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3 years ago

Write the point-slope form of the equation with the given characteristics.

Mathematics

1 answer:

Neporo4naja [7]3 years ago

3 0

Answer:

1. y = 2x+3

2. y= -2x-1

3. y=3/5 x +3

4. y = 1/2 x 23/2

Step-by-step explanation:

1. Use slope intercept, y=mx+b where m =2 and b=3. y=2x+3

2. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.

(y-5)=-2(x--3)

y-5=-2(x+3)

y=-2x-6+5

y=-2x-1

3. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope is 3/5 since parallel lines have the same slope.

(y-3)=3/5(x-0)

y-3=3/5 x

y=3/5 x +3

4. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope is 1/2 since perpendicular lines have the negative reciprocal slopes. So -2 becomes 1/2.

(y-10)=1/2(x--3)

y-10=1/2 (x+3)

y-10 = 1/2 x + 3/2

y = 1/2 x 23/2

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Question 15 (5 points)<br> Find the angle between u = <7, -2> and v= (-1,2>.

Tema [17]

Answer:

Approximately $2.3127$ radians, which is approximately $132.51^{\circ}$ .

Step-by-step explanation:

Dot product between the two vectors:

$\begin{aligned}& u\cdot v \\ =\; & 7 \times (-1) + (-2) \times 2 \\ =\; & (-11) \end{aligned}$ .

Magnitude of the two vectors:

$\begin{aligned} \| u \| &= \sqrt{{7}^{2} + {(-2)}^{2}} \\ &= \sqrt{53} \end{aligned}$ .

$\begin{aligned} \| v \| &= \sqrt{{(-1)}^{2} + {2}^{2}} \\ &= \sqrt{5} \end{aligned}$ .

Let $\theta$ denote the angle between these two vectors. By the property of dot products:

$\begin{aligned} \cos(\theta) &= \frac{u \cdot v}{\|u\| \, \| v \|} \\ &= \frac{(-11)}{(\sqrt{53})\, (\sqrt{5})} \\ &= \frac{(-11)}{\sqrt{265}}\end{aligned}$ .

Apply the inverse cosine function ${\rm arccos}$ to find the value of this angle:

$\begin{aligned} \theta &= \arccos\left(\frac{u \cdot v}{\| u \| \, \| v \|}\right) \\ &= \arccos\left(\frac{(-11)}{\sqrt{265}}\right) \\ & \approx \text{$2.3127$ radians} \\ &= 2.3127 \times \frac{180^{\circ}}{\pi} \\ &\approx 132.51^{\circ}\end{aligned}$ .

8 0

3 years ago

Dan invests £9200 into his bank account. He receives 4% per year compound interest. How much will Dan have after 2 years? Give y

VashaNatasha [74]

Answer:

£9950.72

Step-by-step explanation:

Hello,

The question above relates to compound interest and to solve it, we'll require the formula needed.

A = P(1 + r/n)^nt

A = compound interest

P = principal = £9200

r = rate = 4% = 0.04

n = number of times the interest is compounded = 1

T = time = 2 years.

A = 9200 × (1 + 0.04/1)^(1×2)

A = 9200 × (1.04)²

A = 9200 × 1.0816

A = 9950.72

Dan would have £9950.72 after 2 years

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4 years ago

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Answer:

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3 years ago