Is 10,070 more than 70+10,000

Mathematics

2 answers:

jeka57 [31]3 years ago

6 0

Answer:

No they are equal

Step-by-step explanation:

xxTIMURxx [149]3 years ago

3 0

10,070 would be equal to 10,000+70

You might be interested in

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).