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4 years ago

Help me pls i’ll give you a kiss

Mathematics

1 answer:

Likurg_2 [28]4 years ago

3 0

Answer: 152.46 squared centimeters.

Step-by-step explanation:

The equation to find the area of the trapezoid is A = ½ (6.6 + 16.5) 13.2
Distribute ½ into (6.6 + 16.5) . A = (3.3 + 8.25) 13.2.
Add the numbers inside the parenthesis. A = 11.55 * 13.2
Multiply 11.55 * 13.2. A = 152.46.

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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

Which of the following functions illustrates a change in amplitude?

OLEGan [10]

Answer:

Correct option is A.

Step-by-step explanation:

Given the following functions we have to choose the option which illustrates a change in amplitude.

Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.

Option A: y = 3cos4x

The parent function is f(x) = cos x.

The amplitude of function changes from 1 to 3.

Option B: y = 1+sinx

The parent function is f(x) = sin x

The amplitude remains same i.e 1

Option C: y = -2-cos(x - pi)

Here also remains same.

Option D: y = tan 2x

The tangent function does not have an amplitude because it has no maximum or minimum value.

Hence, correct option is A.

7 0

4 years ago

Read 2 more answers

What is y <-x+2 on a graph???

sertanlavr [38]

Tada! Hope that helps. :)

3 0

3 years ago

4/5 + 3/4 =

marshall27 [118]

The topics you should learn are equating denominators and fractions. This is summing up simple fractions.

So we have to make denominators' numbers the same in order to sum up them all (we can sum fractions if the denominators are the same) , and we did it by cross product (that thing on the picture)

Equating by lcm (least common multiple) is the easiest way, because you might see bigger numbers on other questions, and cross product will bring much bigger numbers, so this technic might confuse you.

By the way lcm of 4 and 5 is already 20

Hope it helps!

5 0

3 years ago

(10 POINTS AND BRAINLIEST FOR BEST)

kramer

Answer:

4 + -6

Step-by-step explanation:

There are four positive counters, and there are 6 negative counters in a group. So I came to the conclusion they are being added.

4 + -6

Hope this helped.

LunarRose3

5 0

4 years ago