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3 years ago

Write and solve an equation to find the value of x and the missing angle measures.

Mathematics

1 answer:

Oksana_A [137]3 years ago

8 0

Answer:

Step-by-step explanation:

1). Since, both the angles are vertically opposite angles,

Measure of both the angles will be same.

6x = 30

x = 5

2). Since, both the angles are the linear pair of angles,

(4 + 5x)° + (x + 2)° = 180°

6x + 6 = 180

6x = 180 - 6

x = $\frac{174}{6}$

x = 29

Therefore, (4 + 5x)° = 4 + 5(29)

= 149°

And (x + 2)° = (29 + 2)

= 31°

3). Since, both the angles are linear pair of angles,

5x° + (3x + 12)° = 180°

8x + 12 = 180

8x = 180 - 12

x = $\frac{168}{8}$

x = 21

Therefore, 5x° = 5(21)

= 105°

(3x + 12)° = 3(21) + 12

= 75°

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A force of $20$ newtons will stretch a spring $5$ centimeters. What is the total number of centimeters that a force of $60$ newt

Aleksandr-060686 [28]

Answer:

Step-by-step explanation:

Hooke's Law applies here, which is a linear relationship. It would be easier to solve this using proportions with N of force on the top and the amount of stretch in cm on the bottom. Set up with our unknown, the number of cm:

$\frac{N}{cm}:\frac{20}{5}=\frac{60}{x}$ and cross multiply:

20x = 300 so

x = 15 cm

6 0

3 years ago

Use the table of integrals, or a computer or calculator with symbolic integration capabilities, to find the indefinite integral.

nignag [31]

Answer:

$-\frac{3}{11}\ln(\cot t + \csc t)+C$

Step-by-step explanation:

We are given: $\int \frac{3}{x\sqrt{121-x^2}} dx$

We will use integration by parts.

$x = 11 \sin t\\dx = 11 \cos t \: dt$

$\int \frac{3}{x\sqrt{121-x^2}} dx=\int \frac{3* 11 \cos t \: dt}{11 \sin t\sqrt{121-121\sin^2 t}} =\int \frac{3* 11 \cos t \: dt}{11 \sin t*11\cos t}} =\\\\= \frac{3}{11} \int \csc t = -\frac{3}{11}\ln(\cot t + \csc t)+C$