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3 years ago

Solve for k : 62=13k-3

1 answer:

4 0

$62=13k-3$

$62+3=13k

$ $\text{Add 3 to both sides}$

$65=13k
$

$65 \div 13 = k$ $\text{Divide both sides by 13}$

$k=5$ $\text{Solution}$

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find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

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2 years ago

Can i have help on this q plz

Alexandra [31]

Answer:

14.8

Step-by-step explanation:

7.4 * 2 = 14.8.

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2 years ago

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In a theater, there are 4 long rows of chairs,each with an equal number of chairs There are 5 ahort rows of chairs,each with an

Hoochie [10]

<span>There are 4 long rows and 5 short rows in the theater. x represents the number of chairs in each long row and y represents the number of chairs in each short row.

So, total number of chairs in 4 long rows= 4x
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When 2 chairs are added to each long row, the number of chairs will change to (x+2).
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So, total number of chairs in 5 short rows will be = 5(y+3)

Thus, total number of chairs in the theater in rush day = 4(x+2) + 5(y+3)
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Thus we can say the number of chairs increase by 23 as compared to a normal day.
</span>

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In terms of rigid transformations (reflections, rotations, and translations), what does this difference represent?

makvit [3.9K]

Solution:

There are four kinds of rigid transformations.

1. Reflection

2. Rotation

3. Translation

4. Dilation

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2. Rotation means rotating an object or geometrical shape through an angle. An angle can be of any measure that is 0,30°,45°,90°,...... In rotation the two , image and preimage are congruent.

3. While in translation , we shift something from a place to another place keeping the two images,that is image and preimage are congruent.

In all three,either in reflection, rotation,or translation there is no change in shape and size, the two that is image and Preimage are congruent.

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alukav5142 [94]

Answer:

I think the other angles are 40 degrees excpet the "x" which is 100 also

Step-by-step explanation:

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