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3 years ago

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Which components are a possible representation of vector u if ||-4u|| ≈ 14.42?

1 answer:

Firdavs [7]3 years ago

3 0

Answer:

Step-by-step explanation:

Check for each vector

$u=\\4u=\\||4u||=\sqrt{12^2+8^2}\\=\sqrt{208} \\=14.42$

Hence this is the required vector.

$u=\\4u=\\||4u||=\sqrt{4^2+16^2}=16.49$

$u=\\4u=\\||4u||=\sqrt{8^2+8^2}=11.31$

$u=\\4u=\\||4u||=\sqrt{8^2+16^2}=17.889$

Hence required vector $=$

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A racquetball club charges $10 for a one-month trial membership. After the trail month, the regular membership fee is $12 per mo

Furkat [3]

Membership is discounted $2 for first month
c=cost of one month
d=discount=$2
x=# of months
xc - 2= total cost
x for 1 month is 1, c is always 12, -2 is constant
1 x(12) - 2=10 for first month
8 months
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5 0

3 years ago

i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

2 years ago

they hold an anual pass that cost $40.00. each canoe rental costs $26.00 and each bicycle rental cost $15.00. use an algebraic e

postnew [5]

Answer:

Cost = 40.00 + 26.00c + 15.00b

Step-by-step explanation:

Let c = number of canoe rentals

and b = number of bicycle rentals. Then

Annual pass = 40.00

Canoe rentals = 26.00c

Bicycle rentals = 15.00b

Total cost = 40.00 + 26.00c + 15.00b

6 0

3 years ago

Find the measure of each angle indicated. Round to the nearest tenth.

Sladkaya [172]

Answer:

D

Step-by-step explanation:

So we want to find<em> θ. </em>We are already given the hypotenuse and the side length opposite to <em>θ. </em>Therefore, we can use the trig function sine to find <em>θ. </em>

Recall that:

$\sin(\theta)=opp/hyp$

Plug in 10.2 for the opposite side and 15 for the hypotenuse:

$\sin(\theta)=10.2/15$

Solve for <em>θ. </em>Use a calculator:

$\theta=\sin^{-1}(10.2/15)\\\theta\approx42.8436\textdegree$

The answer is D.

5 0

2 years ago

3 more than a number x

balu736 [363]

X+3 is the answer.zz

5 0

2 years ago

Read 2 more answers