When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
<h3>Surd operation </h3>
a√b × c√d = (a × c)√(b × d)
<h3>How to simplify (3 + √5)(3 + √2)</h3>
(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
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Answer:
x = 41.2
Step-by-step explanation:
Assuming the dotted line at the top is parallel to the segment with length x, it follows from the alternate interior angles theorem that the interior angle of the triangle (marked in diagram) is also 27º.
Using SOH-CAH-TOA, we get that tan(27º) = 21/x, so x = 21/tan(27º), which is approximately equal to 41.2.
Answer:
1779.33 mm³
Step-by-step explanation:
We are given a candle in a form of a cylinder and a cone
Dimensions;
Common radius is 5 mm
Height of the cylinder is 20 mm
Height of the cone is 8 mm
We are required to determine the amount that it can hold.
To answer the question we are going to determine its volume
Cylinder;
Volume of a cylinder is given by;
V = πr²H
Taking π to be 3.14
Then ;
Volume of cylinder = 3.14 × 5mm² × 20 mm
= 1570 mm³
Cone
Volume of a cone is given by;
V = 1/3πr²H
That is;
Volume =1/3 × 3.14 × 5mm² × 8 mm
= 209.33 mm³
Therefore;
Volume of the solid = 1570 mm³ + 209.33 mm³
= 1779.33 mm³
Thus, the volume of the solid is 1779.33 mm³
You begin with moving all terms to the left side and set them equal to zero. Then you set each factor equal to zero and you should come out with p= 0,8
Let y = ax²+bx+c then substitute all of orders. we'll be doing equations system.
Ok we are at this.
Substitute c = 3 into equation 1 and equation 3.
then addition and subtract for a-b = 3 and a+b = -1
Therefore a = -2, substitute a = -2 in a-b+c=0 or a+b+c=2 but i'm doing a-b+c=0 one.
Therefore b = 1, substitute both a, b and c into y=ax²+bx+c as we get,
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