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vivado [14]
3 years ago
12

50.) Find the value of b so that 330_b= 226_b+5

Mathematics
1 answer:
lyudmila [28]3 years ago
7 0
First u do 330b - 226b then divide 5 by that. b=0.048
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A point on the terminal side of an acute angle in standard position is (1, 2 √2). Find the cosine value of this angle.
kozerog [31]

Answer:

cos\theta=1/3

Step-by-step explanation:

The point at the terminal side of an acute angle is given by (1, 2\sqrt{2} ).

That is,

x = 1 and y= 2\sqrt{2} .

Let r be the length of line segment drawn from the origin to the point and is given by the formula:

r = \sqrt{x^{2} + y^{2}}

Substituting the values of x and y into r,

r = \sqrt{1^{2} + (2\sqrt{2} )^{2}}

r = \sqrt{1 + 8}

r = \sqrt{9}

Thus, r=3

Also, cos\theta is given by:

cos\theta = x/r\\

Substituting values of x and r,

cos\theta = 1/3\\

4 0
3 years ago
X + 5 &gt; 7<br> it’s inequalities
Hatshy [7]

Answer:

X>2

Step-by-step explanation:

X+5>7

X>2

7 0
3 years ago
Read 2 more answers
A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi
mestny [16]

Answer:

  • Base Length of 84cm
  • Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, V=x^2h=296352

h=\dfrac{296352}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}

Step 2: Find the derivative of A(x)

If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}

Step 3: Set A'(x)=0 and solve for x

A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42

Therefore, the dimensions that minimizes the box surface area are:

  • Base Length of 84cm
  • Height of 42 cm.
5 0
3 years ago
Help pleaseeeeeeeeee
storchak [24]
I am pretty sure that the answer is the first one but I’m not 100%
8 0
3 years ago
Read 2 more answers
Best explained and correct answer gets brainliest!
sertanlavr [38]
Same side, interior angles of parallel lines cut by a transversal are supplementary.
The sum of the measures of supplementary angles is 180.

Angles 4 and 6 are same side, interior angles, so their measures add to 180.

m<4 + m<6 = 180

109 + m<6 = 180

m<6 = 180 - 109

m<6 = 71

Answer: m<6 = 71 deg.
8 0
3 years ago
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