The diagonals of a rectangle are congruent so we can set the expressions equal to each other and solve for x:
8x+3=4x+7
8x=4x+4
4x=4
x=1
Using either expression, each diagonal measures 8(1)+3=11 feet.

Question

asked 2021-01-31

Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle.

asked 2021-02-24

\(\displaystyle{f{{\left({x}\right)}}}={\left({8}{x}-{1}\right)}{\left({x}^{{{2}}}+{4}{x}+{7}\right)}{\left({x}^{{{3}}}-{5}\right)}\)

Find the derivatives.

Find the derivatives.

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).

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 2021-03-24

A person bending forward to lift a load "with his back" rather than"with his knees" can be injured by large forces exerted on themuscles and vertebrae. A person is bending over to lift a200-N object. The spine and upper body are represented as auniform horizontal rod of weight 350 N, pivoted at the base of thespine. The erector spinalis muscle, attached at a pointtwo-thirds of the way up the spine, maintains the position of theback. The angle between the spine and this muscle is 12degrees. Find the tension in the back muscle and thecompressional force in the spine.

asked 2021-06-06

For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}\)

asked 2021-01-15

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.

(-4,3), (0,5), and (3,-4)

(-4,3), (0,5), and (3,-4)

asked 2021-02-03

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.

(-3,1), (2,-1), and (6,9)

(-3,1), (2,-1), and (6,9)

asked 2020-12-29

(-3,1), (2,-1), and (6,9)

asked 2021-02-02

(-3,1), (2,-1), and (6,9)

asked 2021-03-02

(-4,3), (0,5), and (3,-4)