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Evgesh-ka [11]
2 years ago
7

Solve for 3/4u = 12 . Simplify your answer as much as possible.

Mathematics
1 answer:
Wittaler [7]2 years ago
6 0

Answer:

u = 16

Step-by-step explanation:

Given

\frac{3}{4} u = 12

Multiply both sides by 4 to eliminate the fraction

3u = 48 ( divide both sides by 3 )

u = 16

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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

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3 0
1 year ago
A bank loaned out $8200, part of it at a rate of 7.9% per year and the rest of it at a rate of 7.4% per year. The total amount o
Lady bird [3.3K]

The amount that the bank loaned out at 7.9% is $1,574.00

How do represent the amounts lent at different rates?

On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate

interest on 7.9% loan=7.9%*x=0.079x

interest on 7.4% loan=7.4%*(8200-x)

interest on 7.4% loan=606.80-0.074x

total interest=0.079x+606.80-0.074x

total interest=0.005x+606.80

total interest on loans=614.67

614.67=0.005x+606.80

614.67-606.80=0.005x

7.87=0.005x

x=7.87/0.005

x=amount loaned at 7.9%=$1,574.00

y=$8200-$1574

y=$6,626.00

Find out more about bank loan interest rate on:brainly.com/question/20796174

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3 0
1 year ago
Please help me with these two following questions ( second question has answer choices ) Thanks!
Nitella [24]
B. i hope this helps

3 0
3 years ago
Read 2 more answers
A line passes through (5,3) with a slope of 3/5. Plot 3 points on this line
Aneli [31]

Answer:

y=3/5*x, A(0,0), B(1,3/5), C(2,6/5)

Step-by-step explanation:

A(5,3)=(x1,y1)....x1=5, y1=3

m=3/5

y-y1=m(x-x1)

y-3=3/5(x-5)

y-3=3/5*x-3/5*5

y-3=3/5*x - 3

y=3/5*x-3+3

y=3/5*x

x=0, y=3/5*x, y=3/5*0=0 A(0,0)

x=1, y=3/5*1=3/5 B(1,3/5)

x=2, y=3/5*2=6/5 C(2,6/5)

3 0
3 years ago
SOMEONE I NEED HELP PLEASE! ITS BEEN 10 HOURS NO ANSWER PLEASE HELP ME! CAN YOU SOLVE THIS PLEASE?
Leokris [45]
Mean

7 days
add them up and divide by 7
50+56+52+46+48+42+38=332
divide that by 7
47.428 about

distance each is from the mean
50 is 2.572 from it
56 is 8.572 from it
52 is 4.572 from it
46 is 1.428 from it
48 is 0.562 from it
42 is 5.428 from it
38 is 9.428 from it

add those and average them
(2.572+8.572+4.572+1.428+0.562+5.428+9.428)/7=4.652

absolute deviation is 4.652 aprox


6 0
3 years ago
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