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3 years ago

Given the isosceles trapezoid below with an area of 33 units squared find the height of the trapezoid

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

Answer:

Can you retake the picture it blurry

Step-by-step explanation:

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Mr. Gardener invested $500,000. His annual interest was $40,000. What was the annual interest rate?

Archy [21]

Mr. Gardener's annual interest rate is 8%.

40,000/500,000 = 0.08

8 0

3 years ago

What is the slope of the line that passes through 0(-4, 8) and (5, 2)?

zlopas [31]

Answer:

(-8,-4) and (-2,5). at reflect on x axis

4 0

2 years ago

compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.

Nina [5.8K]

$\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$

We have been given two vectors $\vec{a}$ and $\vec{b}$ , we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of $\vec{b}$ onto $\vec{a}$ means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

#SPJ4

3 0

1 year ago

Find the slope of the line that passes through (6, 7) and (2, 10). and simplify if needed thx guys.

tekilochka [14]

Answer:

$-\frac{3}{4}$

Step-by-step explanation:

the equation for finding the slope of a line when given two points is $\frac{y_2-y_1}{x_2-x_1}$ , aka the change in y over the change in x.

pick one of your coordinate pairs to be $y_2\\$ and $x_2$ . it doesn't matter which coordinate pair you choose as long as you keep them as $y_2\\$ and $x_2$ . the remaining coordinate pair will be $y_1$ and $x_1$ .

for this example, i'll use (2, 10) for $y_2\\$ and $x_2$ and (6, 7) for $y_1$ and $x_1$ .

**before i begin, i just want to note that you can do these next four steps in any order that you want. i personally prefer to plug in my y-values first and then my x-values, but you can choose to instead plug in the values of each coordinate pair (like starting by plugging in the coordinate pair (2, 10) with 10 for $y_2\\$ and 2 for $x_2$ ). it's up to you. i'm going to explain the steps by plugging in my y-values first and then my x-values because that's the way i normally do it.

first, start by plugging in the y-value from the coordinate pair of your choosing in for $y_2\\$ . since i chose (2, 10) for $y_2\\$ and $x_2$ , i'll plug in 10 for $y_2\\$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-y_1}{x_2-x_1}$

then plug in the remaining coordinate pair's y-value in for $y_1$ . since the coordinate pair that's left is (6, 7), i will plug in 7 for $y_1$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{x_2-x_1}$

now i'm going to plug in the x-values. i chose (2, 10) to plug in for $y_2\\$ and $x_2$ , so now i'll plug in 2 for $x_2$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{2-x_1}$

and all that's left to plug in is the x-value from (6, 7), so i will plug that in for $x_1$ .

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{10-7}{2-6}$

after plugging in all the values, you have $\frac{10-7}{2-6}$ .

subtract 10 - 7 as well as 2 - 6.

$\frac{10-7}{2-6}$ ⇒ $\frac{3}{-4}$

$\frac{3}{-4}$ cannot be simplified, therefore the slope of the line is $\frac{3}{-4}$ or $-\frac{3}{4}$ .

i hope this helps! have a lovely day <3

7 0

2 years ago

Please help me ASAP

Nonamiya [84]

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3 years ago