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3 years ago

In five years, josh will be 21 years old . How old is he now? Let j=Josh's current age.

Mathematics

2 answers:

Andrew [12]3 years ago

8 0

The awnser is b I hope I helped u

mariarad [96]3 years ago

6 0

You could do 21-5 and get the answer 16
A= 16+5 = 21
So therefor, he is 16 years old now.

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erik [133]

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4 years ago

Need help with trig problem in pic

Sidana [21]

Answer:

a) $cos(\alpha)=-\frac{3}{5}\\$

b) $\sin(\beta)= \frac{\sqrt{3} }{2}$

c) $\frac{4+3\sqrt{3} }{10}\\$

d) $\alpha\approx 53.1^o$

Step-by-step explanation:

a) The problem tells us that angle $\alpha$ is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

$tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}$

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

$cos(\alpha)=-\frac{3}{5}$

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

$cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}$

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find $sin(\alpha -\beta)$ by using the identity:

$sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\$

Notice that we need to find $sin(\alpha)$ , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

$sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}$

Then:

$sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}$

Since $sin(\alpha)=\frac{4}{5}$

then $\alpha=arcsin(\frac{4}{5} )\approx 53.1^o$

4 0

3 years ago

A water pitcher holds 3.5 quarts of water. How many liters of water does it hold?

DiKsa [7]

3.5 quarts = 3.31 liters

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3 years ago

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2 1/2 lb = ________ oz

KIM [24]

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3 years ago

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Will give brainliest, please help fast

Gekata [30.6K]

Answer:

Converting the equation $x^2-20x+13=0$ into completing the square method we get: $\mathbf{(x-10)^2=87}$

Step-by-step explanation:

we are given quadratic equation: $x^2-20x+13=0$

And we need to convert it into completing the square method.

Completing the square method is of form: $a^2-2ab+b^2=(a-b)^2$

Looking at the given equation $x^2-20x+13=0$

We have a = x

then we have middle term 20x that can be written in form of 2ab So, we have a=x and b=? Multiplying 10 with 2 we get 20 so, we can say that b = 20

So, 20x in form of 2ab can be written as: 2(x)(10)

So, we need to add and subtract (10)^2 on both sides

$x^2-20x+13=0\\x^2-2(x)(10)+(10)^2-(10)^2+13=0\\(x^2-2(x)(10)+(10)^2) \:can\: be\: written\: as\: (x-10)^2 \\(x-10)^2-100+13=0\\(x-10)^2-87=0\\(x-10)^2=87$

So, converting the equation $x^2-20x+13=0$ into completing the square method we get: $\mathbf{(x-10)^2=87}$

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3 years ago