Answer:
false
Step-by-step explanation:
these measure do not form a right triangle
Answer:63 cm
Step-by-step explanation:
Given
The scale of creation is 2:9
The width of the toy wheel is 14 cm
Suppose x is the actual width of the truck
![\therefore \dfrac{2}{9}=\dfrac{14}{x}\\\\\Rightarrow x=\dfrac{9}{2}\times 14=63\ cm](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cdfrac%7B2%7D%7B9%7D%3D%5Cdfrac%7B14%7D%7Bx%7D%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B9%7D%7B2%7D%5Ctimes%2014%3D63%5C%20cm)
Thus, the width of actual truck is 63 cm
It’s B, the number of cubic units it takes to fill a solid figure
Answer:
The family of possible values for
are:
![(-\infty, -4) \,\cup \,(7, +\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20-4%29%20%5C%2C%5Ccup%20%5C%2C%287%2C%20%2B%5Cinfty%29)
Step-by-step explanation:
By Linear Algebra, we can calculate the angle by definition of dot product:
(1)
Where:
- Angle between vectors, in sexagesimal degrees.
- Norms of vectors
and ![\vec{b}](https://tex.z-dn.net/?f=%5Cvec%7Bb%7D)
If
is acute, then the cosine function is bounded between 0 a 1 and if we know that
and
, then the possible values for
are:
Minimum (
)
![\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0](https://tex.z-dn.net/?f=%5Cfrac%7Bp%5E%7B2%7D-3%5Ccdot%20p%20-28%7D%7B%5Csqrt%7Bp%5E%7B2%7D%2B58%7D%5Ccdot%20%5Csqrt%7B2%5Ccdot%20p%5E%7B2%7D%2B16%7D%7D%20%3E%200)
Maximum (
)
![\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1](https://tex.z-dn.net/?f=%5Cfrac%7Bp%5E%7B2%7D-3%5Ccdot%20p%20-28%7D%7B%5Csqrt%7Bp%5E%7B2%7D%2B58%7D%5Ccdot%20%5Csqrt%7B2%5Ccdot%20p%5E%7B2%7D%2B16%7D%7D%20%3C%201)
With the help of a graphing tool we get the family of possible values for
are:
![(-\infty, -4) \,\cup \,(7, +\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20-4%29%20%5C%2C%5Ccup%20%5C%2C%287%2C%20%2B%5Cinfty%29)
Answer:
![\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BNo.%7D%5C%20%5Cdfrac%7B0.5%7D%7B1%7D%5Cneq%5Cdfrac%7B1%7D%7B1.5%7D%5Cneq%5Cdfrac%7B1.5%7D%7B2%7D%7D)
Step-by-step explanation:
![\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/](https://tex.z-dn.net/?f=%5Ctext%7BLet%7D%5C%5C%20a%2C%5C%20b%2C%5C%20c%5C%20-%5C%20%5Ctext%7Bsides%20of%20a%20triangle%20ABC%2C%20where%7D%5C%20a%5Cleq%20b%5Cleq%20c%5C%5Cd%2C%5C%20e%2C%5C%20f%5C%20-%5C%20%5Ctext%7Bsides%20of%20a%20triangle%7D%5C%20DE%20F%2C%5C%20%5Ctext%7Bwhere%7D%5C%20d%5Cleq%20e%5Cleq%20f.%5C%5C%5C%5C%5Ctriangle%20ABC%5Csim%5Ctriangle%20DE%20F%5Ciff%5Cdfrac%7Ba%7D%7Bd%7D%3D%5Cdfrac%7Bb%7D%7Be%7D%3D%5Cdfrac%7Bc%7D%7Bf%7D%5C%5C%5C%5C%2F%5Ctext%7Bcorresponding%20sides%20are%20in%20proportion%7D%2F)
![\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}](https://tex.z-dn.net/?f=%5Cbold%7BWARNING%20%21%21%21%7D%5C%5C%5C%5C%5Ctext%7BNo%20triangle%20like%20QRS%20exists%21%7D%5C%5C%5C%5C1%20%2B%200.5%20%3D%201.5%20%21%21%21%5C%5C%5C%5C%5Ctext%7BThe%20sum%20of%20the%20lengths%20of%20the%20two%20shorter%20sides%20of%20the%20triangle%7D%5C%5C%5Ctext%7Bmust%20be%20greater%20than%20the%20length%20of%20the%20longest%20side.%7D)
![\text{Despite this, let's check the ratios}](https://tex.z-dn.net/?f=%5Ctext%7BDespite%20this%2C%20let%27s%20check%20the%20ratios%7D)
![\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%3A%7D%5C%5C%5C%5C%5Ctriangle%20XYZ%5Cto%20a%3D1%2C%5C%20b%3D1.5%2C%5C%20c%3D2%5C%5C%5Ctriangle%20QRS%5Cto%20d%3D0.5%2C%5C%20e%3D1%2C%5C%20f%3D1.5)
![\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}](https://tex.z-dn.net/?f=%5Ctext%7BCheck%3A%7D%5C%5C%5C%5C%5Cdfrac%7Bd%7D%7Ba%7D%3D%5Cdfrac%7B0.5%7D%7B1%7D%3D0.5%5C%5C%5C%5C%5Cdfrac%7Be%7D%7Bb%7D%3D%5Cdfrac%7B1%7D%7B1.5%7D%3D%5Cdfrac%7B10%7D%7B15%7D%3D%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%5Cdfrac%7Bf%7D%7Bc%7D%3D%5Cdfrac%7B1.5%7D%7B2%7D%3D%5Cdfrac%7B15%7D%7B20%7D%3D%5Cdfrac%7B3%7D%7B4%7D%5C%5C%5C%5C%5Cdfrac%7Bd%7D%7Ba%7D%5Cneq%5Cdfrac%7Be%7D%7Bb%7D%5Cneq%5Cdfrac%7Bf%7D%7Bc%7D%5Cneq%5Cdfrac%7Bd%7D%7Ba%7D)