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3 years ago

Help I can't seem to get it right

Mathematics

1 answer:

Scilla [17]3 years ago

8 0

Loan + interest= 450+ (9.9%•450)= 494.55
Monthly payment= 494.55/12=41.21
Answer is (2)

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TIMED UNIT TEST

Ymorist [56]

Answer:

distributive property

7 0

3 years ago

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Round 3.184 to the nearest whole number

inn [45]

3.184= 3
.184 = .18
.18= 2
2= 3

7 0

3 years ago

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Help me with trigonometry

poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the Weierstrass substitution, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

$\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}$

Therefore,

$\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}$

Once the double angle identity for sine is

$\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}$

we know $\sin(x)=\dfrac{2t}{1+t^2}$ , but sure, we can derive this formula considering the double angle identity

$\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)$

Recall

$\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}$

Thus,

$\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}$

Similarly for cosine, consider the double angle identity

Thus,

$\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}$

Hence, we showed $\sin(x) \text { and } \cos(x)$

======================================================

$5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]$

Solving

$5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3$

$\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3$

$\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0$

$t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}$

$t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}$

Just note that

$\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}$

and $\tan\left(\dfrac{x}{2}\right)$ is not defined for $x=k\pi , k\in\mathbb{Z}$

6 0

3 years ago

Solve the equation. 5x 8 − 3x = −10 x = −9 x = −1 x = 1 x = 9

gregori [183]

The value of the variable x, of the linear equation 5x 8 − 3x = −10 is -9, which is obtained after solving it. Option 1 is the correct option.

<h3>What is linear equation?</h3>

A linear equation is the equation in which the highest power of the unknown variable is one.

Here, the given linear equation is,

$5x +8 - 3x = -10$

Solve it by arranging the equation as,

$5x - 3x +8= -10\\2x+8=-10$

Subtract number 8 both side of the equation as,

$2x+8-8=-10-8\\2x=-18$

Divide both side of the equation with number 2 as,

$x=\dfrac{-18}{2}\\x=-9$

Hence, the value of the variable x, of the linear equation 5x 8 − 3x = −10 is -9, which is obtained after solving it. Option 1 is the correct option.

Learn more about the linear equation here;

brainly.com/question/14323743

6 0

2 years ago

I NEED HELP PLZ OK plz plz

lyudmila [28]

Answer:

3) 25

4)30

5) right angle

Step-by-step explanation:

3) 115-90=25

4)70-40=30

5)45+45=90

5 0

3 years ago

Read 2 more answers