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3 years ago

The equations 2x+7=3 and bx-10=-2 have the same solution for x. Find the value of b.

Mathematics

1 answer:

White raven [17]3 years ago

4 0

Solve both equations for x:

2x+7 = 3

2x = -4

x = -2

Plug x into the equation which contains b:

b(-2) -10 = -2

-2b = 8

b = -4

Answer:

b = -4

x = -2

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Question 13

Mrac [35]

Answer:

71.6 degrees

Step-by-step explanation:

Given the vectors

u= <8,4> v = <9.-9> (5 points)

u*v = (8, 4)*(9, -9)

u*v = 8(9)+(4)(-9)

u*v = 72 - 36

u*v = 36

|u| = √8²+4²

|u| = √64+16

|u| = √80

|v| = √9²+9²

|v| = √81+81

|v| = √162

Using the formula

u*v = ||u||v| cos theta

36 = √80(√162)cos theta

36 = √12960 cos theta

cos theta = 36/√12960

cos theta = 36/113.8

cos theta = 0.3162

theta = arccos(0.3162)

theta = 71.56 degrees

Hence the angle between the given vectors to the nearest tenth of a

degree is 71.6 degrees

5 0

2 years ago

The polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.

zaharov [31]

Use the lengths of corresponding sides
so answer is 16:40 which simplifies to 2:5.

4 0

3 years ago

What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

Integrals
Definite Integrals
Integration Constant C

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

4 0

2 years ago

What are irrational numbers

eduard

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

7 0

3 years ago

What is the slope of the line that contains the points (-2, 2) and (3, 4)?

Vladimir79 [104]

Answer:

2/5

Step-by-step explanation:

The slope is given by

m= (y2-y1)/(x2-x1)

= (4-2)/(3 - -2)

= 2/(3+2)

= 2 /5

5 0

2 years ago

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