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2 years ago

I need to know how to simplify these problems.

Mathematics

1 answer:

nalin [4]2 years ago

5 0

You need to factor the radicals into products of radicals, and when factoring you should keep in mind you want to obtain perfect square roots. So √125 = √5*√25 and squareroot 25 has a definite answer of 5, so ∛125=∛5×∛25=5×√5. You want to follow the general pattern of factoring perfect squares to obtain a number outside the radical which can be multiplied by the current coefficient

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70 points!!!! Find the horizontal and the vertical components of f.

choli [55]

Answer:

F = (16.74, -2.95)

Explanation:

<u />

<u>1) Horizontal component</u>

The horizontal component is related to the magnitude of the force by the cosine ratio:

cos (α) = Fx / | F |

Where α in the angle (-10º), Fx is the horizontal component, and | F | is the magnitude of the force (17).

cos(-10º) = Fx / 17 ⇒ Fx = cos (-10º) × 17 = 16.74

<u />

<u>2) Vertical component</u>

The vertical component is related to the magnitude of the force by the sine ratio:

sin (α) = Fy / | F |

Where α in the angle (-10º), Fy is the vertical component, and | F | is the magnitude of the force (17).

sin(-10º) = Fy / 17 ⇒ Fy = sin (-10º) × 17 = -2.95

<u />

F = (16.74, -2.95)

6 0

3 years ago

10) A rhombus has a<br> diagonal 8.6 mm long<br> and an area of 81.7 mm. what is the<br> perimeter?

BaLLatris [955]

Answer:

P=41.72

Step-by-step explanation:

S=ACxDB/2

81.7=8.6xDB/2

81.7=4.3xDB|:4.3

19(mm)=DB

DO=19/2=9.5

OC=8.6/2=4.3

(O is the center of the rhombus, where two diagonals meet)

a²+b²=c² (DO²+OC²=DC²)

9.5²+4.3²=c²

90.25+18,49=c²

√108,74=√c²

c≈10.43

P=4c

P=4x10.43

P=41.72

Hope it helps:)

6 0

1 year ago

Please calculate the volume of the triangular prism (MIDDLE SCHOOL MATH)

k0ka [10]

Answer:

52.374 cm*3

Step-by-step explanation:

the upper triangle is equal to the bottom triangle

Btw fyi the formula of calculating the value of a prism is:

area of the base × height

3 0

3 years ago

Find the 97th term of the arithmetic sequence

kozerog [31]

<h2>Answer:</h2><h2>The 97th term in the series is 409</h2>

Step-by-step explanation:

The given sequence is 25, 29, 33, ....

The sequence represents arithmetic progression

In an AP, the first term is a1 = 25

The difference between two terms, d = 29 - 25 = 4

To find the 97th term,

By formula, $a_{n} = a_{1} + (n - 1) d$

Substituting the values in the above equation, we get

$a_{97} = 25 + (97 - 1) 4$

= 25 + (96 * 4)

= 25 + 384

= 409

The 97 th term in the given sequence is 409.

3 0

2 years ago

A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find th

aniked [119]

Answer:

The initial value is 29.5

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept ( also called initial value)

we have the points

(3,42.25) and (5,50.75)

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{50.75-42.25}{5-3}$

$m=\frac{8.5}{2}$

$m=4.25$

substitute in the equation

$y=4.25x+b$

<em>Find the value of b</em>

with the point (3,42.25) ( or the other given point)

substitute the value of x and the value of y in the equation and solve for b

$42.25=4.25(3)+b$

$42.25=12.75+b$

$b=42.25-12.75$

$b=29.5$

substitute

The linear equation is

$y=4.25x+29.5$

The initial value is the y-intercept (value of y when the value of x is equal to zero)

For x=0

$y=4.25(0)+29.5$

$y=29.5$

Therefore

The initial value is 29.5

5 0

3 years ago

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