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3 years ago

Please help and please no links..thanks ¯\_(ツ)_/¯

Mathematics

2 answers:

Agata [3.3K]3 years ago

5 0

Answer:

c / 4 + 5 = 7

Hope this helps!

Step-by-step explanation:

5 + ( more ) than the quotient ( division ) of a number and ( + ) 4 is ( = ) 7

5 + c / 4 = 7

c / 4 + 5 = 7

IrinaVladis [17]3 years ago

3 0

Answer:

$\frac{c}{4} +5 = 7$

Step-by-step explanation:

The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:

$\frac{c}{4} +5 = 7$

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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:

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

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

6 0

3 years ago

Find the differential dy for y =cos(pix) and evaluate it x=1/3 and dx=-.02 and round your results to 3 decimal places.

finlep [7]

Dy / dx = - Pi sin (Pix), so dy = - Pi sin (Pix) dx, for x = 1/3, and dx = -0.2
we get dy = - Pi x sin Pi/3 x (-0.2) = 3.14 x 0.2 x 0.86=0.543

6 0

3 years ago

How do i write and solve for this inequality

ExtremeBDS [4]

9514 1404 393

Answer:

-7/4 < x < 8

Step-by-step explanation:

The value of y can be determined from the sum of the angles, so you know each of the angles exactly. That means you know the ratio of side lengths exactly, which lets you solve for x exactly.

Setting that aside, we observe that angle C is greater than angle A, so side AB will be longer than side BC.

3x +15 > 4x +7

8 > x . . . . . . . . . . subtract 3x+7

We also know that the lengths of these sides must be positive. Since BC is the shorter side, we require ...

4x +7 > 0

4x > -7

x > -7/4

So, the allowable values of x are ...

-7/4 < x < 8

_____

<em>More complete solution</em>

If we read the figure correctly, the sum of angles is ...

(2y +12) +(4y +12) +(y -18) = 180

7y +6 = 180

y = (180 -6)/7 = 24 6/7°

Then (in degrees) ...

∠A = 2(24 6/7) +12 = 61 5/7, and ∠C = 4(24 6/7) +12 = 111 3/7

The Law of Sines tells us ...

AB/sin(C) = BC/sin(A)

sin(A)(3x +15) = sin(C)(4x+7)

x(4sin(C) -3sin(A)) = 15sin(A) -7sin(C)

x = (15sin(A) -7sin(C))/(4sin(C) -3sin(A))

x ≈ 6.1872652

4 0

3 years ago

Which of the following methods would be the easiest to use to solve x2 + 5x – 6 = 0?

EastWind [94]

For me personally, the easiest way to do this is by isolating the x² term, and finding the square root of both sides. The hardest way (well actually, the longest way) would be to use the quadratic formula. It just complicates things unnecessarily.

5 0

3 years ago

Which of the following is the solution to the equation 25(z − 2) = 125? (6 points)

makvit [3.9K]

Answer:

z=7

Step-by-step explanation:

25(−2)=125

25−50=125

3 0

3 years ago