$ .

$289\, k^{2} = 34^{2}$ .

Make use of the fact that $289 = 17^{2}$ whereas $34 = 2 \times 17$ .

$\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}$ .

$k^{2} = 2^{2}$ .

The question also states that the scalar multiple here is positive. Hence, $k = 2$ .

Therefore:

$\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}$ .

$(a + b)$ could also be expressed in terms of $m$ and $n$ :

$\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}$ .

$\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}$ .

Equate the two expressions and solve for $m$ and $n$ :

$\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}$ .

$\begin{cases}m = 5 \\ n = 3\end{cases}$ .

Hence:

$\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}$ .

$\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}$ .

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2 years ago

HELP! DUE AT 5 PM!! 10 BRAINLIST!<br><br> 3x -15x - 30 > 54

ryzh [129]

Answer:x<-7

Step-by-step explanation:

3x -15x - 30 > 54

-12x-30>54

-12x<54+30

I moved 30 from left side to right which becomes positive and > becomes <

-12x<84

-12x/-12<84/-12 I used my calculator to do this

x<-7

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The answer is 50 degrees

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dezoksy [38]

Answer:

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Step-by-step explanation:

3n-6=33

Add 6 to both sides

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Divide both sides by 3

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2 years ago

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