Answer:
168cm^3
Step-by-step explanation:
Q to P is going to be 3cm. it is identical to the length T to U.
R to T , W to Q, S to U is going to be identical to P to V. P to V has been identified as 12 cm.
in the middle of the shape, there are 4 identical triangles. the height time length will give us the area of that one shape:
e.g for shape P to V to W to Q and back to P is one rectangle. the length is 12 cm and the width is 3 cm.
12 x 3= 36
36cm^3 is one rectangles surface area, we have 4 identical triangles that means we need to times 36 by 4.
so 36x4=144.
now on the left and right side, we have two squares. on the right, we have T to U to V to W back to T this has the height of 3 width of 4 then we do 3 X 4 which is 12, we times it by 2 because we have two identical squares.
12 X 2=24
finally we add 24 and 144 = 168cm^3.
hope this helps :)
63 1/4 divided by 2 1/5 is 253/40
The root
can be converted into the power
. Therefore we can rewrite the problem as
and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.
Thus the problem becomes
, which then can be turned into
![\sqrt[8]{10} ^{3x}](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B10%7D%20%5E%7B3x%7D)
, making the last option our answer.
The remainder theorem says that dividing a polynomial <em>f(x)</em> by a 1st-degree polynomial <em>g(x)</em> = <em>x</em> - <em>c</em> leaves a remainder of exactly <em>f(c)</em>.
(a) With <em>f(x)</em> = <em>px</em> ³ + 4<em>x</em> - 10 and <em>d(x)</em> = <em>x</em> + 3, we have a remainder of 5, so
<em>f</em> (-3) = <em>p</em> (-3)³ + 4(-3) - 10 = 5
Solve for <em>p</em> :
-27<em>p</em> - 12 - 10 = 5
-27<em>p</em> = 27
<em>p</em> = -1
(b) With <em>f(x)</em> = <em>x</em> + 3<em>x</em> ² - <em>px</em> + 4 and <em>d(x)</em> = <em>x</em> - 2, we have remainder 8, so
<em>f</em> (2) = 2 + 3(2)² - 2<em>p</em> + 4 = 8
-2<em>p</em> = -10
<em>p</em> = 5
(you should make sure that <em>f(x)</em> was written correctly, it's a bit odd that there are two <em>x</em> terms)
(c) <em>f(x)</em> = 2<em>x</em> ³ - 4<em>x</em> ² + 6<em>x</em> - <em>p</em>, <em>d(x)</em> = <em>x</em> - 2, <em>R</em> = <em>f</em> (2) = 18
<em>f</em> (2) = 2(2)³ - 4(2)² + 6(2) - <em>p</em> = 18
12 - <em>p</em> = 18
<em>p</em> = -6
The others are done in the same fashion. You would find
(d) <em>p</em> = 14
(e) <em>p</em> = -4359
(f) <em>p</em> = 10
(g) <em>p</em> = -13/2 … … assuming you meant <em>f(x)</em> = <em>x</em> ⁴ + <em>x</em> ³ + <em>px</em> ² + <em>x</em> + 20
