Ask question

# Consider rectangel CREB that is formed of squares COAB and OREA, where AE=4ft. Assume squares COAB and OREA are congruent. BO=3m-2nAR=7(m-1)-4.8nDetermine the values of m and n and the length of RB. # Consider rectangel CREB that is formed of squares COAB and OREA, where AE=4ft. Assume squares COAB and OREA are congruent. BO=3m-2nAR=7(m-1)-4.8nDetermine the values of m and n and the length of RB.

Question
Analytic geometry asked 2021-01-04

Consider rectangel CREB that is formed of squares COAB and OREA, where $$AE=4ft$$. Assume squares COAB and OREA are congruent.
$$BO=3m-2n$$
$$AR=7(m-1)-4.8n$$
Determine the values of m and n and the length of RB.

## Answers (1) 2021-01-05

The diagonal of each square divides it into two triangles with angles of $$\displaystyle{45}^{\circ},{45}^{\circ}{\quad\text{and}\quad}{90}^{\circ}$$. The diagonals (BO and AR) are the triangles' hypotenuses. The hypotenuses is $$\displaystyle\sqrt{{2}}$$ times the leg in such triangles. A leg is also a square side, which is 4ft, so
$$\displaystyle{B}{O}={A}{R}={4}\sqrt{{2}}$$
$$\displaystyle{3}{m}-{2}{n}={7}{\left({m}-{1}\right)}-{4.8}{n}={4}\sqrt{{2}}$$
$$\displaystyle{3}{m}-{2}{n}={4}\sqrt{{2}}$$
$$\displaystyle-{2}{n}=-{3}{n}+{4}\sqrt{{2}}$$
$$\displaystyle{n}={1.5}{m}-{2}\sqrt{{2}}$$
$$\displaystyle{7}{\left({m}-{1}\right)}-{4.8}{n}={4}\sqrt{{2}}$$
$$\displaystyle{7}{\left({m}-{1}\right)}-{4.8}{\left({1.5}{m}-{2}\sqrt{{2}}\right)}={4}\sqrt{{2}}$$
$$\displaystyle{7}{m}-{7}-{7.2}{m}+{9.6}\sqrt{{2}}={4}\sqrt{{2}}$$
$$\displaystyle-{0.2}{m}={4}\sqrt{{2}}+{7}-{9.6}\sqrt{{2}}$$
$$\displaystyle-{0.2}{m}=-{5.6}\sqrt{{2}}+{7}$$
$$\displaystyle{m}={28}\sqrt{{2}}-{35}$$
$$\displaystyle{n}={1.5}{m}-{2}\sqrt{{2}}$$
$$\displaystyle={1.5}{\left({28}\sqrt{{2}}-{35}\right)}-{2}\sqrt{{2}}$$
$$\displaystyle={42}\sqrt{{2}}-{52.5}-{2}\sqrt{{2}}$$
$$\displaystyle={40}\sqrt{{2}}-{52.5}$$
$$\displaystyle{R}{B}^{{2}}={B}{A}^{{2}}+{A}{E}^{{2}}$$
$$\displaystyle={8}^{{2}}+{4}^{{2}}$$
$$=64+16$$
$$=80$$
$$\displaystyle{R}{B}=\sqrt{{80}}$$
$$\displaystyle={4}\sqrt{{5}}$$

### Relevant Questions asked 2021-02-01

Point K is on line segment $$\overline{JL}$$. Given $$JK = 2x - 2, KL = x - 9,\ and\ JL = 2x + 8,$$ determine the numerical length of $$\overline{KL}$$. asked 2021-01-10

$$\displaystyle{\cos{{2}}}\theta=\frac{{28}}{{53}}$$
Find $$\displaystyle{\sin{\theta}}$$, if
$$\displaystyle{0}^{\circ}{<}\theta{<}{90}^{\circ}$$ asked 2020-12-16

The gazebo in the photo is built in the shape of a regular octagon. Each side is 13ft long and the enclosed area is $$816.4ft^2$$
What is the length of the apothem? asked 2021-04-25
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius $$\displaystyle{R}={7.4}\times{10}^{{-{15}}}$$ m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit $$\displaystyle={1.66}\times{10}^{{-{27}}}$$ kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes). asked 2021-04-13
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is $$\displaystyle\mu_{{k}}$$, the coefficient of kinetic friction between the chair and the waxed floor? Use $$\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}$$ for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for $$\displaystyle\mu_{{k}}$$, since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k. asked 2020-12-28

Assume that T is a linear transformation. Find the standard matrix of T.
$$\displaystyle{T}=\mathbb{R}^{{2}}\rightarrow\mathbb{R}^{{4}}\ {s}{u}{c}{h} \ {t}\hat \ {{T}}{\left({e}_{{1}}\right)}={\left({7},{1},{7},{1}\right)},{\quad\text{and}\quad}{T}{\left({e}_{{2}}\right)}={\left(-{8},{5},{0},{0}\right)},{w}{h}{e}{r}{e}{\ e}_{{1}}={\left({1},{0}\right)},{\quad\text{and}\quad}{e}_{{2}}={\left({0},{1}\right)}$$. asked 2021-03-13
When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure (a). The total gravitational force on the body, vector F g, is supported by the force vector n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure (b), where vector T is the force exerted by the Achilles tendon on the foot and vector R is the force exerted by the tibia on the foot. Find the values of vector T , vector R , and θ when vector F g = 805 N. (Do not assume that vector R is parallel to vector T .) asked 2020-11-27

A regular hexagon is dilated by a scale factor of $$\frac{4}{3}$$ to create a new hexagon. How does the perimeter of the new hexagon compare with the original perimeter? asked 2021-04-03
At what angle will the electrons leave the uniform electric field at the end of the parallel plates? Assume the plates are 4.9 cm long, $$\displaystyle{E}={5.0}\times{10}^{{3}}$$ and $$\displaystyle{v}_{{0}}={1.00}\times{10}^{{7}}$$ m/s. Ignore fringing on the field.  asked 2021-05-08

Points B and D are points of tangency. Find the value of x. .

...