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3 years ago

How do i find the value of x , i’m so confuseddd !

Mathematics

1 answer:

olasank [31]3 years ago

5 0

Answer:

x ≈ 61.3

Step-by-step explanation:

Using the Sine rule, that is

$\frac{6}{sinx}$ = $\frac{5.8}{sin58}$ ( cross- multiply )

5.8 × sinx = 6 × sin58° ( divide both sides by 5.8 )

sin x = $\frac{6sin58}{5.8}$ ≈ 0.87729, thus

x = $sin^{-1}$ (0.87729) ≈ 61.3

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Root 3 cosec140° - sec140°=4 prove that

Lorico [155]

Answer:

Step-by-step explanation:

We are to show that $\sqrt{3} cosec140^{0} - sec140^{0} = 4\\$

Proof:

From trigonometry identity;

$cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}$

$\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\$

From trigonometry, 2sinAcosA = Sin2A

$= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}$

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

$\frac{4(sin(420-140)) }{sin280}$

= $\frac{4sin280}{sin280}\\ = 4 \ Proved!$

3 0

2 years ago

Find the recursive formula. 8, 12, 16, 20, ...

ArbitrLikvidat [17]

First term, a
1

=4
Second term, a
2

=8
Common difference, d=a
2

=a
1

d=8−4=4
∴ The common difference is 4

7 0

3 years ago

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. how high

bezimeni [28]

Given that grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height.

So if D is the diameter and h is the height of the conical pile then we can write:

D=3h

We know that diameter = 2r, where r is the radius

2r=3h

$r=\frac{3h}{2}$

Volume of conical pile is given by formula

$V=\frac{1}{3}\pi r^2h$

Given that volume is 1110 cubic feet.

Now plug the values of Volume and r into equation of volume

$1110=\frac{1}{3}\pi (\frac{3h}{2})^2h$

$1110=\frac{1}{3}\pi\cdot\frac{9h^2}{4}\cdot h$

$1110=\pi\cdot\frac{3h^3}{4}$

$1110\cdot\frac{4}{3\pi}=h^3$

$471.098631552=h^3$

take cube root of both sides

7.78103342467=h

Hence height is approx 7.78 feet.

7 0

3 years ago

all people who live in Ohio live in the United States.rewrite the statement as a conditional and write the converse of the condi

BigorU [14]

A conditional statement is written in the if-then form. The hypothesis is the first or "if" part while the conclusion is the "then" or then part. Thus, the conditional statement would be

If a person lives in Ohio, then the person lives in the United states

To form the converse of the conditional statement, the hypothesis and conclusion are interchanged. It becomes

If a person lives in the United states, then they live in Ohio

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9 months ago

A cyclist rides 14 miles in 47 minutes. What is the speed of the cyclist in miles per hour

DedPeter [7]

Step-by-step explanation:

20miles per hour HAVE A GOOD DAY

3 0

2 years ago